ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 The blue contour shows the region observed with the EVLA and presented in the right panel. and it covers the entire central region where the sub-sonic non-thermal velocity dispersions are observed.," The blue contour shows the region observed with the EVLA and presented in the right panel, and it covers the entire central region where the sub-sonic non-thermal velocity dispersions are observed."3 The resulting ((1.1) integrated intensity map for BS is shown in right panel of Figure 1.. and it covers a region of size 6.5’. 8.," The resulting (1,1) integrated intensity map for B5 is shown in right panel of Figure \ref{fig-w11}, and it covers a region of size $\arcmin\times$ $\arcmin$ ."4 The new high resolution integrated intensity map (right panel of Figure 1)) reveals that within the region of subsonic non-thermal motions found in the single dish data (orange contour) filamentary structures appear., The new high resolution integrated intensity map (right panel of Figure \ref{fig-w11}) ) reveals that within the region of subsonic non-thermal motions found in the single dish data (orange contour) filamentary structures appear.5" These filaments are narrow. with widths of zc20"" or 5.000 AU at the distance of Perseus (250pe:Hirotaetal.2005)."," These filaments are narrow, with widths of $\approx20\arcsec$ or 5,000 AU at the distance of Perseus \citep[250~pc;][]{Hirota_2008-NGC1333_Distance}."6 An important feature of molecular line observations is the ability to probe the kinematics of the gas., An important feature of molecular line observations is the ability to probe the kinematics of the gas.7 Here we fit simultaneously all hyperfine components of the ((1.1) line using a forward model previously presented by Rosolowskyetal. (2008).. see also Pinedaetal.(2010).," Here we fit simultaneously all hyperfine components of the (1,1) line using a forward model previously presented by \cite{GBT:Perseus}, , see also \cite{Pineda_2010-transition_coherence}."8 This method describes the emission at every position with a centroid velocity (vrsg). velocity dispersion (σι). kinetic temperature (7). excitation temperature οι) and opacity ἔτι). While also including the response of the frequency channel using a sine profile.," This method describes the emission at every position with a centroid velocity $v_{LSR}$ ), velocity dispersion $\sigma_{v}$ ), kinetic temperature $T_{k}$ ), excitation temperature $T_{ex}$ ) and opacity $\tau_{11}$ ), while also including the response of the frequency channel using a sinc profile."9 Since the kinetic temperature is only used to predict the ((2.2) line (not observed due to the constraints in the OSRO program). it does not have any effect on the remaining parameters.," Since the kinetic temperature is only used to predict the (2,2) line (not observed due to the constraints in the OSRO program), it does not have any effect on the remaining parameters."10 We use a fixed value of the kinetic temperature of 10 K for the entire region. which is consistent with the results obtained by Pinedaetal.(2011) using the single dish data.," We use a fixed value of the kinetic temperature of 10 K for the entire region, which is consistent with the results obtained by \cite{Pineda_2011-GBT_Maps} using the single dish data."11" If the resulting fit does not provide an accurate velocity dispersion. σι<0.0Skms7| (velocity dispersion narrower than the expected thermal value for gas at 6 K) or a5,>0.20, (signal-to-noise for the velocity dispersion less than 5). the fit is repeated but with a fixed value of 5 K for excitation temperature."," If the resulting fit does not provide an accurate velocity dispersion, $\sigma_{v} < 0.05\,\kms$ (velocity dispersion narrower than the expected thermal value for gas at 6 K) or $\sigma_{\sigma_{v}} > 0.2\,\sigma_{v}$ (signal-to-noise for the velocity dispersion less than 5), the fit is repeated but with a fixed value of 5 K for excitation temperature."12 The centroid velocity and velocity dispersion maps are shown in Figure 2.., The centroid velocity and velocity dispersion maps are shown in Figure \ref{fig-vc-dv}.13 The centroid velocity map shows little variation (<0.6 kms)) across the entire region. see Figure 2aa. The region close to the YSO displays a velocity gradient at a position angle that is close to the outflow (shown by the arrows) but in opposite direction.," The centroid velocity map shows little variation $<0.6$ ) across the entire region, see Figure \ref{fig-vc-dv}a a. The region close to the YSO displays a velocity gradient at a position angle that is close to the outflow (shown by the arrows) but in opposite direction."14 The velocity dispersion map. see Figure 2bb. shows vast regions where small and uniform velocity dispersion are found.," The velocity dispersion map, see Figure \ref{fig-vc-dv}b b, shows vast regions where small and uniform velocity dispersion are found."15 It is only towards positions close to the YSO where slightly broader lines are found., It is only towards positions close to the YSO where slightly broader lines are found.16 Figure 3. presents the distribution of the derived velocity dispersion towards B5., Figure \ref{fig-hist-dv} presents the distribution of the derived velocity dispersion towards B5.17 Two histograms are shown Figure 3 depending on the proximity to the YSO in B5: (a) positions close to the YSO (separated by 2 beams or less. « 12) in red. and (b) all other pixels in black.," Two histograms are shown Figure \ref{fig-hist-dv} depending on the proximity to the YSO in B5: (a) positions close to the YSO (separated by 2 beams or less, $<$ $\arcsec$ ) in red, and (b) all other pixels in black."18" For points far from the YSO the velocity dispersions are small and the velocity dispersion distribution (black histogram in Figure 3)) is narrow. almost every pixel at a distance larger than 2 beams (12"")) from the central YSO displays sub-sonie non-thermal motions."," For points far from the YSO the velocity dispersions are small and the velocity dispersion distribution (black histogram in Figure \ref{fig-hist-dv}) ) is narrow, almost every pixel at a distance larger than 2 beams ) from the central YSO displays sub-sonic non-thermal motions."19" The velocity dispersion. distribution of pixels far from the YSO. black histogram in Figure 3.. peaks at a value lower than what is expected if the non-thermal component. oy. is equal to half the thermal velocity dispersion. 0.5c,ave."," The velocity dispersion distribution of pixels far from the YSO, black histogram in Figure \ref{fig-hist-dv}, peaks at a value lower than what is expected if the non-thermal component, $\sigma_{NT}$, is equal to half the thermal velocity dispersion, $0.5\, \csave$."20 The velocity dispersion of points close to the YSO. red histogram in Figure 3.. presents lines broader than the rest of the core. but they still display velocity dispersions with a subsonic non-thermal component.," The velocity dispersion of points close to the YSO, red histogram in Figure \ref{fig-hist-dv}, presents lines broader than the rest of the core, but they still display velocity dispersions with a subsonic non-thermal component."21 This increase in the velocity dispersion might be the effect of the radiation from the embedded YSO or due to the interaction between the outflow or stellar wind and the dense gas., This increase in the velocity dispersion might be the effect of the radiation from the embedded YSO or due to the interaction between the outflow or stellar wind and the dense gas.22 Herschel observations of the IC 5146 star forming region (Arzoumanianetal.2011) revealed filamentary structure seen in the column density maps (seealsoAndréetal.2010).., Herschel observations of the IC 5146 star forming region \citep{Arzoumanian_2011-Herschel_Filaments_IC5146} revealed filamentary structure seen in the column density maps \citep[see also][]{Andre_2010-Herschel_GBS_Filaments}.23" Arzoumanianetal.(2011). fitted the column density profile of filaments with a cylindrical filament model. where p, is the filament's central density. r is the cylindrical radius. p is the power-law density exponent at large radit. Αι is the radius of the density profile inner flat section. and A, is à finite constant factor dependent on p and the filament inclination angle."," \cite{Arzoumanian_2011-Herschel_Filaments_IC5146} fitted the column density profile of filaments with a cylindrical filament model, where $\rho_{c}$ is the filament's central density, $r$ is the cylindrical radius, $p$ is the power-law density exponent at large radii, $R_{flat}$ is the radius of the density profile inner flat section, and $A_{p}$ is a finite constant factor dependent on $p$ and the filament inclination angle."24 They find filaments which are well fit with a density exponent in the range p=1.5—2.5 (seealsoLadaetal. 1999).., They find filaments which are well fit with a density exponent in the range $p=1.5-2.5$ \citep[see also][]{Lada_1999-IC5146_Structure}.25 These exponents do not agree with the predicted values of an isothermal filament in hydrostatie equilibrium where a steeper exponent. p24. is expected (Ostriker1964).," These exponents do not agree with the predicted values of an isothermal filament in hydrostatic equilibrium where a steeper exponent, $p=4$, is expected \citep{Ostriker_1964-Filament_Model}."26 Here we focus our attention towards the filament shown in Figure | by the yellow box., Here we focus our attention towards the filament shown in Figure \ref{fig-w11} by the yellow box.27 Since this filament is almost perfectly aligned in the North-South direction we perform a series of horizontal cuts. and define the radius as the distance from the peak at a given cut.," Since this filament is almost perfectly aligned in the North-South direction we perform a series of horizontal cuts, and define the radius as the distance from the peak at a given cut."28 The average velocity dispersion and integrated intensity emission profiles along the filament are shown in panels (a) and (b) of Figure 4.. respectively. where the spread in the distribution is shown by the yellow area.," The average velocity dispersion and integrated intensity emission profiles along the filament are shown in panels (a) and (b) of Figure \ref{fig-fil-prop}, respectively, where the spread in the distribution is shown by the yellow area."29 Figure 4aa shows that the velocity dispersion does not change across the filament. and it is consistent withsubsonic non-thermal velocity dispersions (delimited by the dotted line).," Figure \ref{fig-fil-prop}a a shows that the velocity dispersion does not change across the filament, and it is consistent withsubsonic non-thermal velocity dispersions (delimited by the dotted line)."30 Figure +bb shows the integrated intensity profile. which is much wider than the beamof the combined EVLA and GBT data (shown by the blue dash line).," Figure \ref{fig-fil-prop}b b shows the integrated intensity profile, which is much wider than the beamof the combined EVLA and GBT data (shown by the blue dash line)."31 Since we do not observe the ((2.2) with the EVLA we cannot provide," Since we do not observe the (2,2) with the EVLA we cannot provide"32spectrograph of the Solar Tower Telescope of Nanjing University (παςetal.1995) and byRHESSI.,spectrograph of the Solar Tower Telescope of Nanjing University \citep{hua95} and by.33. A preliminary analvsis of observational aspects for this Hare has been presented in a previous paper (Dingetal.2003a.hereafterPaperΕ).., A preliminary analysis of observational aspects for this flare has been presented in a previous paper \citep[hereafter Paper I]{din03a}.34 A multi-waveleneth analvsis of this flare was also carried out by Ixulinováetal.(2004)., A multi-wavelength analysis of this flare was also carried out by \citet{kul04}.35. In (his paper. we perform a quantitative analvsis of this flare by deriving the energy [hix of non-thermal electrons and discussing the origin of the continuum enhancement in terms of current WLF models.," In this paper, we perform a quantitative analysis of this flare by deriving the energy flux of non-thermal electrons and discussing the origin of the continuum enhancement in terms of current WLF models."36 We first give a brief description of the aad ΗΝ emission of this flare. as presented in Paper 1. This M2.6/2D Lave. associated with a filament eruption. occurred al NOAA 0134(NI2*.. E21°)) on 2002 September 29.," We first give a brief description of the and HXR emission of this flare, as presented in Paper I. This M2.6/2B flare, associated with a filament eruption, occurred at NOAA 0134, ) on 2002 September 29."37 I1 started al 06:32 and peaked at 06:39 UT., It started at 06:32 and peaked at 06:39 UT.38 As in Paper L we pav attention to (wo main kkernels. which are located at different magnetic polarities (see Figure 4).," As in Paper I, we pay attention to two main kernels, which are located at different magnetic polarities (see Figure 4)."39 ln particular. we select (wo points (A and D) representative of the two kernels to check their evolutionary behaviors based on the signatures of the lline profile (see 333.2).," In particular, we select two points (A and B) representative of the two kernels to check their evolutionary behaviors based on the signatures of the line profile (see 3.2)."40 Point A. at the center of the first kernel. is already hot at the start ol ground-based observations ancl cools down gradually.," Point A, at the center of the first kernel, is already hot at the start of ground-based observations and cools down gradually."41 Point D. at the center of the second kernel (also the brightest kernel). is relatively cool al first ancl is heated rapidlv in the impulsive phase.," Point B, at the center of the second kernel (also the brightest kernel), is relatively cool at first and is heated rapidly in the impulsive phase."42 The continuum enhancement (caleulated at ILa-4-4-6. A)) at Point B rises rapidly and reaches its maxinium (ου 8%)) roughly coincident with the peak of the 2550 keV ΗΝ emission., The continuum enhancement (calculated at +6 ) at Point B rises rapidly and reaches its maximum $\sim 8$ ) roughly coincident with the peak of the 25–50 keV HXR emission.43 It is interesting that the maximum continuum enhancement at Point D is nearly twice that at Point A. To study the INR emission. we first use the CLEAN algorithm (see.e.g..Ixyucker&Lin2002) to reconstruct the IINBR. images.," It is interesting that the maximum continuum enhancement at Point B is nearly twice that at Point A. To study the HXR emission, we first use the CLEAN algorithm \citep[see, e.g.,][]{kru02} to reconstruct the HXR images."44 A strong INR source appears to encompass both kernels in (he early impulsive phase. and it (hen shows a motion across the magnetic neutral line.," A strong HXR source appears to encompass both kernels in the early impulsive phase, and it then shows a motion across the magnetic neutral line."45 Compared to data from theObservatory MIDI magnetograam. the bright INR source seenis {ο straddle over the magnetic neutral line al earlier (mies: therefore. it is thought to contain two spatially unresolved FP sources: the motion of the IIXR. source reflects a change of the relative weights of its two components.," Compared to data from the MDI magnetogram, the bright HXR source seems to straddle over the magnetic neutral line at earlier times; therefore, it is thought to contain two spatially unresolved FP sources; the motion of the HXR source reflects a change of the relative weights of its two components."46 In addition. we emplov the Maximum Entropy Method (MEM) algorithm provided by the immagine software (Ilurlordetal.2002) to reconstruct INR. images around the peak of ihe impulsive phase.," In addition, we employ the Maximum Entropy Method (MEM) algorithm provided by the imaging software \citep{hur02}47 to reconstruct HXR images around the peak of the impulsive phase."48 It is worth noting that. the CLEAN algorithun is a straight lorwared ilerative algorithan involving a convolution of source enussion wilh instrumental Point Spread Function (PSF): thus. it often gives diffuse images with large FWIIM (see.e.g...Aschwan- 2004).," It is worth noting that, the CLEAN algorithm is a straight forward iterative algorithm involving a convolution of source emission with instrumental Point Spread Function (PSF); thus, it often gives diffuse images with large FWHM \citep[see, e.g.,][]{asc04}."49. In comparison. the MEM algorithm (Sato.IXosugi.&Makishima1999) eenerally vields relatively sharp images.," In comparison, the MEM algorithm \citep{sat99} generally yields relatively sharp images."50 In this paper. we use both the CLEAN and MEM algorithms lor different. purposes.," In this paper, we use both the CLEAN and MEM algorithms for different purposes."51 Except for the integration time and energy band. the imaging parameters (hal are explicitly set in (his paper are the same as (hat in Paper I for," Except for the integration time and energy band, the imaging parameters that are explicitly set in this paper are the same as that in Paper I for"52also produces an asvmuametrey of the velocity profiles. in ealaxies that do not have a high inclination.,also produces an asymmetry of the velocity profiles in galaxies that do not have a high inclination.53 The result is that the standard methods (e.g. first-moment analysis ancl sinele-Gaussian fitting). which implicitly assume symmetry of the profiles. provide velocities that are biased towards the svstemic velocity (see Fig. 3))," The result is that the standard methods (e.g. first-moment analysis and single-Gaussian fitting), which implicitly assume symmetry of the profiles, provide velocities that are biased towards the systemic velocity (see Fig. \ref{spectrum}) )"54 and cannot be used to determine the true rotation velocity in the galaxies of our sample., and cannot be used to determine the true rotation velocity in the galaxies of our sample.55 In order to solve the problems discussed. in the previous Section. we built à method similar to the Einvelope-Tracing method (e.g. Sancisi&Allen1979.. Sofueetal.1997): the aim ds to fit only the side of the profiles which we are interested. in. Le. the extreme velocity side. (with the assumption that the gas is present at. these extreme velocitics).," In order to solve the problems discussed in the previous Section, we built a method similar to the Envelope-Tracing method (e.g. \citealt{S:79}, \citealt{So:97}) ); the aim is to fit only the side of the profiles which we are interested in, i.e. the extreme velocity side (with the assumption that the gas is present at these extreme velocities)."56 The first step was to fit a hall-Gaussian from the peak of the profiles to their extreme velocity. side (1.6. the side opposite to the svstemic velocity). considering the velocity at half maximum. the terminal velocity (17).," The first step was to fit a half-Gaussian from the peak of the profiles to their extreme velocity side (i.e. the side opposite to the systemic velocity), considering the velocity at half maximum, the terminal velocity $V_{t}$ )."57" The rotation velocity Via, at à certain position is then given by: where / is the inclination. Vo. Is the svstemic velocity. and the terms indicated. with AV describe. the profile broadenings (in terms of full width to half. maximum. FWILAL: οτω ds the broadening due to the turbulence of the interstellar medium. by assuming a constant velocity dispersion of the ISM. aysay=109 km (a typical value for spiral galaxies). which implies: Notice that following Ixamphuis(1993)— (i.c. taking arsyy going [rom 12 to 7 km s. +) would not significantly allect the derived rotation curves."," The rotation velocity $V_{rot}$ at a certain position is then given by: where $i$ is the inclination, $V_{sys}$ is the systemic velocity, and the terms indicated with $\delta V$ describe the profile broadenings (in terms of full width to half maximum, FWHM): $\delta V_{ISM}$ is the broadening due to the turbulence of the interstellar medium, by assuming a constant velocity dispersion of the ISM, $\sigma_{ISM}=10 $ km $^{-1}$ (a typical value for spiral galaxies), which implies: Notice that following \citet{K:93} (i.e. taking $\sigma_{ISM}$ going from 12 to 7 km $^{-1}$ ) would not significantly affect the derived rotation curves."58 Vie. is the instrumental contribution to the profile broadening. whieh we set equal to the channel resolution: 6.6 km ! for the galaxies observed. with the ALCA and 5.2 km + for those observed. with the VLA.," $\delta V_{obs}$ is the instrumental contribution to the profile broadening, which we set equal to the channel resolution: 6.6 km $^{-1}$ for the galaxies observed with the ATCA and 5.2 km $^{-1}$ for those observed with the VLA."59" V, is an estimate of t16 broadening of the profiles due to the beam: as is eviden in Lig. 4.."," $\delta V_{b}$ is an estimate of the broadening of the profiles due to the beam: as is evident in Fig. \ref{plane},"60 a larger beam will sample a larger portion of the velocity Ποιάancl will thus broaden the profiles. even on their extreme velocity side.," a larger beam will sample a larger portion of the velocity fieldand will thus broaden the profiles, even on their extreme velocity side."61" According to Sancii&Alon(1979).. a lower limit to dV), can be given by setting it to zero. vielding an upper limit to the rotation velocity."," According to \citet{S:79}, a lower limit to $\delta V_{b}$ can be given by setting it to zero, yielding an upper limit to the rotation velocity."62" To estimate an upper limit to dV). we assume as in. Draun{997).. that the expected. beam uncertainty in the profile widths is 2-Vr+4,/2)Vti). where the 71 corresponcs to a positive gradient of the velocitv [field and 7 to a negative one: &, is the beam EWIHIAL."," To estimate an upper limit to $\delta V_{b}$, we assume as in \citet{B:97}, that the expected beam uncertainty in the profile widths is $2\cdot[V(r \pm \theta_{b}/2)-V(r)]$, where the $+$ ” corresponds to a positive gradient of the velocity field and $-$ ” to a negative one; $\theta_{b}$ is the beam FWHM."63" With an upper limit and a lower limit to dV). we decided to estimate 91, using their average. Le: ALZE/WAMIZT has the following advantages:"," With an upper limit and a lower limit to $\delta V_{b}$ , we decided to estimate $\delta V_{b}$ using their average, i.e: MET/WAMET has the following advantages:"64Accretion powers the most luminous objects in the universe by converting gravitational potential energy into highly energetic radiation.,Accretion powers the most luminous objects in the universe by converting gravitational potential energy into highly energetic radiation.65 In order to understand this mechanism it ts crucial to study the primary engine of accreting black-hole systems: the accretion disk., In order to understand this mechanism it is crucial to study the primary engine of accreting black-hole systems: the accretion disk.66 Accretion disks form when gaseous matter. usually an assembly of free electrons and various types of tons. spirals onto a central gravitating body by gradually losing its initial angular momentum as a result of viscous and magnetic stresses.," Accretion disks form when gaseous matter, usually an assembly of free electrons and various types of ions, spirals onto a central gravitating body by gradually losing its initial angular momentum as a result of viscous and magnetic stresses."67 The simplest analytical model of an accretion disk is the standard disk model (??) which assumes that at a given radius. r. all dissipated energy ts released as radiation and that the emission at each radius is locally given by à blackbody spectrum.," The simplest analytical model of an accretion disk is the standard disk model \citep{sha+73, nov+73} which assumes that at a given radius, $r$, all dissipated energy is released as radiation and that the emission at each radius is locally given by a blackbody spectrum."68 The innermost stable circular orbit (ISCO). beyond which the particles m orbit become dynamically unstable and plunge into the black hole. is taken to be a manifestation of the inner disk boundary.," The innermost stable circular orbit (ISCO), beyond which the particles in orbit become dynamically unstable and plunge into the black hole, is taken to be a manifestation of the inner disk boundary."69 This model. however. is only self-consistent in the limit at which the disk 1s geometrically razor thin.," This model, however, is only self-consistent in the limit at which the disk is geometrically razor thin."70 Consequently. its validity is restricted to luminosities below ~30% of the Eddington luminosity. Zjj4=1.26x10°8(M/M..) erg/s. when radiation pressure will cause the disk to be minimally inflated (seee.g.?)..," Consequently, its validity is restricted to luminosities below $\sim 30\%$ of the Eddington luminosity, $L_{\rm Edd} \equiv 1.26 \,\times\, 10^{38}\,(M/\Msun)\,{\rm erg/s}$ , when radiation pressure will cause the disk to be minimally inflated \citep[see e.g.][]{mcc+06}."71" High luminosity. optically thick accretion disks are better described by accretion disks models. introduced by ? and later elaborated by several authors. including the most recent contribution of ? and ?.. who computed a network of fully relativistic slim-disk models (in Kerr geometry) that densely samples the relevant parameter space (accretion rate M. alpha viscosity a. Kerr spin parameter «,)."," High luminosity, optically thick accretion disks are better described by accretion disks models, introduced by \citet{abr+88} and later elaborated by several authors, including the most recent contribution of \citet{sad09} and \citet{sad+11}, who computed a network of fully relativistic slim-disk models (in Kerr geometry) that densely samples the relevant parameter space (accretion rate $\dot M$, alpha viscosity $\alpha$, Kerr spin parameter $a_*$ )."72 Tables and routines to extract information from the slim disk database are available., Tables and routines to extract information from the slim disk database are available.73. is à black hole (BH) binary system in the Large Magellanic Cloud (LMC) at a distance of 48.1 kpe (derivedfrom ?).., is a black hole (BH) binary system in the Large Magellanic Cloud (LMC) at a distance of $48.1$ kpc \citep[derived from][]{oro+09}.74 It was discovered by the UHURU satellite in 1971 and reported to be a discrete X-ray source by ?.., It was discovered by the UHURU satellite in 1971 and reported to be a discrete X-ray source by \citet{leo+71}.75 The optical counterpart of was first identified as a faint OB star (2). and by subsequent spectroscopic studies pinpointed as a B3 V main-sequence star in a 1.7 day orbit (2).., The optical counterpart of was first identified as a faint OB star \citep{war+75} and by subsequent spectroscopic studies pinpointed as a B3 V main-sequence star in a $1.7$ day orbit \citep{cow+83}.76 From the radial velocity shifts of H and He absorption lines ? derived a large mass function. fay=2.3+0.3Mi. which established positively as a BH candidate with a BH mass 7M€May14M. and the mass of the secondary star 4M<M»€8Ms.," From the radial velocity shifts of H and He absorption lines \citet{cow+83} derived a large mass function, $f_M = 2.3\pm0.3\,\Msun$, which established positively as a BH candidate with a BH mass $7\,\Msun \le M_{BH} \le 14\,\Msun$ and the mass of the secondary star $4\,\Msun \le M_2 \le 8\,\Msun$."77 They also pointed out the possibility that the donor star is not filling its Roche lobe., They also pointed out the possibility that the donor star is not filling its Roche lobe.78 The source exhibits large intensity variations. mostly soft spectra and a low absorption column density along the line of sight.," The source exhibits large intensity variations, mostly soft spectra and a low absorption column density along the line of sight."79 These properties make an ideal laboratory for testing our understanding of accretion. disk physics., These properties make an ideal laboratory for testing our understanding of accretion disk physics.80 Presently. the two binary parameters of interest to us are poorly known. namely the orbital inclination angle ; and the mass M of the black hole (e.g..see?)..," Presently, the two binary parameters of interest to us are poorly known, namely the orbital inclination angle $i$ and the mass $M$ of the black hole \citep[e.g., see][]{sor+01}."81 For the former. we adopt /=66° (2) and for the latter. the round value M-10M...," For the former, we adopt $i=66^{\circ}$ \citep{kui+88} and for the latter, the round value $M = 10 \Msun$."82 Because the spin. a... derived via the continuum-fitting method depends strongly on these two uncertain parameters. the spin values we quote in this paper are highly uncertain and cannot be considered reliable estimates of the spin of.," Because the spin, $a_*$, derived via the continuum-fitting method depends strongly on these two uncertain parameters, the spin values we quote in this paper are highly uncertain and cannot be considered reliable estimates of the spin of."83. In the continuum fitting technique. one determines the radius of the inner edge of the accretion disc. from. the temperature maximum of the soft X-ray flux and assumes that this radius corresponds to the innermost stable circular orbit of the black hole. from which then the black hole spin can be deduced (seethepioneeringworksby??)..," In the continuum fitting technique, one determines the radius of the inner edge of the accretion disc from the temperature maximum of the soft X-ray flux and assumes that this radius corresponds to the innermost stable circular orbit of the black hole, from which then the black hole spin can be deduced \citep[see the pioneering works by][]{zha+97,gie+01}."84 This method of measuring ας requires accurate estimates of the binary’s black hole mass. distance and inclination.," This method of measuring $a_*$ requires accurate estimates of the binary's black hole mass, distance and inclination."85 Given those. it depends only on the properties of the accretion dise model.," Given those, it depends only on the properties of the accretion disc model."86 The most recent studies of by means of the continuum fitting method. based on Newtonian or relativistic thin disk models in the low luminosity limit. include measurements of the inner disk radius (??) and estimates of the spin (?) as well as an analysis of the intrinsic disk emission (?)..," The most recent studies of by means of the continuum fitting method, based on Newtonian or relativistic thin disk models in the low luminosity limit, include measurements of the inner disk radius \citep{ste+10, dun+10} and estimates of the spin \citep{ddb06} as well as an analysis of the intrinsic disk emission \citep{kub+10}."87 In this paper. we analyze hundreds of RXTE observations of using the newly developed spectral fitting routine (?) which is an improvement upon and successor to the commonly used models (?) to the extent that it allows to fit high luminosity data as it builds upon a more general. relativistic model of slim accretion disks and uses photor ray-tracing from the actual location of the disk photosphere.," In this paper, we analyze hundreds of RXTE observations of using the newly developed spectral fitting routine \citep{bur+11} which is an improvement upon and successor to the commonly used models \citep{li+05} to the extent that it allows to fit high luminosity data as it builds upon a more general, relativistic model of slim accretion disks and uses photon ray-tracing from the actual location of the disk photosphere."88 We explore the properties of the binary system by analyzing fits for different viscosity parameters., We explore the properties of the binary system by analyzing fits for different viscosity parameters.89 In Section 2 we introduce the main features of slim accretion disks and, In Section \ref{sec:slimdisk} we introduce the main features of slim accretion disks and90distance of 1000 pc.,distance of 1000 pc.91 This again gives two parameters for determining the goodness of the fil. V7 and the white dwarl radius computed using the parallax distance.," This again gives two parameters for determining the goodness of the fit, $\chi^{2}$ and the white dwarf radius computed using the parallax distance."92 The best filling accretion disk and photosphere models were also combined in an altempt to achieve a better fit., The best fitting accretion disk and photosphere models were also combined in an attempt to achieve a better fit.93 We used our codeDISKFPIT. which allows us to vary. the accretion rate linearly between 0.1 and 10.," We used our code, which allows us to vary the accretion rate linearly between 0.1 and 10."94 This effectively alters the contribution of the disk to the observed fIux. giving the underlying white dwarla greater or lesser flux contribution depending on the ratio.," This effectively alters the contribution of the disk to the observed flux, giving the underlying white dwarf a greater or lesser flux contribution depending on the ratio."95 The fitting routine computes a scale factor (hat is related to the system distance as given by d=100/47 with distance given in pc., The fitting routine computes a scale factor that is related to the system distance as given by $d=100/\sqrt{(S)}$ with distance given in pc.96" For VY Aquari. the best fitting optically thick steady-state aceretion disk model vields an accretion rate of LO? NL, 4."," For VY Aquari, the best fitting optically thick steady-state accretion disk model yields an accretion rate of $10^{-9}$ $_{\sun}$ $^{-1}$."97" This compares to the prediction of a time averaged accretion rate of approximately 5x10.1 NI, 1 for OY Car. an SU UMa system with an orbital period very similar to that of VY Aqr. given by Patterson (1934)."," This compares to the prediction of a time averaged accretion rate of approximately $5\times 10^{-10}$ $_{\sun}$ $^{-1}$ for OY Car, an SU UMa system with an orbital period very similar to that of VY Aqr, given by Patterson (1984)."98 The white dwarl mass and disk inclination used in this best [it (shown in Figure 4) are 0.55 M. and rrespectivelv. giving a scale-Iactor distance of 93 pe.," The white dwarf mass and disk inclination used in this best fit (shown in Figure 4) are $0.55$ $_{\sun}$ and respectively, giving a scale-factor distance of 93 pc."99 This is in very good agreement with the parallax distance of 97£13 pe obtained by Thorstensen (2003)., This is in very good agreement with the parallax distance of $97 \pm 13$ pc obtained by Thorstensen (2003).100 Notice that this best fit agrees well with the observations. and does not show anv significant deviations [rom a steady-state disk longward of 1600.," Notice that this best fit agrees well with the observations, and does not show any significant deviations from a steady-state disk longward of 1600."101À.. Note (hat in the case of VY Aqr. no previous mass determinations existed and the inclination was uncertain.," Note that in the case of VY Aqr, no previous mass determinations existed and the inclination was uncertain."102" In our fitting therefore. we examined the widest range of Alva and the inclination i. Since the goocdness-o[-fit is sensitive to both M, and i. it is most"," In our fitting therefore, we examined the widest range of $M_{wd}$ and the inclination i. Since the goodness-of-fit is sensitive to both $M_{wd}$ and i, it is most"103Due to the low value of the plasma ? (the ratio of gas pressure to magnetic pressure). the solar corona is maegneticallvy dominated.,"Due to the low value of the plasma $\beta$ (the ratio of gas pressure to magnetic pressure), the solar corona is magnetically dominated."104 To describe the equilibrium structure of the coronal magnetic fiel when eravily is negligible. (he force-[ree assuniption is then appropriate: where a=0 gives (he potential (or current-[ree) field. a=cs! gives (he linear lorce-free field (Uff). anda being a function of space gives the nonlinear force-free field n/ff)).," To describe the equilibrium structure of the coronal magnetic field when gravity is negligible, the force-free assumption is then appropriate: where $\alpha = 0$ gives the potential (or current-free) field, $\alpha = cst$ gives the linear force-free field ), and $\alpha$ being a function of space gives the nonlinear force-free field )."105 The properties of force-free fields have been well described, The properties of force-free fields have been well described106"where D=EF, for $€Sp, aud FP=Το lor $>ορ.",where $\Gamma = \Gamma_1$ for $S \leq S_b$ and $\Gamma = \Gamma_2$ for $S > S_b$.107 With an addition of ouly two more moclel parameters than iu the sinele power law. this model fit gives a C-statistic value of 8.87. which is satisfactory (Fig.," With an addition of only two more model parameters than in the single power law, this model fit gives a C-statistic value of 8.87, which is satisfactory (Fig."108 10)., 10).109 The best-fit parameters are .Vy=1.7x10!sources/(COULLSslj 2.1υπl.lx10oE u. P»4=L6LOTτο Fig.oque," The best-fit parameters are $N_b=1.7 \times 10^4 {\rm~sources/(counts~s^{-1}})$, $S_b = 2.1_{-0.7}^{+1.1}\times 10^{-3}$ , $\Gamma_1 = 1.4_{-0.3}^{+0.3}$ , $\Gamma_2 = 4.6_{-1.2}^{+2.7}$."110 Q4., Fig.111ll presents the confidence⋅ contours. Py4 vs. Ds.," 11 presents the confidence contours, $\Gamma_1$ vs. $\Gamma_2$."1125 In coiiparisou. tle aualvsis by Di Stefano et al. (," In comparison, the analysis by Di Stefano et al. ("113"2003) sieeests D4=0.7EOSqu1 To=2.580.35 TEE aud a luniuosity brea cat 924ToxIU""137erg5 La'OlTespocling to a count rate break lo assuming a power law spectdun of photor index 2 and an absorption of (Di Stefano et :i.","2003) suggests $\Gamma_1 = 0.74_{-1.04}^{+0.84}$, $\Gamma_2 = 2.58_{-0.28}^{+0.35}$ , and a luminosity break at $9_{-1.6}^{+2.0} \times 10^{37} {\rm~erg~s^{-1}}$, corresponding to a count rate break $S_b \sim 1.8_{-0.32}^{+0.40} 114\times 10^{-3} {\rm~counts~s^{-1}}$ , assuming a power law spectrum of photon index 2 and an absorption of $N_H =1155 \times 10^{20} {\rm~cm^{-2}}$ (Di Stefano et al."116 2003)., 2003).117" Wule tese pa""alnnete ‘sare tuareinally cousistent with those obtained f£'om our analysis. 1jelr constralnts o1 5, seel 110 )e conside‘ably tighter than «US."," While these parameters are marginally consistent with those obtained from our analysis, their constraints on $S_b$ seem to be considerably tighter than ours."118 This «ill'erence is p'obably largely di elo le simplificatslijon 1uade 1 the analysis by Di Stefauo et al. (, This difference is probably largely due to the simplification made in the analysis by Di Stefano et al. (119200:3).,2003).120" Their analysis ignored both tle ποdl παonrce contribution ald the Exldiugtou bias aud assumed a siiple »ource-detection reshod of L5x10%e""O0esS1 OY a COUL rate of 0x10!CountssLÍ. inferre from the pea t S/N~3.2 lu a /N ilstogran of the detected sysurces."," Their analysis ignored both the background source contribution and the Eddington bias and assumed a single source-detection threshold of $4.5 \times 10^{37} {\rm~erg~s^{-1}}$, or a count rate of $ 9 \times12110^{-4} {\rm~counts~s^{-1}}$, inferred from the peak at $S/N \sim 3.2$ in a $S/N$ histogram of the detected sources."122 However. Fig.," However, Fig."123 8 sliows tha ὁ average cleection pre)ability is still oul yoSO% at this cotud rate., 8 shows that the average detection probability is still only $\sim 80\%$ at this count rate.124 A cletection. probability o>ο Or exauple. ree]res a source COUL| rate p ," A detection probability $\gtrsim 95\%$, for example, requires a source count rate $\gtrsim 1.4 \times12510^{-3} {\rm~counts~s^{-1}}$ ."126Clearly. part. of the 1τςrover in the observed iuuber-flux. relation at ορ (Fie.," Clearly, part of the turn-over in the observed number-flux relation at $S_b$ (Fig."127 10) is due to the |ux-cdepeuclent source cleection thresldd.CL. whiel should be aecouned for in the iiodeliug.," 10) is due to the flux-dependent source detection threshold, which should be accounted for in the modeling."128 Setting a threshold at a higher count rate slotlc lave pecuced this [lux depeudence., Setting a threshold at a higher count rate should have reduced this flux dependence.129 But more than half of the sources would thenbe excluded ii the anal“SIs., But more than half of the sources would thenbe excluded in the analysis.130 Of course. the [Iux-depeucdence of the threshold is a resuLo ‘the detection sensitivity variatlou," Of course, the flux-dependence of the threshold is a resultof the detection sensitivity variation"131bulges and pseudo-bulges can not follow a single Mau—Mpuige relationand a single Mgu—c relation.,bulges and pseudo-bulges can not follow a single $M_{\rm{BH}}-M_{\rm{Bulge}}$ relation a single $M_{\rm{BH}}-\sigma$ relation.132 This conclusion follows directly from the fact that these systems have different Mpuige—c relations., This conclusion follows directly from the fact that these systems have different $M_{\rm{Bulge}}-\sigma$ relations.133" Therefore, it does not depend on whether the relation we use here correctly predicts black hole masses."," Therefore, it does not depend on whether the relation we use here correctly predicts black hole masses."134" In order to precisely determine such relations, with direct black hole mass measurements, one should thus look carefully at the different stellar systems for which such measurements are available."," In order to precisely determine such relations, with direct black hole mass measurements, one should thus look carefully at the different stellar systems for which such measurements are available."135 These differences could partially account for the discordant relations found in the literature?)., These differences could partially account for the discordant relations found in the literature.136". have recently raised and discussed the fact that Mp derived from c is inconsistent with Mgu derived from bulge luminosity or mass, in a sample of early-type galaxies from the SDSS."," have recently raised and discussed the fact that $M_{\rm{BH}}$ derived from $\sigma$ is inconsistent with $M_{\rm{BH}}$ derived from bulge luminosity or mass, in a sample of early-type galaxies from the SDSS."137 They have also discussed the importance of the relation between c and bulge luminosity or mass in this regard., They have also discussed the importance of the relation between $\sigma$ and bulge luminosity or mass in this regard.138" We briefly discuss their results, in connection with our results and others in the recent literature, in Sect. 4.2.."," We briefly discuss their results, in connection with our results and others in the recent literature, in Sect. \ref{sec:dis2}."139" Figure 1 shows that barred galaxies, particularly with pseudo-bulges, have bulges with lower masses, at fixed velocity dispersion, on average, than their unbarred counterparts."," Figure \ref{fig:smbh} shows that barred galaxies, particularly with pseudo-bulges, have bulges with lower masses, at fixed velocity dispersion, on average, than their unbarred counterparts."140 This is in agreement with the results from the fundamental plane in Paper I (see Fig., This is in agreement with the results from the fundamental plane in Paper I (see Fig.141 16)., 16).142" Indeed, the offset from the Mpuige—c relation for pseudo-bulges is caused mostly by barred galaxies."," Indeed, the offset from the $M_{\rm{Bulge}}-\sigma$ relation for pseudo-bulges is caused mostly by barred galaxies."143" Furthermore, the Mpg--σ relation found by for pseudo-bulges originatesexclusively from barred galaxies."," Furthermore, the $M_{\rm{BH}}-\sigma$ relation found by for pseudo-bulges originates from barred galaxies."144" In fact, one sees in the bottom right panel of Fig."," In fact, one sees in the bottom right panel of Fig."145 1 that his relation describes reasonably well the pseudo-bulges in barred galaxies in our sample., \ref{fig:smbh} that his relation describes reasonably well the pseudo-bulges in barred galaxies in our sample.146 This also agrees with the results in?., This also agrees with the results in.147". It is thus interesting to confirm with higher resolution data whether the deviation of pseudo-bulges from the Mpuige—σ and Μῃη—c relations occurs regardless of its host galaxy being barred or unbarred, or if the presence of a bar is a necessary condition, as our results suggest."," It is thus interesting to confirm with higher resolution data whether the deviation of pseudo-bulges from the $M_{\rm{Bulge}}-\sigma$ and $M_{\rm{BH}}-\sigma$ relations occurs regardless of its host galaxy being barred or unbarred, or if the presence of a bar is a necessary condition, as our results suggest."148 It thus seems that studies on black hole demographics whether black hole masses are obtained using an Mpu—c relation or an Man—Mpuige relation., It thus seems that studies on black hole demographics might have different results depending on whether black hole masses are obtained using an $M_{\rm{BH}}-\sigma$ relation or an $M_{\rm{BH}}-M_{\rm{Bulge}}$ relation.149" This comes not only from the possibility of different relations for ellipticals and bulges, but also from the fact that we find a flatter relation between Mpg and o, using the Man—Mnuige relation, than published Mgu—c relations."," This comes not only from the possibility of different relations for ellipticals and bulges, but also from the fact that we find a flatter relation between $M_{BH}$ and $\sigma$, using the $M_{\rm{BH}}-M_{\rm{Bulge}}$ relation, than published $M_{\rm{BH}}-\sigma$ relations."150 This could affect both the total black hole mass density and the black hole mass distribution., This could affect both the total black hole mass density and the black hole mass distribution.151" To quantitatively assess how strong such effects can be, we have recalculated the black hole masses of the galaxies in our sample using the Mag—o relation in?."," To quantitatively assess how strong such effects can be, we have recalculated the black hole masses of the galaxies in our sample using the $M_{\rm{BH}}-\sigma$ relation in."152". The total black hole mass density using this Mpu—c relation is £z 70 per higher than that using the Mpu—Mnuige relation, if one does not take into account the intrinsic scatter in these relations."," The total black hole mass density using this $M_{\rm{BH}}-\sigma$ relation is $\approx$ 70 per higher than that using the $M_{\rm{BH}}-M_{\rm{Bulge}}$ relation, if one does not take into account the intrinsic scatter in these relations."153" Interestingly, this is mostly a result from the different Mpu estimates in classical bulges."," Interestingly, this is mostly a result from the different $M_{\rm{BH}}$ estimates in classical bulges."154 Although, Although155good agreement with the Grattonοἱal.(2006) value of [C'/Fe|—-0.2.,good agreement with the \citet{gra06} value of [C/Fe]=-0.2.156 Our and Green(1998). solar [O/Fe] is (vice the value found by Grattonetal.(2006)..., Our and \citet{pet98} solar [O/Fe] is twice the value found by \citet{gra06}. .157 An overall Solar ω /Fe] is consistent with a standard disk chemical enrichment scenario where both SN IH and SN Ia contributed to the enrichment of the interstellar medium., An overall Solar $\alpha$ /Fe] is consistent with a standard disk chemical enrichment scenario where both SN II and SN Ia contributed to the enrichment of the interstellar medium.158 However. it is interesting that the iron abundance of NGC 6791 reached +0.35 dex. more than a [nctor of two greater than Solar. only a lew Gvrs after the first stars were formed. relatively early in the history of the Galaxy.," However, it is interesting that the iron abundance of NGC 6791 reached +0.35 dex, more than a factor of two greater than Solar, only a few Gyrs after the first stars were formed, relatively early in the history of the Galaxy."159 In comparison with the Galactic bulge. NGC 6791 stars reach [Fe/1]—-4-0.35. only 0.15 dex lower (han the most metal rich bulge IX giants reported by Fulbright. (2005).," In comparison with the Galactic bulge, NGC 6791 stars reach [Fe/H]=+0.35, only 0.15 dex lower than the most metal rich bulge K giants reported by \citet{fmr05}."160. The a-element abundances are distinctly lower than those seen in the bulge giants (MeWilliamn&Rich1994)., The $\alpha$ -element abundances are distinctly lower than those seen in the bulge giants \citep{mr94}.161. In our sample of 11 bulge M. giants observed with II. echelle spectroscopy (Rich&Origlia2005) we find |Fe/1l] between 1/3 and Solar and enhanced io /Fe] abundance ratios as for Ix giants., In our sample of 11 bulge M giants observed with IR echelle spectroscopy \citep{ro05} we find [Fe/H] between 1/3 and Solar and enhanced $\alpha$ /Fe] abundance ratios as for K giants.162 The processes that enrich the bulge rapidly and early evidently require a star Formation rate high enough to retain an alpha enhanced composition to nearly the Solar metallicity: (ais does not appear to have been the case for NGC 6191., The processes that enrich the bulge rapidly and early evidently require a star formation rate high enough to retain an alpha enhanced composition to nearly the Solar metallicity; this does not appear to have been the case for NGC 6791.163 The age of the Galactic bulge has been debated over the vears. and ages as voung as 8-9 Gyr have been discussed seriously. especially when the luminous OIL/IB. stars are considered (cf. vanLoonetal. (2003))).," The age of the Galactic bulge has been debated over the years, and ages as young as 8-9 Gyr have been discussed seriously, especially when the luminous OH/IR stars are considered (cf. \citet{vanloon03}) )."164 In terms of chemistry. there does appear to be a distinct difference between NGC 6791 and the bulge.," In terms of chemistry, there does appear to be a distinct difference between NGC 6791 and the bulge."165 The Solar falpha/Fe] does not prove that NGC 6791 is vounger (han the bulge. but it does point to the cluster having formed well after SNe la were able to contribute substantial iron to the interstellar medium.," The Solar [alpha/Fe] does not prove that NGC 6791 is younger than the bulge, but it does point to the cluster having formed well after SNe Ia were able to contribute substantial iron to the interstellar medium."166 Yet another population of disk stars with similarly high abunclances are the metal rich dwarls found in the disk 2003).," Yet another population of disk stars with similarly high abundances are the metal rich dwarfs found in the disk \citep{castro97,pomp03}."167. These dwarls appear to have an inner disk origin and exhibit some alpha enhancement. and are therelore different from NGC 6791.," These dwarfs appear to have an inner disk origin and exhibit some alpha enhancement, and are therefore different from NGC 6791."168 Our resulis would appear to indicate that the enrichment. of metals is not a monotonic process in galaxies., Our results would appear to indicate that the enrichment of metals is not a monotonic process in galaxies.169 A proto Milkv. Way. 4-5 Gyr after the Dig Dang had some disk regions with twice Solar metallicity., A proto Milky Way 4-5 Gyr after the Big Bang had some disk regions with twice Solar metallicity.170 Our low C/Cyy5. indicates. that extra-mixing. processes. due toburning are ab work during the RGB evolution also at very high metallicity. confirming our findings [ου the metal rich giants in the Galactic bulge (Origliaetal.2005.andreferencestherein)..," Our low $\rm ^{12}C/^{13}C$ indicates that extra-mixing processes due to are at work during the RGB evolution also at very high metallicity, confirming our findings for the metal rich giants in the Galactic bulge \citep[][ and references therein]{ori05}."171 R. Michael Rich acknowledges support from grants AST-0098739 and AST-0307931 from the National Science Foundation., R. Michael Rich acknowledges support from grants AST-0098739 and AST-0307931 from the National Science Foundation.172 LO. ERE aud EV acknowledge the financial support by the Ministero Istruzzionne. Università e RicercaThis publication makes use of data products from the Two Mieron All Skv Survey. which," LO, FRF and EV acknowledge the financial support by the Ministero ne, Università e RicercaThis publication makes use of data products from the Two Micron All Sky Survey, which"173the black hole candidate GX 339—4 (Wilkinson&Uttley2009) using the soft X-ray response of the EPIC-pn CCD detector on board theXMM-Newton satellite.,the black hole candidate GX $-$ 4 \citep{Wilkinson09} using the soft X-ray response of the EPIC-pn CCD detector on board the satellite.174" In that work, we found that the disc blackbody emission does vary with an rms amplitude of tens of per cent and that the blackbody variability amplitude is greater relative to the correlated power-law variations on longer time-scales (>1 s)."," In that work, we found that the disc blackbody emission does vary with an rms amplitude of tens of per cent and that the blackbody variability amplitude is greater relative to the correlated power-law variations on longer time-scales $>1$ s)."175" We used these results to argue that, although on time-scales «1 s disc blackbody variability could be explained by X-ray heating of the disc by the varying power-law emission, on longer time-scales the disc is intrinsically variable."," We used these results to argue that, although on time-scales $<1$ s disc blackbody variability could be explained by X-ray heating of the disc by the varying power-law emission, on longer time-scales the disc is intrinsically variable."176" A natural physical interpretation is that instabilities in the standard disc are responsible for driving the observed power-law variability on time-scales at least down to a few seconds, perhaps through mass-accretion variations which propagate through the disc (Lyubarskii1997;Arévalo&Uttley2006),, before reaching the power-law emitting region."," A natural physical interpretation is that instabilities in the standard disc are responsible for driving the observed power-law variability on time-scales at least down to a few seconds, perhaps through mass-accretion variations which propagate through the disc \citep{Lyubarskii97,Arevalo06}, before reaching the power-law emitting region."177" An even stronger argument can be made for disc-driven variability if we can establish thecausal relationship between correlated variations in the disc and power-law components, through the detection of X-ray time-lags between variations in different energy bands."," An even stronger argument can be made for disc-driven variability if we can establish the relationship between correlated variations in the disc and power-law components, through the detection of X-ray time-lags between variations in different energy bands."178" Previous work to measure time-lags in BHXRBs has used proportional counter instruments to measure lags between variations at harder energies, above 2 keV (e.g. Miyamoto&Kitamoto1989;Nowaketal. 1999)), however we can also do this analysis using the sameXMM-Newton EPIC-pn timing mode data that we use to study the covariance spectrum."," Previous work to measure time-lags in BHXRBs has used proportional counter instruments to measure lags between variations at harder energies, above 2 keV (e.g. \citealt{Miyamoto89,Nowak99}) ), however we can also do this analysis using the same EPIC-pn timing mode data that we use to study the covariance spectrum."179 In this Letter we use these data to present the first time-lag study of the hard state which is extended to soft X-rays to cover the disc component., In this Letter we use these data to present the first time-lag study of the hard state which is extended to soft X-rays to cover the disc component.180 We confirm that there is indeed a clear signature in the lags at soft energies which shows that variations on time-scales of seconds or longer in the disc blackbody emission lead correlated variations in the emission., We confirm that there is indeed a clear signature in the lags at soft energies which shows that variations on time-scales of seconds or longer in the disc blackbody emission lead correlated variations in the power-law emission.181" We also show that the sign of the lag changes on time-scales «1 s, so that the disc component lags behind the power-law variations by a few milliseconds."," We also show that the sign of the lag changes on time-scales $<1$ s, so that the disc component lags behind the power-law variations by a few milliseconds."182" These lags are consistent with light-travel time-lags expected by disc thermal ‘reverberation’, caused by X-ray heating of the disc by the power-law which dominates over the intrinsic disc blackbody variability on these short time-scales."," These lags are consistent with light-travel time-lags expected by disc thermal `reverberation', caused by X-ray heating of the disc by the power-law which dominates over the intrinsic disc blackbody variability on these short time-scales."183 We analysed EPIC-pn (Strüderetal.2001) timing mode data from the 2004 March 16-19XMM-Newton observations of GX-339 in a stable hard state., We analysed EPIC-pn \citep{Strueder01} timing mode data from the 2004 March 16-19 observations of GX-339 in a stable hard state.184" The data were reduced in the standard manner usingSAS 10.0.0, processing the raw data products using the toolsEPSPLITPROC andEPFAST, taking account of background flaring and extracting only events with RAWX from columns 31 to 45 using theSAS toolEVSELECT."," The data were reduced in the standard manner using 10.0.0, processing the raw data products using the tools and, taking account of background flaring and extracting only events with RAWX from columns 31 to 45 using the tool."185" Although the tool was used on the events file, the Charge Transfer Inefficiency (CTI) corrections were insufficient to remove features at 1.8 and 2.2 keV (Si and Au edges) in the 2004 spectrum."," Although the tool was used on the events file, the Charge Transfer Inefficiency (CTI) corrections were insufficient to remove features at 1.8 and 2.2 keV (Si and Au edges) in the 2004 spectrum."186" Although the source is relatively bright, previous analyses have shown that the EPIC-pn data are not significantly piled up (Done&DiazTrigo 2010)."," Although the source is relatively bright, previous analyses have shown that the EPIC-pn data are not significantly piled up \citep{Done10}."187. The tools and were used to generate the ancillary response file (ARF) and redistribution matrix file (RMF) for the 15 columns used for source extraction., The tools and were used to generate the ancillary response file (ARF) and redistribution matrix file (RMF) for the 15 columns used for source extraction.188 Background was not accounted for as it is very small compared to the source and in any case background variations are uncorrelated with those of the chosen reference energy bands and so do not contribute to the lags or covariance spectra., Background was not accounted for as it is very small compared to the source and in any case background variations are uncorrelated with those of the chosen reference energy bands and so do not contribute to the lags or covariance spectra.189 The total exposure time for the combined 2004 data was 155 ks., The total exposure time for the combined 2004 data was 155 ks.190" We used the event lists, together with Good Time Intervals (GTIs) excluding telemetry dropouts, to extract light curves in three geometrically-spaced energy bands (soft 0.5— keV, medium 2-3 keV and hard 6-9 in order to measure the cross-spectra and determine lags between"," We used the event lists, together with Good Time Intervals (GTIs) excluding telemetry dropouts, to extract light curves in three geometrically-spaced energy bands (soft 0.5--0.9 keV, medium 2–3 keV and hard 6–9 in order to measure the cross-spectra and determine lags between"19150 kn s+ for the largest blucshitts. TOO kun st.,"50 km $^{-1}$ for the largest blueshifts, 700 km $^{-1}$."192 While the density of objects is highest around the origin. two tails ave clearly secu.," While the density of objects is highest around the origin, two tails are clearly seen."193 About of the objects show almost uo 10 III| velocity shift. but sienificaut Fe ΤΠ redslift.," About of the objects show almost no [O III] velocity shift, but significant Fe II redshift."194 About of the objects show almost uo Fe II velocity shift. but siguificaut [ο III] blueshift.," About of the objects show almost no Fe II velocity shift, but significant [O III] blueshift."195 IIuetal.(2008) argue that the Fe IT redshift is caused by iufall of material in the outer part of the BLR., \citet{hu08} argue that the Fe II redshift is caused by infall of material in the outer part of the BLR.196 Thev find that the Fe II lines are uuiforuilv narrower than I> and that the objects with large Fe II redshifts show excess cuiission ou the red side of the IT) liue., They find that the Fe II lines are uniformly narrower than $\beta$ and that the objects with large Fe II redshifts show excess emission on the red side of the $\beta$ line.197 They also fluc that the Fe II redshifts are inversely correlate with ER., They also find that the Fe II redshifts are inversely correlated with ER.198 Thev speculate that the Fe II iufall is driven by eravitv and opposed by radiation pressure., They speculate that the Fe II infall is driven by gravity and opposed by radiation pressure.199 The rise in radiation pressure with increasing ER decreases the inflow., The rise in radiation pressure with increasing ER decreases the inflow.200 There is direct evidence supporting the idea that the blucshift of |O IIT] is indicative of a polar outflow., There is direct evidence supporting the idea that the blueshift of [O III] is indicative of a polar outflow.201 Studies of very ucarby objects (Ruizetal.2005:Crenshawetal.2010) are able to resolve the NLR sufficicutly to map the spatial aud kinematic distribution of cutting material and match it to models of outflowing material and a biconical illuuination pattern.," Studies of very nearby objects \citep{ruiz05, crenshaw10} are able to resolve the NLR sufficiently to map the spatial and kinematic distribution of emitting material and match it to models of outflowing material and a biconical illumination pattern."202 Tn light of these explanations of the velocities of the Fe IT and [O TH] emitting material. the obvious conclusionis that the tails in the VS. VFell diaeraim are indicative of orthogoual τωmotions - Fe Ἡ in the disk aud [O ITI] iu the perpendicular polar direction.," In light of these explanations of the velocities of the Fe II and [O III] emitting material, the obvious conclusion is that the tails in the $_{[O III]}$ vs. $_{Fe II}$ diagram are indicative of orthogonal motions - Fe II in the disk and [O III] in the perpendicular polar direction."203 Iu this case. the objects with larec Fe II inflow velocities are seen with the disk ecec-on to our line of sight. aud the objects with large O III| outflow velocities are sccu with the disk »ole-ou. to our line of sight.," In this case, the objects with large Fe II inflow velocities are seen with the disk edge-on to our line of sight, and the objects with large [O III] outflow velocities are seen with the disk pole-on to our line of sight."204 Therefore. we define hree regions. shown in figure 1 as »ole-on. aud edee-on subsets; and a third subset that includes objects with ucither large Fe II velocities nor large O ΠΠ velocities.," Therefore, we define three regions, shown in figure 1 as pole-on and edge-on subsets, and a third subset that includes objects with neither large Fe II velocities nor large [O III] velocities."205 The boundaries of these regions are arbitrarv: they merely serve to isolate the two ails of the distribution., The boundaries of these regions are arbitrary; they merely serve to isolate the two tails of the distribution.206 These boundaries result iu 829 edge-on objects. 226 pole-on objects. and 1081 intermediate objects.," These boundaries result in 829 edge-on objects, 226 pole-on objects, and 1081 intermediate objects."207 Note that the term edec-on is used in a relative sense: an obscuring torus iu the same plane as the Fe ΤΠ cmitting disk would lait actual viewing angles to be outside of a true edee-on value., Note that the term edge-on is used in a relative sense; an obscuring torus in the same plane as the Fe II emitting disk would limit actual viewing angles to be outside of a true edge-on value.208 Some confirmation that this explanation is correct comes from the radio-loud objects in the saluple., Some confirmation that this explanation is correct comes from the radio-loud objects in the sample.209 Within the edec-on subset. there are 778 objects within the footprint of the FIRST radio survev (Beckeretal.1995).," Within the edge-on subset, there are 778 objects within the footprint of the FIRST radio survey \citep{becker95}."210".. A search of the FIRST archive at these positions vielded 59 objects with Ro 10, where RB is the ratio of 6 cu to 2500 ‘flix."," A search of the FIRST archive at these positions yielded 59 objects with R $>$ 10, where R is the ratio of 6 cm to 2500 flux."211 The FIRST nuages of cach of these matches was inspected visually and classified as core. extended or resolved single source. core plus obe. core plus 2 lobes. or 2 lobes with no COLO.," The FIRST images of each of these matches was inspected visually and classified as core, extended or resolved single source, core plus lobe, core plus 2 lobes, or 2 lobes with no core."212 Thirty of hese edee-on objects are not conipact radio sources. ad of these. 17 show two ohes.," Thirty of these edge-on objects are not compact radio sources, and of these, 17 show two lobes."213 Similarly. the pole-on subset was analyzed.," Similarly, the pole-on subset was analyzed."214 Within that smaller subset. there are 7 radio-oud objects. of which 5 are compact. oue is a resolved single source. anc one has a core plus one obe morphology.," Within that smaller subset, there are 7 radio-loud objects, of which 5 are compact, one is a resolved single source, and one has a core plus one lobe morphology."215 Assuuing that the radio source axis is aligned with the |O ΠΠ outflow direction. lis is as expected: double lobed objects are only seen within the edge-on subset.," Assuming that the radio source axis is aligned with the [O III] outflow direction, this is as expected; double lobed objects are only seen within the edge-on subset."216 The intermediate subset shows intermediate radio properties: of the 10 objects in this subset that are radio-loud. five show two lobes.," The intermediate subset shows intermediate radio properties; of the 40 objects in this subset that are radio-loud, five show two lobes."217 However. note that the radio-loud fraction of all these subsets is :120all. ancl the salple-wide characteristics apply to the quiet objects as well.," However, note that the radio-loud fraction of all these subsets is small, and the sample-wide characteristics apply to the radio-quiet objects as well."218 The argument that the tails iu figure 1 isolate pole-on and edge-on subsets does not preclude the possibility that other factors plav a role., The argument that the tails in figure 1 isolate pole-on and edge-on subsets does not preclude the possibility that other factors play a role.219 One that should certainly be considered is Líjg4/Lrg. or Eddington ratio.," One that should certainly be considered is $_{bol}$ $_{Edd}$ , or Eddington ratio."220 Many trends in ACN characteristics. and. in particular. both of the effects that contribute to the νοη VS. Vgc44 Gagram have been related to Eddington ratio.," Many trends in AGN characteristics, and, in particular, both of the effects that contribute to the $_{[O III]}$ vs. $_{Fe II}$ diagram have been related to Eddington ratio."221" IIuctal.(2008) argued that as Eddington ratio increases, radiation pressure opposes and eventually prevents the Fe ID inflow."," \citet{hu08} argued that as Eddington ratio increases, radiation pressure opposes and eventually prevents the Fe II inflow."222 Siuilarh. Borosou(2005) and Zamanovetal.(2002) both find correlations between the objects with largest [O TT} blucshifts and Eddington ratio.," Similarly, \citet{boroson05} and \citet{zamanov02} both find correlations between the objects with largest [O III] blueshifts and Eddington ratio."223 More generally. Eddington ratio has Όσσα proposed as a driver for the EVI correlations (Boroson&Crecu1992).. which include EWIIM of IT./ and EW of both Fe IT aud |O III].," More generally, Eddington ratio has been proposed as a driver for the EV1 correlations \citep{bg92}, which include FWHM of $\beta$ and EW of both Fe II and [O III]."224 We begin with the hypothesis that the sequence of objects in theο Vs. Νεο Magram is due ouly to orientation., We begin with the hypothesis that the sequence of objects in the$_{[O III]}$ vs. $_{Fe II}$ diagram is due only to orientation.225 ηAs one’s viewing angle changes from edee-on to pole-on aud passing, As one's viewing angle changes from edge-on to pole-on and passing226Nordstrometal.(2004) catalog.,\citet{nordstrom} catalog.227 Early works. addressing (he rate of binary svstems among Population 11 stars. showed that this value is small. as compared to the analogous value for Population I stars (Abt&Levi1969:CramptonIartwick1972:AbtWillmarth:1937).," Early works, addressing the rate of binary systems among Population II stars, showed that this value is small, as compared to the analogous value for Population I stars \citep{abt_levi,228crampton_hartwick,abt_willmarth}."229. In subsequent works (Preston&Snecen2000:Goldbergetal.2002:Latham it was concluded that thesevalues are indistinguishable (idem Abt2008)).," In subsequent works \citep{preston_sneden,goldberg_2002,latham_2002} it was concluded that thesevalues are indistinguishable (idem \citealt{abt}) )."230 A long-term spectroscopic monitoring of about 1500 nearby stars with hieh proper motions (Carneyοἱ (hereinafter CLLA). 2001:; Goldbergetal.2002:Latham 2002)) has plaved an important role in the study of the multiplicity of metal-poor stars.," A long-term spectroscopic monitoring of about $1\ 500$ nearby stars with high proper motions \citealt{clla} (hereinafter CLLA), \citeyear{carney_2001}; \citealt{goldberg_2002,latham_2002}) ) has played an important role in the study of the multiplicity of metal-poor stars."231 Spectroscopic studies cover (he svstems with relatively short orbital periods (2?<10 vears)., Spectroscopic studies cover the systems with relatively short orbital periods $P\lesssim10$ years).232 The study of long-period couples with common proper motion components (ZapateroOsorio&Martin2004) confirms the hypothesis of an equal Irequeney. of binary svstems among the old and voung stellar populations (idem Allen.Poveda&Herrera 2000))., The study of long-period couples with common proper motion components \citep{zapatero} confirms the hypothesis of an equal frequency of binary systems among the old and young stellar populations (idem \citealt*{allen}) ).233" Meanwhile. an intermediate"" period range of Pzz10—1000 vears. which corresponds to {he semi-major orbital axes of e2z10—100 AU in the solar neighbourhood. remains poorly understood to date."," Meanwhile, an `intermediate' period range of $P\approx10-1\ 000$ years, which corresponds to the semi-major orbital axes of $a\approx10-100$ AU in the solar neighbourhood, remains poorly understood to date."234 This range can be studied with the use of adaptive optics. speckle interferometry and long baseline interferometry.," This range can be studied with the use of adaptive optics, speckle interferometry and long baseline interferometry."235 The scarce Population I stars observations. made by means of the interferometric techniques. were ran either for the brightest stars (Luetal.1987). or with relatively low angular resolution (Zinnecker.Kohler 2004).," The scarce Population II stars observations, made by means of the interferometric techniques, were ran either for the brightest stars \citep{lu} or with relatively low angular resolution \citep*{zinnecker}."236. Notwithstanding the empirical data available to date. the number of known binary and mulüple systems with metal-poor components remains small.," Notwithstanding the empirical data available to date, the number of known binary and multiple systems with metal-poor components remains small."237 In order (to enlarge the database of binary and multiple Population IH stars. to define their orbital parameters aud the properties of their components. we conducted speckle interferometric observations of 223 metal-poor subdwarls with hieh proper motions located in the solar neighbourhood (Rastegaev.Dalega&Malogolovets2007:Rastegaev 2008)..," In order to enlarge the database of binary and multiple Population II stars, to define their orbital parameters and the properties of their components, we conducted speckle interferometric observations of 223 metal-poor subdwarfs with high proper motions located in the solar neighbourhood \citep*{rastegaev_2007,rastegaev_2008}. ."238 The observations were mace with the dilfraction-limited resolution of the 6 m Dig, The observations were made with the diffraction-limited resolution of the 6 m Big239Since some level of non-Caussianity is generically expected in all inflation models. due to interactions of the inflaton with eravity and/or from inflaton self-interactions. seeking for deviations from the Gaussian. paradigm. has recently become a major effort anc a minor industry in cosmology.,"Since some level of non-Gaussianity is generically expected in all inflation models, due to interactions of the inflaton with gravity and/or from inflaton self-interactions, seeking for deviations from the Gaussian paradigm has recently become a major effort – and a minor industry – in cosmology."240 Properties of the primordial. perturbations are uniquely imprinted in the cosmic microwave background. (CMD) anisotropy. distribution: hence. its analysis is a powerful wav of looking at the specifics of the inflationary mocels (or alternatives to inflation).," Properties of the primordial perturbations are uniquely imprinted in the cosmic microwave background (CMB) anisotropy distribution; hence, its analysis is a powerful way of looking at the specifics of the inflationary models (or alternatives to inflation)."241 t the present time. the main challenge is either to detect or to constrain mild or weak departures from. primordial Gaussian initial conditions. as the level of non-Gaussianity predicted in the simplest single-ficld slow-roll inllation is slightlv below the minimum value detectable by the Planck satellite. anc not within reach of future galaxy surveys.," At the present time, the main challenge is either to detect or to constrain mild or weak departures from primordial Gaussian initial conditions, as the level of non-Gaussianity predicted in the simplest single-field slow-roll inflation is slightly below the minimum value detectable by the Planck satellite, and not within reach of future galaxy surveys."242 This is essentially why primorclial non-Gaussianity is regarded as one of the most. promising probes of the inflationary universe (Ixomatsu et al., This is essentially why primordial non-Gaussianity is regarded as one of the most promising probes of the inflationary universe (Komatsu et al.243 2009b). and it has received a recent boost. both theoretically ancl observationally. mainly because of the. Hülkinson Afiicrowave Annisotropy Prrobe (WALAD) data which seems to favor a slightly positive value of the dimensionless non-linearity parameter fxn (Yadav Wandelt 2008: Komatsu et al.," 2009b), and it has received a recent boost, both theoretically and observationally, mainly because of the ilkinson icrowave nisotropy robe (WMAP) data which seems to favor a slightly positive value of the dimensionless non-linearity parameter $f_{\rm NL}$ (Yadav Wandelt 2008; Komatsu et al."244 2009a. 2010: Smith et al.," 2009a, 2010; Smith et al."245 2009)., 2009).246 From the theoretical side. much ellort has been directed: towards the development. of competing scenarios [or perturbation generation which go beyond. the single-Ποιά. slow-voll paradigm. for instance by the inclusion in the Lagrangian of non-trivial kinetic terms. the presence of more than one light field. during inflation. the temporary," From the theoretical side, much effort has been directed towards the development of competing scenarios for perturbation generation which go beyond the single-field slow-roll paradigm, for instance by the inclusion in the Lagrangian of non-trivial kinetic terms, the presence of more than one light field during inflation, the temporary"247We computed models for 14 values of Zar between 28.000 and 34.000 Ix. We fit for each temperature separately since the derived radius from the parallax distance depends on the temperature. ancl the derived radius is used as an external constraint.,"We computed models for 14 values of $T_{\rm eff}$ between 28,000 and 34,000 K. We fit for each temperature separately since the derived radius from the parallax distance depends on the temperature, and the derived radius is used as an external constraint."248 For each model at each temperature. ELC's genetic code was run (wice using dillerent initial populations ancl ihe Monte Carlo Markov. Chain (AICAIC) code was run once.," For each model at each temperature, ELC's genetic code was run twice using different initial populations and the Monte Carlo Markov Chain (MCMC) code was run once."249 The best solutions were then refined using a simple grid search., The best solutions were then refined using a simple grid search.250 We computed uncertainties on the fitted parameters ancl on the derived parameters tthe black hole mass M. the gravity of the O-star logg. etc.)," We computed uncertainties on the fitted parameters and on the derived parameters the black hole mass $M$, the gravity of the O-star $\log g$, etc.)"251 using (he procedure discussed in Oroszetal.(2002)., using the procedure discussed in \cite{oro+2002}.252. The results for all 14 temperatures are shown in Table Al and AAI and A2., The results for all 14 temperatures are shown in Table A1 and A1 and A2.253 As discussed in the main text. the improvement in the 47 values as one goes from Model A to Model D is evident.," As discussed in the main text, the improvement in the $\chi^2$ values as one goes from Model A to Model D is evident."254 For Model A. we consistently find Row<Baia.," For Model A, we consistently find $R_{\rm opt}< R_{\rm dist}$."255 Furthermore. the rotational velocity derived from the model is consistently larger than the observed value.," Furthermore, the rotational velocity derived from the model is consistently larger than the observed value."256 By allowing nonsvuchronous rotation for the circular orbit (as in Model D). the model-derived stellar radius agrees with the radius computed from the distauce. and the mocdel-derived rotational velocity agrees with the measured one.," By allowing nonsynchronous rotation for the circular orbit (as in Model B), the model-derived stellar radius agrees with the radius computed from the distance, and the model-derived rotational velocity agrees with the measured one."257 Generally speaking. (he star rotates slower (han its svnelironous value.," Generally speaking, the star rotates slower than its synchronous value."258 ILowever. an inspection of the light curves (see Figure 2 in the main text) shows that the maxinuun near phase 0.25 is slightly higher (han the maximum near 0.75.," However, an inspection of the light curves (see Figure 2 in the main text) shows that the maximum near phase 0.25 is slightly higher than the maximum near 0.75."259 Because an ellipsoidal model predicts maxima of equal intensity. the fit to the data is not optimal.," Because an ellipsoidal model predicts maxima of equal intensity, the fit to the data is not optimal."260 We accommodate (he unequal maxima by adding eccentricity to the svnchronous model (as in Model C)., We accommodate the unequal maxima by adding eccentricity to the synchronous model (as in Model C).261" However. in this case. the model stellar radius 0,5, is consistently larger than the radius derived from the distance Haa ancl the model rotational velocity is smaller than the observed value."," However, in this case, the model stellar radius $R_{\rm opt}$ is consistently larger than the radius derived from the distance $R_{\rm dist}$ and the model rotational velocity is smaller than the observed value."262 By allowing nonsvnchronous rotation in the eccentric orbit (Model. D). Ro. agrees with Lai and the model rotational velocity agrees with the measured value.," By allowing nonsynchronous rotation in the eccentric orbit (Model D), $R_{\rm263opt}$ agrees with $R_{\rm dist}$ and the model rotational velocity agrees with the measured value."264" One can argue, that there might exist some uncertainty in weak interactions (electron/positroncapturesand2003;Jankaetal.2007;Cole2012) which determine Y,, especially due to recent developments of including charged-current rates that are consistent with the EOS (fordetails,seeMartínez-Pinedoetal.2012;Roberts&Reddy 2012)."," One can argue, that there might exist some uncertainty in weak interactions \citep[electron/positron captures and neutrino captures; see, e.g.][]265{LangankePinedo:2003, Janka:etal:2007, Cole:etal:2012}266 which determine $Y_e$, especially due to recent developments of including charged-current rates that are consistent with the EOS \citep[for details, see][]{MartinezPinedo:2012,Roberts:2012}."267" These very recent preliminary investigations include medium effects for the (electron) neutrino and antineutrino capture reactions, which lead to changed reaction Q-values by adding nucleon interaction potential differences for neutrons and protons, enhancing as a result the difference between average anti-neutrino and neutrino energies."," These very recent preliminary investigations include medium effects for the (electron) neutrino and antineutrino capture reactions, which lead to changed reaction $Q$ -values by adding nucleon interaction potential differences for neutrons and protons, enhancing as a result the difference between average anti-neutrino and neutrino energies."268" This causes a change in Y,.", This causes a change in $Y_e$.269" All our earlier discussions had the main emphasis that the influence of the neutrino flux from the proto-neutron star would cause an increase in Y,. The preliminary analysis of such effects by Martínez-Pinedoetal.(2012) and Roberts&Reddy(2012),, which were not yet included in the present calculations, shows that the Y, increase is weakened or even moderately rich conditions (Y;< 0.5) can result."," All our earlier discussions had the main emphasis that the influence of the neutrino flux from the proto-neutron star would cause an increase in $Y_e$ The preliminary analysis of such effects by \citet{MartinezPinedo:2012} and \citet{Roberts:2012}, which were not yet included in the present calculations, shows that the $Y_e$ increase is weakened or even moderately neutron-rich conditions $Y_e \lesssim 0.5$ ) can result."270" For this reason, we also repeated the present nucleosynthesis calculations with variations in the initial Y, for the mass zones experiencing prompt and delayed explosions, according to the following recipe: where the Y, cor’s are the corrected ones and poor denotes the percentage of uncertainty in deviations of Y, from the symmetric value 0.5, which enlarges these deviation from 0.5."," For this reason, we also repeated the present nucleosynthesis calculations with variations in the initial $Y_e$ for the mass zones experiencing prompt and delayed explosions, according to the following recipe: where the ${Y_{e,\; \rm{cor}}}$ 's are the corrected ones and $p_{\rm{cor}}$ denotes the percentage of uncertainty in deviations of $Y_e$ from the symmetric value $0.5$ , which enlarges these deviation from $0.5$."271 This lowers the initially only moderately neutron-rich Y;'s in regions which already produced A—130 nuclei., This lowers the initially only moderately neutron-rich $Y_e$ 's in regions which already produced $A=130$ nuclei.272 The nucleosynthesis results are presented in Figures 11 and 15 and show the options of obtaining a full or weak r-process., The nucleosynthesis results are presented in Figures \ref{fig-integ} and \ref{fig-honda} and show the options of obtaining a full or weak $r$ -process.273" However, we expect that any uncertainties beyond 2096 are unrealistic for the explosion model we adopt in the current work."," However, we expect that any uncertainties beyond $20$ are unrealistic for the explosion model we adopt in the current work."274" As is obvious from the discussion above, that only a “weak” r-process can be supported by the nucleosynthesis conditions found in the explosion mechanism discussed and presented here, one might wonder whether such conditions support abundance features found in “weak r-process"" low-metallicity stars as observed by Hondaetal.(2006)."," As is obvious from the discussion above, that only a “weak"" $r$ -process can be supported by the nucleosynthesis conditions found in the explosion mechanism discussed and presented here, one might wonder whether such conditions support abundance features found in “weak $r$ -process"" low-metallicity stars as observed by \citet{Honda:etal:2006}."275". For this reason, we also show such a comparison in Figure 15.."," For this reason, we also show such a comparison in Figure \ref{fig-honda}."276" What can be seen is that these observations also show sizable r-process features above the A=130 peak, although weaker than in solar r-element abundances."," What can be seen is that these observations also show sizable $r$ -process features above the $A=130$ peak, although weaker than in solar $r$ -element abundances."277" If such abundance distributions are the result ofa single nucleosynthesis pollution, also the weak"" r-process found in the present paper can only marginally explain such features."," If such abundance distributions are the result ofa single nucleosynthesis pollution, also the “weak"" $r$ -process found in the present paper can only marginally explain such features."278One,One279"relevant features (i.e., traversing erupting flux rope as discussed above in Section 2.2.2}, inflow-outflow region (green), region where a current sheet may potentially develop, and core flaring site (red)) is proposed in Figure Γή. (","relevant features (i.e., traversing erupting flux rope as discussed above in Section \ref{inflow101103:orientation_mag_pfss}, inflow-outflow region (green), region where a current sheet may potentially develop, and core flaring site (red)) is proposed in Figure \ref{orientation_cartoon}. ("280"To reduce clutter in the diagram, the blue core flaring site is omitted.)","To reduce clutter in the diagram, the blue core flaring site is omitted.)"281 The inset contains two duplicate, The inset contains two duplicate282and. respective observable counterpart reads: This has certain consequences both advantageous and disadvantageous.,and respective observable counterpart reads: This has certain consequences both advantageous and disadvantageous.283" The positive side is that the. Hubble constant Lf, gets. cancelled. hence it does not. introduce any uncertainty to the results."," The positive side is that the Hubble constant $H_0$ gets cancelled, hence it does not introduce any uncertainty to the results."284" On the other hand. we have a disadvantage that the power of estimating Q,,, is poor (which could be seen by inspection into specific formulae for h(z:p) σος Table 1 below).", On the other hand we have a disadvantage that the power of estimating $\Omega_m$ is poor (which could be seen by inspection into specific formulae for $h(z;{\mathbf p})$ – see Table 1 below).285" Therefore we only attempted to fit O,, in the case of AC'DAL model. (where itis the only free parameter in flat cosmology) ancl it was successful only for the restricted sample (see below).", Therefore we only attempted to fit $\Omega_m$ in the case of $\Lambda$ CDM model (where it is the only free parameter in flat cosmology) and it was successful only for the restricted sample (see below).286" In other cases we assumed fixed. values for ,,.", In other cases we assumed fixed values for $\Omega_m$.287 Cosmological moclel parameters (coefficients in the equation of state) have been estimated by minimizing the chi-square: where the sum is over the sample and m5; denotes the variance of D. (contextual use of the same svnibol for variances and velocity dispersions should. not. lead. to confusion).," Cosmological model parameters (coefficients in the equation of state) have been estimated by minimizing the chi-square: where the sum is over the sample and $\sigma_{{\cal D},i}^2$ denotes the variance of ${\cal D}^{obs}$ (contextual use of the same symbol for variances and velocity dispersions should not lead to confusion)."288 In calculating ep we assumed that only velocity dispersion. errors. contribute and the Einstein radii are determined. accurately., In calculating $\sigma_{{\cal D}}$ we assumed that only velocity dispersion errors contribute and the Einstein radii are determined accurately.289 We used a combined sample of 7=20 strong lensing systems with goor spectroscopic nieasurements of central dispersions from the SLACS ancl LSD surveys (essentially the same sample as used by Grillo et al. (, We used a combined sample of $n=20$ strong lensing systems with good spectroscopic measurements of central dispersions from the SLACS and LSD surveys (essentially the same sample as used by Grillo et al. (2902008)).,2008)).291 Original data concerning SLACS sample came from Treu et al. (, Original data concerning SLACS sample came from Treu et al. (2922006) (see also an erratum. (Trea et al.,2006) (see also an erratum (Treu et al.293 2006a) - very. important one)., 2006a) - very important one).294 Data concerning LSD lenses are taken after Treu ancl Ixoopmans (2004). IxXoopmans and Treu (2003. 2002).," Data concerning LSD lenses are taken after Treu and Koopmans (2004), Koopmans and Treu (2003, 2002)."295 As already noticed. in Treu ct al. (, As already noticed in Treu et al. (2962006) the SLAC'S sample has an average D)./D. ratio equal to 0.58. with an rms scatter. O15.,2006) the SLACS sample has an average $D_{ls}/D_s$ ratio equal to 0.58 with an rms scatter 0.15.297 Whereas for their purpose i0 was advantageous. in our context it weakens the performance of the method.," Whereas for their purpose it was advantageous, in our context it weakens the performance of the method."298 Vherclore we selected a sub-sample of n=7 enses with the D ratio deviating from the mean more than rms in either direction., Therefore we selected a sub-sample of $n=7$ lenses with the ${\cal D}$ ratio deviating from the mean more than rms in either direction.299 Lt is summarized in Table 1 where he names of lenses in the restricted: sample are given in rolcl., It is summarized in Table 1 where the names of lenses in the restricted sample are given in bold.300 For comparison of our results with the cata which riggerecd the dark. energv problem. we also performed its to the SNla data (n2307 supernovae) using Unionüs compilation by Ixowalski ct al. (," For comparison of our results with the data which triggered the dark energy problem, we also performed fits to the SNIa data (n=307 supernovae) using Union08 compilation by Kowalski et al. ("3012008).,2008).302" The ©,,,=0.27 prior was used throughout. except in the ACDAL model where the it was attempted."," The $\Omega_m = 0.27$ prior was used throughout, except in the $\Lambda$ CDM model where the fit was attempted."303 Several scenarios have been put forward as an explanation of presently accelerating expansion of the Universe., Several scenarios have been put forward as an explanation of presently accelerating expansion of the Universe.304 The most obvious candidate is the cosmological constant A representing the energv of the vacuum., The most obvious candidate is the cosmological constant $\Lambda$ representing the energy of the vacuum.305 Corresponding cosmological model. which turned out to be in agreement with all existing (independent ancl alternative) observations is the ACDAL moclel.," Corresponding cosmological model, which turned out to be in agreement with all existing (independent and alternative) observations is the $\Lambda$ CDM model."306" Lt is equivalent tow =l in the cosmic equation of statep=wp anc the only free parameter here is the ©), representing the density of barvonic plus cold. dark matter as a fraction of critical density (as alreacly said spatial Hlatness is assumed).", It is equivalent to $w = -1$ in the cosmic equation of state $p= w \rho$ and the only free parameter here is the $\Omega_m$ representing the density of baryonic plus cold dark matter as a fraction of critical density (as already said spatial flatness is assumed).307 On one hand it is therefore the most. parsimonious one. but. well known fine tuning problems led many people to seek bevone the A framework and to develop the concept of. quintessence.," On one hand it is therefore the most parsimonious one, but well known fine tuning problems led many people to seek beyond the $\Lambda$ framework and to develop the concept of quintessence."308 Usually the quintessence is described in a phenomenologica manner. as a scalar field with an appropriate potential.," Usually the quintessence is described in a phenomenological manner, as a scalar field with an appropriate potential."309 La first approximation it could be tested: observationally by promoting w to the role of a free parameter to be fittec from the data., In first approximation it could be tested observationally by promoting $w$ to the role of a free parameter to be fitted from the data.310 Llowever there is no à priori reason to expec that «6 should then be à constant., However there is no a priori reason to expect that $w$ should then be a constant.311 “Phe parametrization of ες)=uy|dul developed by Chevalier. Polarski (2001) and. Linder (2003) turned out to be well suited ane robust for such case., The parametrization of $w(z) = w_0 + w_a \frac{z}{1+z}$ developed by Chevalier Polarski (2001) and Linder (2003) turned out to be well suited and robust for such case.312 In the past. alternative parametrization (2)—angες was used Gvhich is a truncated Taylor series representation of dw(2)).," In the past, alternative parametrization $w(z) = w_0 + w_1 z$ was used (which is a truncated Taylor series representation of $w(z)$ )."313 Chevalier-Polarski-Linder parametrization instead. uses an expansion with respect to the physical degree of freedom Le. the scale factor (expanded: arouncl its present value)., Chevalier-Polarski-Linder parametrization instead uses an expansion with respect to the physical degree of freedom i.e. the scale factor (expanded around its present value).314 Dimensionless (i.e. with {1ο factored out) expansion rates for respective modcls are given in Table 2., Dimensionless (i.e. with $H_0$ factored out) expansion rates for respective models are given in Table 2.315" For comparison we also performed fits of the models considered. above to the supernova la data with the same prior assumptions (spatial Uatness of the Universe and £9,,).", For comparison we also performed fits of the models considered above to the supernova Ia data with the same prior assumptions (spatial flatness of the Universe and $\Omega_m$ ).316 We have taken Union0s compilation (Ixowalski et al., We have taken Union08 compilation (Kowalski et al.317 2008) and instead of straightforward. «72 fitting m(z) , 2008) and instead of straightforward $\chi^2$ fitting $m(z)$ 318At all but the most modest redshifts. the measurement of the velocity width of broad permitted lines (e.g. Ho. ΜΡΠ. CIV) from unobscured Type-I active galactic nuclei (AGN) offers the only direct way to estimate the masses of super-massive black holes (Wandel. Peterson Malkan 1999: Kaspi et al.,"At all but the most modest redshifts, the measurement of the velocity width of broad permitted lines (e.g. $\beta$, MgII, CIV) from unobscured Type-1 active galactic nuclei (AGN) offers the only direct way to estimate the masses of super-massive black holes (Wandel, Peterson Malkan 1999; Kaspi et al."319 2000: McLure Dunlop 2001: Ho 2002: MeLure Jarvis 2002: Willott et al., 2000; McLure Dunlop 2001; Ho 2002; McLure Jarvis 2002; Willott et al.320 2003: MeLure Dunlop 2004: Vestergaard Peterson 2006: Peng et al., 2003; McLure Dunlop 2004; Vestergaard Peterson 2006; Peng et al.321 2006a: Vestergaard et al., 2006a; Vestergaard et al.322 2008: Willott et al., 2008; Willott et al.323 2010)., 2010).324 For this reason. determining the properties of AGN host galaxies remains of erucia importance for exploring the relationship between black-hole and galaxy evolution over cosmic history. and in particular for testing alternative theories for the origin of the now well-establishec proportionality between black-hole and galaxy bulge mass founc in the local/present-day Universe (Kormendy Richstone 1995: Magorrian et al.," For this reason, determining the properties of AGN host galaxies remains of crucial importance for exploring the relationship between black-hole and galaxy evolution over cosmic history, and in particular for testing alternative theories for the origin of the now well-established proportionality between black-hole and galaxy bulge mass found in the local/present-day Universe (Kormendy Richstone 1995; Magorrian et al."325 1998: Silk Rees 1998: Gebhardt et al., 1998; Silk Rees 1998; Gebhardt et al.326 2000: Merritt Ferrarese 2001: MeLure Dunlop 2002: Tremaine e al., 2000; Merritt Ferrarese 2001; McLure Dunlop 2002; Tremaine et al.327 2002: Bettoni et al., 2002; Bettoni et al.328 2003: Marconi Hunt 2003. Merloni et al.," 2003; Marconi Hunt 2003, Merloni et al."329 2010: Jahnke Maccio 2011)., 2010; Jahnke Maccio 2011).330 Quasars. as the most extreme of AGN. offer potentially the," Quasars, as the most extreme of AGN, offer potentially the"331A Κον objective to understanding star formation is to explain how molecular clouds anc stars form in clillerent types of galaxies.,A key objective to understanding star formation is to explain how molecular clouds and stars form in different types of galaxies.332 “Phe presence of spiral shocks in grand design galaxies explains the predominance of voung stars in spiral arms (?2?7?777).. and can also account [or the observed: velocity dispersions in molecular clouds (??:: 2)).," The presence of spiral shocks in grand design galaxies explains the predominance of young stars in spiral arms \citep{Roberts1969,Woodward1976,Cepa1990, Knapen1992,Knapen1996}, and can also account for the observed velocity dispersions in molecular clouds \citealt{Zhang2001,Bonnell2006}; \citealt*{KKO2006}) )."333 Otherwise. star formation is thought to occur. through trigeering by supernovae (77). spontaneously through eravitational. thermal or magnetic instabilities. or bw turbulent compression (as reviewed in ?)).," Otherwise, star formation is thought to occur through triggering by supernovae \citep{Mueller1976,Gerola1978}, spontaneously through gravitational, thermal or magnetic instabilities, or by turbulent compression (as reviewed in \citealt{Elmegreen1996}) )."334 From optical images. spiral galaxies can be classified as i) grand design. usually consisting of 2 symmetrical spiral armis. ii) multi-armed. with several asymmetric spiral arms or ii) Hlocculent. with multiple shorter arms.," From optical images, spiral galaxies can be classified as i) grand design, usually consisting of 2 symmetrical spiral arms, ii) multi-armed, with several asymmetric spiral arms or iii) flocculent, with multiple shorter arms."335 Using the classification scheme of 7.. grand design. galaxies. are inclusive of multi-armed: spiral galaxies. but we retain this terminology to. distinguish between the two types.," Using the classification scheme of \citet{Elmegreen1987}, grand design galaxies are inclusive of multi-armed spiral galaxies, but we retain this terminology to distinguish between the two types."336 Classical grand. design. structure is thought to originate [rom perturbations due to bars or companion galaxies which induce a density wave in the underlving stellar disk., Classical grand design structure is thought to originate from perturbations due to bars or companion galaxies which induce a density wave in the underlying stellar disk.337 Flocculent (and multi-armed) structure develops from loca eravitational instabilities. which are sheared into short. ransient spiral arms.," Flocculent (and multi-armed) structure develops from local gravitational instabilities, which are sheared into short, transient spiral arms."338 Most Docculent galaxies are also founc o have a weak density wave in the older stellar population visible in the Ix band (?7)..," Most flocculent galaxies are also found to have a weak density wave in the older stellar population visible in the K band \citep{Thornley1997,Grosbol1998}."339 Several hvdrodvnamical simulations have investigate he response of the ESAL to spiral density waves in grax design galaxies. by assuming a rigidly rotating spira »»tential. usually with an isothermal medium (72?7)..," Several hydrodynamical simulations have investigated the response of the ISM to spiral density waves in grand design galaxies, by assuming a rigidly rotating spiral potential, usually with an isothermal medium \citep*{Patsis1997,Chak2003,Kim2002,Dobbs2006}."340 Phe spiral pattern in these simulations is assumed to be lone-asting. of at least several rotation periods.," The spiral pattern in these simulations is assumed to be long-lasting, of at least several rotation periods."341 The formation of dense structures along the spiral arms are associated with molecular clouds (???) and the shearing of these features xoduces spurs perpendicular to the arms (?72)..," The formation of dense structures along the spiral arms are associated with molecular clouds \citep*{Kim2003,DBP2006,Dobbs2007} and the shearing of these features produces spurs perpendicular to the arms \citep*{Kim2002,Dobbs2006,Shetty2006}."342 For the surely hiydrodyvnamic simulations (2?).. the development of molecular clouds and spurs is controlled by the dynamics of he shock.," For the purely hydrodynamic simulations \citep{Wada2004,DBP2006}, the development of molecular clouds and spurs is controlled by the dynamics of the shock."343 Similar features are formed through gravitational instabilities (?7)..," Similar features are formed through gravitational instabilities \citep{Kim2002,Shetty2006}. ."344 The generation of turbulence has also been examined in simulations of galactic disks., The generation of turbulence has also been examined in simulations of galactic disks.345 ? showthat gravitational, \citet{Wada2002} showthat gravitational346A very fundamental characteristic of galactic disks is the flatness. defined by the ratio between exponential scaleleusths iu the vertical aud radial direction P./h.,"A very fundamental characteristic of galactic disks is the flatness, defined by the ratio between exponential scalelengths in the vertical and radial direction $h_z/h$."347 The deteiuiuation of the thickness of stellar disks is a difficult enterprise and has been determined mostly for ecdec-on ealaxies. although attempts have been made in other cases. too (Ma et al.," The determination of the thickness of stellar disks is a difficult enterprise and has been determined mostly for edge-on galaxies, although attempts have been made in other cases, too (Ma et al."348 1998)., 1998).349 Typical values are found to be between 0.15 and 1 (van der Ixuit Searle 1981. 1982: de ας 1998) with a svstematic treu for galaxies to become thinner frou SU to Se if a more complex multicompoucut structure (thick/thin disk) is no taken iuto account.," Typical values are found to be between 0.15 and 1 (van der Kruit Searle 1981, 1982; de Grijs 1998) with a systematic trend for galaxies to become thinner from S0 to Sc if a more complex multicomponent structure (thick/thin disk) is not taken into account."350" Stellar velocity dispersion nieasureiieuts show that the dispersion teuds to grow with total |niüuositv. and vary racially as the square roo of surface density, so as to support a constant scalehcight (Bottcma 1993)."," Stellar velocity dispersion measurements show that the dispersion tends to grow with total luminosity, and vary radially as the square root of surface density, so as to support a constant scaleheight (Bottema 1993)."351 Recently τοσο] et al. (, Recently Kregel et al. (3522002) have shown that the flatteimg of disks lnereases with the auplituc ΟΕ their asin rotation. aud their total IIT mass.,"2002) have shown that the flattening of disks increases with the amplitude of their maximum rotation, and their total HI mass."353 This flatuess is an nupxrtant clue to the formation aud evolution history of galaxies., This flatness is an important clue to the formation and evolution history of galaxies.354 Disk stars are thought o be formed out of a very thin gaseous disk., Disk stars are thought to be formed out of a very thin gaseous disk.355 The observed structure then thickens due to scattering by local Huctuatiouns of the gravitational field as caused. ¢.¢.. by eiut iolecular clouds or spiral structure in the disk.," The observed structure then thickens due to scattering by local fluctuations of the gravitational field as caused, e.g., by giant molecular clouds or spiral structure in the disk."356 The velocity dispersion of the stars increases in roth he radial and vertica direction by this diffusion through yhase space (Wiclen 1977. Binney Lacey 1988).," The velocity dispersion of the stars increases in both the radial and vertical direction by this diffusion through phase space (Wielen 1977, Binney Lacey 1988)."357 The disk iav thicken iore οποιον through interactions with small companions or minor mergers. as suggested wo nmunperical simulations (Quinn et al.," The disk may thicken more efficiently through interactions with small companions or minor mergers, as suggested by numerical simulations (Quinn et al."358 1993. Walker et al. 1996. Velazquez White 1999).," 1993, Walker et al, 1996, Velazquez White 1999)."359 The thickening could annot to a factor of 1.52 iux cau be a coustraint ou he frequency of 1iergers if disks are observed today to be oo thin (c.g. Toth Ostriker 1992)., The thickening could amount to a factor of 1.5–2 and can be a constraint on the frequency of mergers if disks are observed today to be too thin (e.g. Toth Ostriker 1992).360 The existence of a hick stellar disk in our own Galaxy has heen attributed o an old merger eveut (Robin ct al 1996. Dalcautou Derustein 2002).," The existence of a thick stellar disk in our own Galaxy has been attributed to an old merger event (Robin et al 1996, Dalcanton Bernstein 2002)."361 ILowever. other phenomena lave to ο taken duto account since the thin disk could also be maintained through eas infall with sibsequent star formation.," However, other phenomena have to be taken into account since the thin disk could also be maintained through gas infall with subsequent star formation."362 Many observational facts strougly suggest a lüeh eas infall rate (0.8. Toonue. 1990. Sancisi et al.," Many observational facts strongly suggest a high gas infall rate (e.g. Toomre, 1990, Sancisi et al."363 1990. Jiang Binney 1999).," 1990, Jiang Binney 1999)."364 Dynamics of galaxy disks. bar and spiral reformation constrain this rate such that ealaxies av double their mass in less than 10 Ciis (Bournaud Combes 2002. Block et al 2002).," Dynamics of galaxy disks, bar and spiral reformation constrain this rate such that galaxies may double their mass in less than 10 Gyrs (Bournaud Combes 2002, Block et al 2002)."365 The influence of tidal iuteraction on the flatuess of ealaxy disks has Όσοι addressed by Reshetuilkov ct al. (, The influence of tidal interaction on the flatness of galaxy disks has been addressed by Reshetnikov et al. (3661993) aud Reshetuikov Combes (1997) who found in interacting galaxies the ratio h./h to be a factor of wo higher. due to a lish thicker iu absolute values. mit also shorter in radial dimensions.,"1993) and Reshetnikov Combes (1997) who found in interacting galaxies the ratio $h_z/h$ to be a factor of two higher, due to a disk thicker in absolute values, but also shorter in radial dimensions."367 Sclavarzkopt Dettinar (2000. 2001) confined this trend on a arvecy sample. 11 essentially because of a larger absolute hickuess of interacting disks.," Schwarzkopf Dettmar (2000, 2001) confirmed this trend on a larger sample, but essentially because of a larger absolute thickness of interacting disks."368 They also noted that tically interacting galaxies are iore frequently warped aux that he thickening was more noticeable iu the outer parts., They also noted that tidally interacting galaxies are more frequently warped and that the thickening was more noticeable in the outer parts.369 All these studies suseest that the relative fatuess of a galaxw disk can vary by both effects during its evolution since the majority of galaxies have experienced interactions in the past., All these studies suggest that the relative flatness of a galaxy disk can vary by both effects during its evolution since the majority of galaxies have experienced interactions in the past.370 It appears that sealaxies were dynamically “hotter” iu the past (Abraham οἳ al., It appears that galaxies were dynamically “hotter” in the past (Abraham et al.371 1999). which ds seen in a smaller fraction of barred ealaxies. aud this could also have some consequences: for the flattening.," 1999), which is seen in a smaller fraction of barred galaxies, and this could also have some consequences for the flattening."372 As the frequency of interactions/merecrs stronely increases with redshift (c.g. Le Fevyre et al 2000). it is iutercsting to trace the evolution of the disk flatuess with time by studving photometrically distant calaxics with high spatial resolution.," As the frequency of interactions/mergers strongly increases with redshift (e.g. Le Fèvvre et al 2000), it is interesting to trace the evolution of the disk flatness with time by studying photometrically distant galaxies with high spatial resolution."373 This is now possible in the IIubble Deep Fields IIDE-N aud. IIDE-S aud we preseut below the results of such a study., This is now possible in the Hubble Deep Fields HDF-N and HDF-S and we present below the results of such a study.374 Section 2 describes our sample aud Sect., Section 2 describes our sample and Sect.375 3 eives the derived general characteristics of disks iu ternis of racial and vertical profiles., 3 gives the derived general characteristics of disks in terms of radial and vertical profiles.376 The last section discusses the main results on the evolution of the flatucss for stellar disks., The last section discusses the main results on the evolution of the flatness for stellar disks.377 Throughout the paper. we adopt a flat cosmology with Qo= Land fy=το lau | 1. (," Throughout the paper, we adopt a flat cosmology with $\Omega_0=1$ and $H_0 = 70$ km $^{-1}$ $^{-1}$ . ("378"For a model with Q,,=1/3. Ὃν=2/33 and O,,|O4=1. lincar sizes at D—(4(7lL will be 25 laveerand absolute maguitudes","For a model with $\Omega_m=1/3$, $\Omega_{\Lambda}=2/3$ and $\Omega_m+\Omega_{\Lambda}=1$, linear sizes at $z=0.7-1$ will be $\approx$ largerand absolute magnitudes"379"Iu coutravariant form. 5h?""ab is The functions τος) are given in Appendix Α of Clampedalkis Babak (2006).","In contravariant form, $h^{\rm ab}$ is The functions $\mathcal{F}_{1,2}(r)$ are given in Appendix A of Glampedakis Babak (2006)."380 In its full form. the quasi-Ίνα metric is valid ouly for slowly rotating black holes with values of the spingX0.LAL.," In its full form, the quasi-Kerr metric is valid only for slowly rotating black holes with values of the spin $a\lesssim0.4M$."381 Note. however. that the nuperturbed spacetime (.c.. €= 0) is formally correct up to the maxima value of the spin.," Note, however, that the unperturbed spacetime (i.e., $\epsilon=0$ ) is formally correct up to the maximum value of the spin."382 Since the quasi-Iserr metric Is stationary aud axisviunietrie. particle trajectories in this metric are characterized by three integrals of 1iotion.," Since the quasi-Kerr metric is stationary and axisymmetric, particle trajectories in this metric are characterized by three integrals of motion."383" For a particle with Lauomentuu these are its rest mass qp (which we will set equal to unitv from here ou). cucrey £=p,. and angular momentum about the z-axis L,νι."," For a particle with 4-momentum these are its rest mass $\mu$ (which we will set equal to unity from here on), energy $E=-p_{\rm t}$, and angular momentum about the $z$ -axis $L_{\rm z}=p_{\rm \phi}$."384 We use the conservation of energev aud axial aneular 1uoenutun to express the momentum components pt and po of a particle in the form We then bring the conservation equation for the particle's rest mass. iuto the form with Via plaving the role of an effective potential for the particle motion in the coordinates + aud 0.," We use the conservation of energy and axial angular momentum to express the momentum components $p^{\rm t}$ and $p^{\rm \phi}$ of a particle in the form We then bring the conservation equation for the particle's rest mass, into the form with $V_{\rm eff}$ playing the role of an effective potential for the particle motion in the coordinates $r$ and $\theta$."385 The radial motion in the equatorial plane cau be analyzed in terms of the equation while the @-notiou (for coustant radi r) is governed by the equatiou Iu Paper 1. we solved the equatious aud which characterize circular equatorial orbits. aud obtained the eunergv and axial angular monieutunm These expression sare expansions to inear order in the parameter e. where we have neglected erus of the order €a.," The radial motion in the equatorial plane can be analyzed in terms of the equation while the $\theta$ -motion (for constant radii $r$ ) is governed by the equation In Paper I, we solved the equations and which characterize circular equatorial orbits, and obtained the energy and axial angular momentum These expressions are expansions to linear order in the parameter $\epsilon$, where we have neglected terms of the order $\epsilon a$."386 Án expausion o this type is nuplicitly understood for all expressions tlicmehout the paper in accordance with the form of the meric specified by expression (5))., An expansion of this type is implicitly understood for all expressions throughout the paper in accordance with the form of the metric specified by expression \ref{qKerr}) ).387 Note. however. that we ¢o not expand iu the spin parauieter « so that our results are correct for arbitrary values of the spin in the special Case €=0.," Note, however, that we do not expand in the spin parameter $a$ so that our results are correct for arbitrary values of the spin in the special case $\epsilon=0$."388 For a particle moving on a circular orbit in the equatorial plane. tje time and azimuthal compoucuts of the [Lnomenutu ake the form (Cdampedakis Dabak 2006) where," For a particle moving on a circular orbit in the equatorial plane, the time and azimuthal components of the 4-momentum take the form (Glampedakis Babak 2006) where"389 and ~12 percent for CoRoT-6 (Lanzaetal.2011b)., and $\sim 12$ percent for CoRoT-6 \citep{Lanzaetal11b}.390. are interesting also in view of the different methods applied to extract the signal associated with SPMI according to the ratio Prot/Porb-, are interesting also in view of the different methods applied to extract the signal associated with SPMI according to the ratio $P_{\rm rot}/P_{\rm orb}$.391 The light curve of CoRoT-2 has been extensively modelled by several researchers., The light curve of CoRoT-2 has been extensively modelled by several researchers.392 Lanzaetal.(2009a) applied a maximum entropy spot model to the out-of-transit light curve to derive the distribution of the covering factor of the active regions vs. longitude along successive rotations., \citet{Lanzaetal09a} applied a maximum entropy spot model to the out-of-transit light curve to derive the distribution of the covering factor of the active regions vs. longitude along successive rotations.393" A comparison of this approach with other spot modelling methods is provided by, e.g., Mosseretal.(2009), Frohlichetal. (2009), and Huberetal.(2010), while a detailed test with solar observations is presented by Lanzaetal.(2007)."," A comparison of this approach with other spot modelling methods is provided by, e.g., \citet{Mosseretal09}, \citet{Frohlichetal09}, and \citet{Huberetal10}, while a detailed test with solar observations is presented by \citet{Lanzaetal07}."394". 'The modelling technique exploits the modulation of the visibility of the active regions by the rotation of the star, so that a good phase coverage of each rotation is needed to derive a stable and reliable map."," The modelling technique exploits the modulation of the visibility of the active regions by the rotation of the star, so that a good phase coverage of each rotation is needed to derive a stable and reliable map."395" The advantage of CoRoT is the almost perfect time sampling (the duty cycle is virtually 100 percent for spot modelling), but the duration of the stellar rotation sets a minimum timescale for an accurate mapping that is ~3 days in our case, i.e., about 65 percent of a rotation."," The advantage of CoRoT is the almost perfect time sampling (the duty cycle is virtually 100 percent for spot modelling), but the duration of the stellar rotation sets a minimum timescale for an accurate mapping that is $\sim 3$ days in our case, i.e., about 65 percent of a rotation."396" Morover, since the active regions evolve rapidly, it is not possible to obtain an adequate best fit for time intervals longer than 3—4 days."," Morover, since the active regions evolve rapidly, it is not possible to obtain an adequate best fit for time intervals longer than $3-4$ days."397" In conclusion, the time resolution of the mapping of Lanzaetal.(2009a) is longer than the orbital period of the planet making impossible a direct search for SPMI features in those maps."," In conclusion, the time resolution of the mapping of \citet{Lanzaetal09a} is longer than the orbital period of the planet making impossible a direct search for SPMI features in those maps."398 The distribution of the active regions versus longitude] and time on the surface of CoRoT-2 is plotted in Fig., The distribution of the active regions versus longitude and time on the surface of CoRoT-2 is plotted in Fig.399" 1 where we see two persistent active longitudes in which individual active regions appear, grow, and decay with lifetimes up to ~50—60 days."," \ref{corot2_ff} where we see two persistent active longitudes in which individual active regions appear, grow, and decay with lifetimes up to $\sim 50-60$ days."400 The model by Lanzaetal.(2009a) assumes that each active region consists of dark spots and bright solar-like faculae with a facular-to-spotted area ratio indicated by Q., The model by \citet{Lanzaetal09a} assumes that each active region consists of dark spots and bright solar-like faculae with a facular-to-spotted area ratio indicated by $Q$.401 The models in Fig., The models in Fig.402" 1 have been computed for Q= 0.0, i.e., without faculae."," \ref{corot2_ff} have been computed for $Q=0.0$ , i.e., without faculae."403 The variation of the total spotted area vs. time is plotted in Fig., The variation of the total spotted area vs. time is plotted in Fig.404" 2 and shows oscillations with a period of 29.6+4.0 days, both in the model assuming only dark spots as well as in that with a facular component having Q=1.5."," \ref{corot2_tot_area} and shows oscillations with a period of $29.6 \pm 4.0$ days, both in the model assuming only dark spots as well as in that with a facular component having $Q=1.5$."405" Note that for the Sun Q=9, while for more active stars, such as CoRoT-2, lower values of Q are expected (Lanzaetal.2007).."," Note that for the Sun $Q=9$, while for more active stars, such as CoRoT-2, lower values of $Q$ are expected \citep{Lanzaetal07}."406 Two possible interpretations have been suggested for the oscillations ofthe total spotted area., Two possible interpretations have been suggested for the oscillations ofthe total spotted area.407 The first considers them analogous to the oscillations of the total sunspot area observed close to some of, The first considers them analogous to the oscillations of the total sunspot area observed close to some of408in the last vears. I want to focus on (wo projects we have carried oul with the multi-object spectrograph. IHectospec. on the MALT.,"in the last years, I want to focus on two projects we have carried out with the multi-object spectrograph, Hectospec, on the MMT."409 These (wo projects grow oul of features revealed in our first slice of the universe: (1) the hint of a trunmpet-shaped infall pattern around the Coma cluster and (2) the Great Wall., These two projects grow out of features revealed in our first slice of the universe: (1) the hint of a trumpet-shaped infall pattern around the Coma cluster and (2) the Great Wall.410 The work I discuss here has not been published previously., The work I discuss here has not been published previously.411 I thus include. Antonaldo Dialerio ancl Michael INurtz as co-authors., I thus include Antonaldo Diaferio and Michael Kurtz as co-authors.412 This inclusion is a small (thank. vou for their support and [ον the jov of working with them on these projects and many others., This inclusion is a small thank you for their support and for the joy of working with them on these projects and many others.413 The Introduction ancl Concluding Remarks are my voice alone., The Introduction and Concluding Remarks are my voice alone.414 Section 2. is co-authored. by Antonaldo Dialerio and Section 3. is co-authored by Michael Ixiutz., Section \ref{caustics} is co-authored by Antonaldo Diaferio and Section \ref{HectoMAP} is co-authored by Michael Kurtz.415 section 2 discusses redshift survevs of the infall regions of clusters of galaxies., Section \ref{caustics} discusses redshift surveys of the infall regions of clusters of galaxies.416 It includes a tutorial movie of a simulation of the evolution of a cluster in real and redshiift space., It includes a tutorial movie of a simulation of the evolution of a cluster in real and redshift space.417 We review the idea of the caustic method for estimating the mass within the infall region and we briefly discuss some of the results of applving this technique to data from the SDSS along with new data[rom Iectospec., We review the idea of the caustic method for estimating the mass within the infall region and we briefly discuss some of the results of applying this technique to data from the SDSS along with new datafrom Hectospec.418 Section 3. announces IHectoMAT. a redshift survey with a median depth :=0.34.," Section \ref{HectoMAP} announces HectoMAP, a redshift survey with a median depth $ z = 0.34$."419 The survey covers a 50 square degree strip of the northern sky ancl will eventually include 60.000 redshifts.," The survey covers a 50 square degree strip of the northern sky and will eventually include 60,000 redshifts."420 The goals of the survey include the study of elusters of galaxies and (heir environment at moderate redshift., The goals of the survey include the study of clusters of galaxies and their environment at moderate redshift.421 We preview (he survey and ciscuss (he suggestion of Great Walls al greater and greater redshift., We preview the survey and discuss the suggestion of Great Walls at greater and greater redshift.422 Clusters of galaxies are a cornerstone of modern cosmology., Clusters of galaxies are a cornerstone of modern cosmology.423 Zwickys first application of the virial theorem to a few redshifts in the Coma cluster showed that clusters must contain dark matter (Zwickv 1933)., Zwicky's first application of the virial theorem to a few redshifts in the Coma cluster showed that clusters must contain dark matter (Zwicky 1933).424 This pioneering paper set the stage for the use of kinematic measures as a route (to understanding the matter distribution in the universe., This pioneering paper set the stage for the use of kinematic measures as a route to understanding the matter distribution in the universe.425 Today studies of clusters of galaxies reaching [from the nearby universe to large recshilt provide constraints on the growth of structure in (he universe and on the cosmological parameters (e.g. Llaiman. Mohr Holder 2001: Voit 2005: C'unha. Huterer Frieman 2009: Pierre et al.," Today wide-ranging studies of clusters of galaxies reaching from the nearby universe to large redshift provide constraints on the growth of structure in the universe and on the cosmological parameters (e.g. Haiman, Mohr Holder 2001; Voit 2005; Cunha, Huterer Frieman 2009; Pierre et al."426 POLL)., 2011).427 Now a host of techniques are available to probe the matter distribution within clusters of ealaxies., Now a host of techniques are available to probe the matter distribution within clusters of galaxies.428 Dillerent techniques are applicable at different radii., Different techniques are applicable at different radii.429 The fiducial radii 34; ancl Igi are (he radii enclosing a matter density 500 and 200 (mes. respectively. the critical density.," The fiducial radii $_{500}$ and $_{200}$ are the radii enclosing a matter density 500 and 200 times, respectively, the critical density."430 Within Rsoo. x-ray observations and strong lensing provide important constraints.," Within $_{500}$, x-ray observations and strong lensing provide important constraints."431 Galaxy dvnamics and scaling relations extend the reach of our knowledge to Ig., Galaxy dynamics and scaling relations extend the reach of our knowledge to $_{200}$ .432 Generally Rag , Generally $_{200}$ 433emission from a region coincident with this pulsar (Adboetal.2009).,emission from a region coincident with this pulsar \citep{abdo09}.434. The model proposed bv Fujitaetal.(2009) expects emission in (he Fermi band coincident with the 5-rav emission. but such emission is not vet. detected by Fermi observations.," The model proposed by \citet{fujita09} expects emission in the Fermi band coincident with the $\gamma$ -ray emission, but such emission is not yet detected by Fermi observations."435 ILowever. the observed. configuration of a cavity surrounded. by a molecular shell. with associated: VILE -ravs emission. and a bright Fermi source in the vicinity. are common to both. Wel2 and the expanding shell discussed in our work.," However, the observed configuration of a cavity surrounded by a molecular shell, with associated VHE $\gamma$ -rays emission, and a bright Fermi source in the vicinity, are common to both, Wd2 and the expanding shell discussed in our work."436 L.B. acknowledges partial support from Centro de Astroffssica FONDAP 15010003 and from Center of Excellence in Astrophvsies ancl Associated Technologies PFB 06., L.B. acknowledges partial support from Centro de Astrofíssica FONDAP 15010003 and from Center of Excellence in Astrophysics and Associated Technologies PFB 06.437 The authors are grateful to an anouvimous referee whose comments and suggestions have largely improved (he clarity of this paper., The authors are grateful to an anonymous referee whose comments and suggestions have largely improved the clarity of this paper.438During the transit of an exoplanet. the light from its host-star filters through the planet's atmosphere. and atmospheric signatures from molecules and atoms get imprinted on the transmission spectrum.,"During the transit of an exoplanet, the light from its host-star filters through the planet's atmosphere, and atmospheric signatures from molecules and atoms get imprinted on the transmission spectrum."439 The strength of the atmospheric features is dependent on the atmospheric scale height H. which in turn depends on the temperature T. the mean molecular weight µ. and the planet’s surface gravity g as ," The strength of the atmospheric features is dependent on the atmospheric scale height H, which in turn depends on the temperature T, the mean molecular weight $\mu$ and the planet's surface gravity g as $\frac{kT}{\mu g}$."440"Por hot-Jupiters this scale height is a few hundred H="".kilometers.", For hot-Jupiters this scale height is a few hundred kilometers.441 For instance. the expected atmospheric scale height of HD189733b for an H» dominated atmosphere is. ~200 km. while for HD209458b this is about 700 km.," For instance, the expected atmospheric scale height of HD189733b for an $_2$ dominated atmosphere is $\sim$ 200 km, while for HD209458b this is about 700 km."442" For transit observations. the observable parameter we are interested in is AR,/R, ~H/R,. which is «0.0004. for HD189733b. and ~0.0009 for HD209458b."," For transit observations, the observable parameter we are interested in is $\Delta$ $_p$ $_*\sim$ $_*$, which is $\sim$ 0.0004 for HD189733b, and $\sim$ 0.0009 for HD209458b."443 Nevertheless. signatures from the atmospheres of hot-Jupiters have been detected in transmission spectra. both from atoms. including sodium (eg.???).. potassium (22).. hydrogen (?).. carbon (2) and oxygen (?).. as well as from molecules such as water (?).. although this is disputed by ?.. methane (?).. which has been challenged by ? and ?. and carbon monoxide (?)..," Nevertheless, signatures from the atmospheres of hot-Jupiters have been detected in transmission spectra, both from atoms, including sodium \citep[eg.][]{charbonneauetal02,snellenetal08,redfieldetal08}, potassium \citep{singetal11a,colonetal11}, hydrogen \citep{vidalmadjaretal03}, carbon \citep{vidalmadjaretal04} and oxygen \citep{vidalmadjaretal04}, , as well as from molecules such as water \citep{tinettietal07}, although this is disputed by \cite{desertetal09}, methane \citep{swainetal08}, which has been challenged by \cite{singetal09} and \cite{gibsonetal11}, and carbon monoxide \citep{snellenetal10}."444 In addition. à. gradual increase of the planet-to-star radius ratio of HD189733b has been detected toward shorter wavelengths. which has been attributed to the scattering by haze particles (??)..," In addition, a gradual increase of the planet-to-star radius ratio of HD189733b has been detected toward shorter wavelengths, which has been attributed to the scattering by haze particles \citep{pontetal08,singetal11b}."445" For cooler and smaller planets. the scale height decreases. and the AR,/R. becomes much smaller."," For cooler and smaller planets, the scale height decreases, and the $\Delta$ $_p$ $_*$ becomes much smaller."446 For the Earth the scale height is only 8.5 km. which corresponds to à change in the radius ratio of - 107. which is very small.," For the Earth the scale height is only 8.5 km, which corresponds to a change in the radius ratio of $\sim$ $^{-5}$, which is very small."447 However. for the recently discovered super-Earth GJ1214b. (2)... the scale height can be similar to that of HD189733b. due to the low (-θ. 25ο) density of the planet. if the atmosphere is dominated by H>.," However, for the recently discovered super-Earth GJ1214b \citep{charbonneauetal09}, the scale height can be similar to that of HD189733b, due to the low $\sim$ $\rho_{earth}$ ) density of the planet, if the atmosphere is dominated by $_2$."448" Since its host-star. GJI214. is. ~4 times smaller than the host-star of HD189733b. the change in the planet-to-star radius ratio is ~4x larger at AR,/R,=0.0016."," Since its host-star, GJ1214, is $\sim$ 4 times smaller than the host-star of HD189733b, the change in the planet-to-star radius ratio is $\sim$ $\times$ larger at $\Delta$ $_p$ $_*$ =0.0016."449 This makes GJI214b an ideal candidate to search for the signatures of its atmosphere. despite its small mass and radius.," This makes GJ1214b an ideal candidate to search for the signatures of its atmosphere, despite its small mass and radius."450 ? presented three formation scenarios for GJ1214b that explain its low density., \cite{rogersetal10} presented three formation scenarios for GJ1214b that explain its low density.451 These scenarios also. provide predictions on the composition of the planets atmosphere., These scenarios also provide predictions on the composition of the planets atmosphere.452 If GJ1214b formed as a predominantly water-rich planet. the atmospheric scale height would be small. since the mean molecular weight of water is high.," If GJ1214b formed as a predominantly water-rich planet, the atmospheric scale height would be small, since the mean molecular weight of water is high."453 However. if GJ1214b’s low density is due to out-gassing from a rocky planet. or due to it being formed as a mini-Neptune. the atmosphere ts expected to consist predominantly of hydrogen and helium. with a low mean molecular weight.," However, if GJ1214b's low density is due to out-gassing from a rocky planet, or due to it being formed as a mini-Neptune, the atmosphere is expected to consist predominantly of hydrogen and helium, with a low mean molecular weight."454 Atmospheric models by ? showed that it is possible to get detectable signatures from an atmosphere with a large scale height. especially from molecules in near-infrared. but also from the scattering of light in the optical part of the spectrum.," Atmospheric models by \cite{millerricciandfortney10} showed that it is possible to get detectable signatures from an atmosphere with a large scale height, especially from molecules in near-infrared, but also from the scattering of light in the optical part of the spectrum."455 Recently. the first transit transmission results for. theatmosphere of GJ1214b have been presented in the literature.," Recently, the first transit transmission results for theatmosphere of GJ1214b have been presented in the literature."456 ? found that their spectroscopy in the z-band showed no sign for the presence of a thick. hydrogen-rich atmosphere. which argues for a water-rich atmosphere. something which is also consistent with the mid-infrared observations of ?..," \cite{beanetal10} found that their spectroscopy in the z-band showed no sign for the presence of a thick, hydrogen-rich atmosphere, which argues for a water-rich atmosphere, something which is also consistent with the mid-infrared observations of \cite{desertetal11}."457" These observations are in contrast with the results from ?.. who show that the transit in the K,-band is deeper than the transit in the J- and therefore consistent with an atmosphere with a large scale-height and low mean-molecular weight."," These observations are in contrast with the results from \cite{crolletal11}, who show that the transit in the $_s$ -band is deeper than the transit in the J-band, and therefore consistent with an atmosphere with a large scale-height and low mean-molecular weight."458" In this paper we present the results for our multiband transit photometry of GJI214b. covering a wavelength range from the g-band in the optical to the K,-band in the near-infrared."," In this paper we present the results for our multiband transit photometry of GJ1214b, covering a wavelength range from the g-band in the optical to the $_c$ -band in the near-infrared."459 In section 2? we present our observations. followed by the data reduction in section 3. and transit fitting in section ??..," In section \ref{sec:obs} we present our observations, followed by the data reduction in section \ref{sec:dr} and transit fitting in section \ref{sec:tf}."460 Subsequently we discuss the influence of stellar variability in section ?? and present and discuss thetransmission spectrum of GJI214b in section ??.., Subsequently we discuss the influence of stellar variability in section \ref{sec:starvar} and present and discuss thetransmission spectrum of GJ1214b in section \ref{sec:discuss}. .461 Finally we give the conclusions in section ??.., Finally we give the conclusions in section \ref{sec:concl}. .462with that seen at GGHz than there is at 100 tm (r—0.610).,with that seen at GHz than there is at $\mu$ m $r=0.61$ ).463 There is no source coincident with the AMI emission at either |.4 or GGHz., There is no source coincident with the AMI emission at either 1.4 or GHz.464 The AMI data itself towards this source is poor due to interference and the combined channel map is heavily weighted towards Channel 6 GGHz) making a determination of the spectrum using AMT data alone unreliable., The AMI data itself towards this source is poor due to interference and the combined channel map is heavily weighted towards Channel 6 GHz) making a determination of the spectrum using AMI data alone unreliable.465 Of the fourteen clouds observed here two are clear candidates for possessing anomalous dust emission at GGHz: L675 and LIlt., Of the fourteen clouds observed here two are clear candidates for possessing anomalous dust emission at GHz: L675 and L1111.466 A further three are possible candidates: L944. L1103 and L.1246.," A further three are possible candidates: L944, L1103 and L1246."467 Nine of the fourteen showed no emission inconsistent with that seen at lower radio frequencies., Nine of the fourteen showed no emission inconsistent with that seen at lower radio frequencies.468 We divide the five clouds where there is an excess of emission into two groups on the basis of three criteria: (1) Extent. of the emission seen at GGHz i.e. non-point like sources: (2) Coincident with the sub-mm position of the cloud to within a 2’ radius: (3) Likelihood of alternative explanations for the GGHz emission., We divide the five clouds where there is an excess of emission into two groups on the basis of three criteria: (1) Extent of the emission seen at GHz i.e. non-point like sources; (2) Coincident with the sub-mm position of the cloud to within a $'$ radius; (3) Likelihood of alternative explanations for the GHz emission.469 We summarize our results in Table 3.., We summarize our results in Table \ref{tab:emissivity}.470 Column [5] of Table 3 summarizes which dark clouds have a possible spinning dus association. defined as being a microwave counterpart within a 2uaremin radius which shows an excess at GGHz relative to ower frequency data.," Column [5] of Table \ref{tab:emissivity} summarizes which dark clouds have a possible spinning dust association, defined as being a microwave counterpart within a arcmin radius which shows an excess at GHz relative to lower frequency data."471 Columns [6-8] then divide the certainty of hese detections based on the three criteria stated in the previous »aragraph., Columns [6–8] then divide the certainty of these detections based on the three criteria stated in the previous paragraph.472 On the basis of these three criteria we see that all are satistiec by L675 and LILLE which display extended emission coinciden with the pointing centre., On the basis of these three criteria we see that all are satisfied by L675 and L1111 which display extended emission coincident with the pointing centre.473 The extended nature of this emission makes the possibility of the emission being em-wave radiation Tom either a protostar or proto-planetary dise unlikely., The extended nature of this emission makes the possibility of the emission being cm-wave radiation from either a protostar or proto-planetary disc unlikely.474 L944 shows compact emission which is coincident with the pointing centre., L944 shows compact emission which is coincident with the pointing centre.475 The compact nature of this emission means that em-wave radiation from a protostar cannot be ruled out in this case., The compact nature of this emission means that cm-wave radiation from a protostar cannot be ruled out in this case.476 LI246 shows emission just within a radius of aaremin from the SCUBA position of this cloud which has no lower frequency counterpart., L1246 shows emission just within a radius of arcmin from the SCUBA position of this cloud which has no lower frequency counterpart.477 However. the compact nature of this emission suggests that it may again be emission from a protostar.," However, the compact nature of this emission suggests that it may again be cm-wave emission from a protostar."478 L!I103 shows extended emission which is coincident with the pointing centre., L1103 shows extended emission which is coincident with the pointing centre.479 However. although the microwave spectrum appears to be consistent with emission from spinning dust this source has a high flux density at um (Visser et al.," However, although the microwave spectrum appears to be consistent with emission from spinning dust this source has a high flux density at $\mu$ m (Visser et al."480 2001) relative to IRAS measurements at. um. (CYH9I3., 2001) relative to IRAS measurements at $\mu$ m (CYH91).481 This raises questions over the suitability of a standard. grevbody fit to the thermal dust emission from this cloud and. in the absence of further observations between 100 and GGHz. it is not possible to rule out a flattened tail to the thermal dust spectrum which may account for the excess seen at GGHz.," This raises questions over the suitability of a standard greybody fit to the thermal dust emission from this cloud and, in the absence of further observations between 100 and GHz, it is not possible to rule out a flattened tail to the thermal dust spectrum which may account for the excess seen at GHz."482 In their theoretical. models for the emission from rotating grains DL98 considered a number of gas-grain. plasma. and radiative contributions to the excitation and damping of spinning dust grains.," In their theoretical models for the emission from rotating grains DL98 considered a number of gas-grain, plasma, and radiative contributions to the excitation and damping of spinning dust grains."483 For their several models of grain environment it was found that collisions with ions were the dominant excitation mechanism in all but two scenarios: reflection nebulae and photodissociation regions. where photoelectric effects dominated due to the intense radiation field.," For their several models of grain environment it was found that collisions with ions were the dominant excitation mechanism in all but two scenarios: reflection nebulae and photodissociation regions, where photoelectric effects dominated due to the intense radiation field."484 For the environments relevant to dark nebulae (molecular. cloud and. cold. neutral. medium environments) this suggests that objects which are embedded in or exposed to strongly ionized environments are the most likely candidates for observing spinning dust emission., For the environments relevant to dark nebulae (molecular cloud and cold neutral medium environments) this suggests that objects which are embedded in or exposed to strongly ionized environments are the most likely candidates for observing spinning dust emission.485 The presence of an anomalous component in the spectra of the objects presented here appears to be correlated with the average free-free emission within a | degree area centred on each pointing centre. see Fig 22..," The presence of an anomalous component in the spectra of the objects presented here appears to be correlated with the average free-free emission within a 1 degree area centred on each pointing centre, see Fig \ref{fig:11cmcor}."486 We assess this correlation following the method of Franzen et al. (, We assess this correlation following the method of Franzen et al. (487"2009). where we express the covariance matrix of our data points. C. ας Sj, and Sao are the variances of the 2.7 and GGHz data points respectively and S42(—5541) is the covariance of the 2.7 and GGHz data points.","2009), where we express the covariance matrix of our data points, $C$, as $S_{11}$ and $S_{22}$ are the variances of the 2.7 and GHz data points respectively and $S_{12} (=S_{21})$ is the covariance of the 2.7 and GHz data points."488 It follows that the correlation co-efficient. denoted Α to distinguish it from the standard Pearson co-efficient. is given by Following Franzen et al. (," It follows that the correlation co-efficient, denoted $R$ to distinguish it from the standard Pearson co-efficient, is given by Following Franzen et al. ("4892009) we used a Gaussian likelihood and the nested sampling algorithm implemented in the MultiNest code (Feroz Hobson 2008: Feroz. Hobson Bridges 2008) to obtain A.,"2009) we used a Gaussian likelihood and the nested sampling algorithm implemented in the MultiNest code (Feroz Hobson 2008; Feroz, Hobson Bridges 2008) to obtain $R$."490 For the averaged GGHz flux density we find a correlation coefficient of R=0.81—0.15., For the averaged GHz flux density we find a correlation coefficient of $R=0.81\pm0.15$.491 For the GGHz flux density at the position of the cloud with the GGHz flux density at the same position we find a weaker correlation. A=0.66.0.20.," For the GHz flux density at the position of the cloud with the GHz flux density at the same position we find a weaker correlation, $R=0.66\pm0.20$."492 We repeated these evaluations setting the noise covariance matrix to zero and found values of A=0.70.0.18 and &=0.65.0.20 for the averaged flux density at GGHz and the GGHz flux density at the position of the cloud. respectively.," We repeated these evaluations setting the noise covariance matrix to zero and found values of $R=0.70\pm0.18$ and $R=0.65\pm0.20$ for the averaged flux density at GHz and the GHz flux density at the position of the cloud, respectively."493 We can see that the noise in the first instance leads to an decrease in correlation unless it is accounted for., We can see that the noise in the first instance leads to an decrease in correlation unless it is accounted for.494 Of the fourteen clouds observed. those with the highest background levels at GGHz are L675. LHELI. L860 and L1103: all of which have a background level above mmK. Indeed the correlation is dominated by the high surface brightness regions. suggesting a radio surface brightness threshold between those regions which exhibit spinning dust emission and those which do not.," Of the fourteen clouds observed, those with the highest background levels at GHz are L675, L1111, L860 and L1103; all of which have a background level above mK. Indeed the correlation is dominated by the high surface brightness regions, suggesting a radio surface brightness threshold between those regions which exhibit spinning dust emission and those which do not."495 There appears to be no correlation between GGHz specitic intensity and 100 4m emission., There appears to be no correlation between GHz specific intensity and $\mu$ m emission.496 Following the same correlation, Following the same correlation497emission is powered by star formation.,emission is powered by star formation.498 In this case. with standard assumptions for the conversion of emission to star formation rate. the luminosities correspond. to star formation rates of 0.07 - 1.5 vr.+. similar to that inferred by Wolfe.Prochaska.&CGawiser(2003). from the CLP A1335.7 absorption in DLAs.," In this case, with standard assumptions for the conversion of emission to star formation rate, the luminosities correspond to star formation rates of 0.07 - 1.5 $^{-1}$, similar to that inferred by \citet{2003ApJ...593..215W} from the CII* $\lambda$ 1335.7 absorption in DLAs."499 No continuum is detected. so there is no information about stellar or total masses of the object.," No continuum is detected, so there is no information about stellar or total masses of the object."500 Our modelling is thus currently the only handle we have on the masses (Gand virial velocities) of what should be a statistically representative sample of DLA host galaxies., Our modelling is thus currently the only handle we have on the masses (and virial velocities) of what should be a statistically representative sample of DLA host galaxies.501 In Figure 4.. we show the contribution of DM halos of different masses ancl virial velocities to the incidence rate of DLAs in our model. for the range of parameters used to model the suppression of the cross-section for damped absorption in low-mass DAL halos.," In Figure \ref{fig:plot2}, we show the contribution of DM halos of different masses and virial velocities to the incidence rate of DLAs in our model, for the range of parameters used to model the suppression of the cross-section for damped absorption in low-mass DM halos."502 We also show the results from two recently published numerical simulations of DLAs (Razoumoyetal.2007:Pontzenct2008)..," We also show the results from two recently published numerical simulations of DLAs \citep{2007arXiv0710.4137R,2008arXiv0804.4474P}."503" The cilferential line density for DLAs is calculated similarly to ANC excopt that we consider intervals of LY and clog),M. Note that larger. values of à result in a sharper turnover at low masses. at the expense of increasing the abundance of DLAs with high masses (the area under the plot. is normalise)."," The differential line density for DLAs is calculated similarly to $N$, except that we consider intervals of $\dd X$ and $\dd \log_{10}M$, Note that larger values of $\alpha$ result in a sharper turnover at low masses, at the expense of increasing the abundance of DLAs with high masses (the area under the plot is normalised)."504 The majority of the DLAs in our model have virial velocities in the range 50 to 900 kms corresponding to total masses of 1077 to 1072AZ.," The majority of the DLAs in our model have virial velocities in the range 50 to 200 $\kmsec$, corresponding to total masses of $10^{10}$ to $10^{12} \Msol $."505 As discussed. in. the previous sections. the turn-over at small virial velocities is most constrained by the velocity width distribution of the associated Iow-ionization metal absorption and is most likely attributable to feedback effects due to star formation.," As discussed in the previous sections, the turn-over at small virial velocities is most constrained by the velocity width distribution of the associated low-ionization metal absorption and is most likely attributable to feedback effects due to star formation."506 The decline at large virial velocities ancl masses is due to the decline of the space density of DM halos., The decline at large virial velocities and masses is due to the decline of the space density of DM halos.507 The incidence rate in the numerical simulations of ltazoumovetal.(2007) shows a similar peak. albeit shifted to somewhat smaller masses/virial velocities than our model requires to fit the kinematical data of the DLAs.," The incidence rate in the numerical simulations of \citet{2007arXiv0710.4137R} shows a similar peak, albeit shifted to somewhat smaller masses/virial velocities than our model requires to fit the kinematical data of the DLAs."508 This is perhaps not surprising ltazoumovetal.(2007). find that the velocity widths in their simulations fall somewhat short. of. those observed., This is perhaps not surprising — \citet{2007arXiv0710.4137R} find that the velocity widths in their simulations fall somewhat short of those observed.509 Their simulation also takes into account DLAs that are not contained within any halo ic. intergalactic DLAs., Their simulation also takes into account DLAs that are not contained within any halo i.e. intergalactic DLAs.510 The numerical simulations of Pontzenctal.(2008) show a sharper peak centered on virial velocities of 30-80 kms5., The numerical simulations of \citet{2008arXiv0804.4474P} show a sharper peak centered on virial velocities of 30-80 $\kmsec$.511 Such a sharp peak at rather low virial velocities appears. however. at odds with the observed velocity widths of the associated low-ionization metal absorption.," Such a sharp peak at rather low virial velocities appears, however, at odds with the observed velocity widths of the associated low-ionization metal absorption."512 In the simulations of Pontzenetal... the decline of the contribution to the incidence rate with increasing mass is much Laster than the decline of the space density of massive halos.," In the simulations of \citeauthor{2008arXiv0804.4474P}, the decline of the contribution to the incidence rate with increasing mass is much faster than the decline of the space density of massive halos."513 This [ast decline is due to a Lattening of the absorption cross section with increasing mass in massive halos al... Figure 4)," This fast decline is due to a flattening of the absorption cross section with increasing mass in massive halos \citeauthor{2008arXiv0804.4474P}, Figure 4)."514 We have considered an updated version of the Llachnelt ct al., We have considered an updated version of the Haehnelt et al.515 mocel for the kinematies of DLAs. in light of the discovery of a new population of extended low surface brightness emitters with a total inferred incidence rate similar to that of DLAs.," model for the kinematics of DLAs, in light of the discovery of a new population of extended low surface brightness emitters with a total inferred incidence rate similar to that of DLAs."516 The main dillerences with the modelling of Lachnelt.Steinmetz.&Rauch(2000) are the use of the modification to the formalism. an update of cosmological parameters. and the use of an exponential suppression of the cross section for danmped absorption for low virial velocities instead of an sharp cut-olf.," The main differences with the modelling of \citet{2000ApJ...534..594H} are the use of the modification to the formalism, an update of cosmological parameters, and the use of an exponential suppression of the cross section for damped absorption for low virial velocities instead of an sharp cut-off."517 Our main results are the following., Our main results are the following.518formation in protogalaxics (Wasserburg Qian 20000).,formation in protogalaxies (Wasserburg Qian 2000b).519 Thus the ages obtained from r-process chirouonieters are substantially less than the age of the universe., Thus the ages obtained from $r$ -process chronometers are substantially less than the age of the universe.520 We would like to dedicate this paper to Wille. Fowler and Fred Iovle who night at sometime have enjoyed aud engaged in these efforts;, We would like to dedicate this paper to Willy Fowler and Fred Hoyle who might at sometime have enjoyed and engaged in these efforts.521 Support. iuterest. aud provocation bv Roger Blaucdtord are ereatly appreciated.," Support, interest, and provocation by Roger Blandford are greatly appreciated."522 We thank Tim Beers for a thorough. insightful. aud prompt review.," We thank Tim Beers for a thorough, insightful, and prompt review."523 We acknowledge I&is Davidson aud Roberta Προς for information on the proper motion of the U-star., We acknowledge Kris Davidson and Roberta Humphreys for information on the proper motion of the U-star.524 This work was supported in part bv DOE erauts DE-STER10328 aud DE-ECGO2-00ER11119 (Y.Z.Q.) aud MGby NASA eraut.mmm NAGB5-1083. (CL... Caltech Division Contribution 87," This work was supported in part by DOE grants DE-FG02-87ER40328 and DE-FG02-00ER41149 (Y.Z.Q.) and by NASA grant NAG5-4083 (G.J.W.), Caltech Division Contribution 8764(1075)."525observed scattered (polarised) optical broad lines. shows no X-ray flux detectable by ASCA and ROSAT (Ogasaka et al 1997: Fabian et al 1996).,"observed scattered (polarised) optical broad lines, shows no X-ray flux detectable by ASCA and ROSAT (Ogasaka et al 1997; Fabian et al 1996)."526 The difference between these sources is probably determined by the geometry of the obscuring medium. which may pe torus-like in the case of 11068 and more spherical for F15307.," The difference between these sources is probably determined by the geometry of the obscuring medium, which may be torus-like in the case of 1068 and more spherical for F15307."527 Since synthesis models for the XRB spectrum indicate hat most (85 per cent) of the AGN power is absorbed (Fabian Iwasawa 1999). a spherical geometry is more likely to be relevant o the sources dominating the hard XRB than a torus one.," Since synthesis models for the XRB spectrum indicate that most (85 per cent) of the AGN power is absorbed (Fabian Iwasawa 1999), a spherical geometry is more likely to be relevant to the sources dominating the hard XRB than a torus one."528 The scattered flux fraction is likely to be small., The scattered flux fraction is likely to be small.529 It is the absorbed direct Hux which we are interested in here., It is the absorbed direct flux which we are interested in here.530 Redshift does help to shift so render mildly Compton- quasars detectable. leading to an inverse K-correction effect (Wilman Fabian 1999).," Redshift does help to shift so render mildly Compton-thick quasars detectable, leading to an inverse K-correction effect (Wilman Fabian 1999)."531 However the sources still need to be luminous ο be detectable., However the sources still need to be luminous to be detectable.532" For the spectrum of the XRB. it is the mildly Compton-thick objects which dominate at the v/,, XRB peak."," For the spectrum of the XRB, it is the mildly Compton-thick objects which dominate at the $\nu I_{\nu}$ XRB peak."533 The owest redshift members of the Compton-thick class contribute most to the highest energy part of that peak., The lowest redshift members of the Compton-thick class contribute most to the highest energy part of that peak.534 To assess whether Compton-thick quasars ought to. be detected. we have taken one simple obscured AGN model for the XRB (from Wilman. Fabian Nulsen 2000: WEN). and predicted he number of Compton-thick sources expected per square degree.," To assess whether Compton-thick quasars ought to be detected, we have taken one simple obscured AGN model for the XRB (from Wilman, Fabian Nulsen 2000; WFN), and predicted the number of Compton-thick sources expected per square degree."535 We have then passed the predicted spectra through the response curves of Chandra and XMM to predict the number expected to be detected., We have then passed the predicted spectra through the response curves of Chandra and XMM to predict the number expected to be detected.536 Our results indicate that some Compton-thick sources should be detectable. particularly in the Chandra | Ms images (Alexander et al 2001: Rosati et al 2001).," Our results indicate that some Compton-thick sources should be detectable, particularly in the Chandra 1 Ms images (Alexander et al 2001; Rosati et al 2001)."537 Chandra does not have he collecting area above 8 keV to detect such hard sources readily: XMM has too much internal background (relevant because of its much larger PSF) at those energies., Chandra does not have the collecting area above 8 keV to detect such hard sources readily; XMM has too much internal background (relevant because of its much larger PSF) at those energies.538 There may vet be renewed claims to resolve the XRB when distant Compton-thick sources are finally found in reasonable numbers., There may yet be renewed claims to resolve the XRB when distant Compton-thick sources are finally found in reasonable numbers.539 We argue that our results are not strongly dependent on the model adopted., We argue that our results are not strongly dependent on the model adopted.540 For the sake of completeness. we provide here an outline of the WEN model.," For the sake of completeness, we provide here an outline of the WFN model."541 At its heart is the semi-analytic galaxy formation code developed by Nulsen Fabian (1995). in which the Cole Kaiser (1988) block model is used to simulate the hierachical growth of clustering. and the scheme of Nulsen Fabian (1995) is used to treat the behaviour of the gas within a collapsed halo.," At its heart is the semi-analytic galaxy formation code developed by Nulsen Fabian (1995), in which the Cole Kaiser (1988) block model is used to simulate the hierachical growth of clustering, and the scheme of Nulsen Fabian (1995) is used to treat the behaviour of the gas within a collapsed halo."542 In short. gas within a radius /?=Mey. where the free-fall time is less than the cooling time. rapidly forms stars. producing supernovae which can then expel some (for normal galaxies) or all (in the ease of dwarf galaxies) of the remaining gas from the system.," In short, gas within a radius $R=R_{\rm{CF}}$, where the free-fall time is less than the cooling time, rapidly forms stars, producing supernovae which can then expel some (for normal galaxies) or all (in the case of dwarf galaxies) of the remaining gas from the system."543 Any gas at oSoy participates in a cooling flow (CF)., Any gas at $R>R_{\rm{CF}}$ participates in a cooling flow (CF).544 Newly formed normal galaxies are elliptieals unless all the hot gas is able to cool before the present or the next hierarchical collapse. in which case they are spirals.," Newly formed normal galaxies are ellipticals unless all the hot gas is able to cool before the present or the next hierarchical collapse, in which case they are spirals."545 Any collapse with at most one infalling normal galaxy forms a normal galaxy. with the stars of dwarf galaxies contributing to the spheroid of the new system.," Any collapse with at most one infalling normal galaxy forms a normal galaxy, with the stars of dwarf galaxies contributing to the spheroid of the new system."546 Collapses with more than one normal galaxy form a group or a cluster. as mergers between normal galaxies are ignored.," Collapses with more than one normal galaxy form a group or a cluster, as mergers between normal galaxies are ignored."547 Each of the smallest block model units contains a seed black hole of mass 1.610AL... and when a block collapses all the black holes associated with its merging subblocks are assumed to merge into a single black hole at the centre of the new galaxy.," Each of the smallest block model units contains a seed black hole of mass $1.6 \times 10^{6}$, and when a block collapses all the black holes associated with its merging subblocks are assumed to merge into a single black hole at the centre of the new galaxy."548 Such nuclear black holes are then fed by Bondi accretion of hot gas from the cooling flow atmospheres which surround them. in accordance with the model of Nulsen Fabian (2000).," Such nuclear black holes are then fed by Bondi accretion of hot gas from the cooling flow atmospheres which surround them, in accordance with the model of Nulsen Fabian (2000)."549 Whilst thus accreting. the black hole is assumed to radiate with an efficiency of 10 per cent. with a luminosity equal to 3 per cent of the bolometric one. with a power law plus reflection spectrum.," Whilst thus accreting, the black hole is assumed to radiate with an efficiency of 10 per cent, with a luminosity equal to 3 per cent of the bolometric one, with a power law plus reflection spectrum."550 This intrinsic spectrum is then absorbed by the isothermal distribution of cold dusty clouds deposited by the cooling flow. as suggested by Fabian (1999).," This intrinsic spectrum is then absorbed by the isothermal distribution of cold dusty clouds deposited by the cooling flow, as suggested by Fabian (1999)."551 The accretion is terminated by wind-driven gas expulsion when the mass of the black hole reaches a critical fraction of that in the surrounding spheroid. thereby accounting for the observed correlation between the mass of the remnant black hole and its host spheroid.," The accretion is terminated by wind-driven gas expulsion when the mass of the black hole reaches a critical fraction of that in the surrounding spheroid, thereby accounting for the observed correlation between the mass of the remnant black hole and its host spheroid."552" Thereafter the object shines as an optical quasar for 9.LO""yr..", Thereafter the object shines as an optical quasar for $9 \times 10^{7}$.553 For full details of the model. see WEN.," For full details of the model, see WFN."554 The eritieal mass of the black hole was determined by invoking a wind from the central engine (Fabian 1999: see also Silk Rees 1998 who use an energy argument rather than the force one used here)., The critical mass of the black hole was determined by invoking a wind from the central engine (Fabian 1999; see also Silk Rees 1998 who use an energy argument rather than the force one used here).555 We note here that the radiation pressure of the absorbed radiation alone yields a similar limit (i.e. if the force due to the radiation μιςὃς where the absorbed power LaixLea ," We note here that the radiation pressure of the absorbed radiation alone yields a similar limit (i.e. if the force due to the radiation $\sim556L_{\rm abs}/c$, where the absorbed power $L_{\rm abs}\propto L_{\rm557Edd}$ )."558"To pursue this in detail. we adopt the scenario of Fabian (1999), where a fraction f of the mass in the core of an isothermal suluxy Aj(«r)=evrfC) is in cold. X-ray absorbing gas."," To pursue this in detail, we adopt the scenario of Fabian (1999), where a fraction $f$ of the mass in the core of an isothermal galaxy $M(<r)=2v^2r/G$ is in cold, X-ray absorbing gas."559" The gas within radius 7, has been accreted into a black hole of mass Aden=f/2e7r7;/C. leaving a column density oofro/228€mr, beyond."," The gas within radius $r_1$ has been accreted into a black hole of mass $M_{\rm BH}=f 2 v^2560r_1/G,$ leaving a column density $N=f v^2/2\pi G m_{\rm p} r_1$ beyond."561" Rearranging these formulae means that Much of the radiation from the black hole is absorbed by the gas beyond r, giving rise to a force on the column of fiL.dace. where [i accounts for how much the matter traps and reradiates the energy."," Rearranging these formulae means that Much of the radiation from the black hole is absorbed by the gas beyond $r_1$ giving rise to a force on the column of $f_1 L_{\rm562abs}/4\pi r^2 c,$ where $f_1$ accounts for how much the matter traps and reradiates the energy."563 fj.~0.5 for an isolated cloud but may be several for the envisaged optically-thick cloud surrounding the nucleus., $f_1\sim 0.5$ for an isolated cloud but may be several for the envisaged optically-thick cloud surrounding the nucleus.564" Then at the limit where the outward force due to radiation balances the inward gravitational force on the column. (The formula assumes that the column is all at one radius: if it extends to 7,44 then a factor of οςμμις{1) enters into the inward force expression.)"," Then at the limit where the outward force due to radiation balances the inward gravitational force on the column, (The formula assumes that the column is all at one radius; if it extends to $r_{\rm max}$ then a factor of $\log(r_{\rm max}/r)$ enters into the inward force expression.)"565" Let Lii,=foLgafotrGAlmefor. where er is the Thomson cross section."," Let $L_{\rm abs}=f_2 L_{\rm Edd}=f_2 4\pi GMm_{\rm p}c/\sigma_{\rm T},$ where $\sigma_{\rm T}$ is the Thomson cross section."566 Then Substituting this into the above black hole mass formula then gives or This is the mass of the black hole when the gas (which fuels it) is, Then Substituting this into the above black hole mass formula then gives or This is the mass of the black hole when the gas (which fuels it) is567"Based on the relatively clean water ice surface and higher than average bulk density, ? argue that Haumea is differentiated with a rocky core and icy mantle.","Based on the relatively clean water ice surface and higher than average bulk density, \citet{Brown2007} argue that Haumea is differentiated with a rocky core and icy mantle."568 They propose that the family members and satellites are collisionally-derived fragments that originated primarily from the icy mantle., They propose that the family members and satellites are collisionally-derived fragments that originated primarily from the icy mantle.569" The satellites and family members are orders of magnitude less massive than Haumea, and the family members have a minimum velocity at infinity (Vi) of about 150 m s! (??).."," The satellites and family members are orders of magnitude less massive than Haumea, and the family members have a minimum velocity at infinity $V_{\infty}$ ) of about 150 m $^{-1}$ \citep{Ragozzine2007,Ragozzine2009}."570" The velocity dispersion is much less than expected if the Haumea family formed as the result of a catastrophic impact, as in the formation of asteroid belt families (e.g.,?7).."," The velocity dispersion is much less than expected if the Haumea family formed as the result of a catastrophic impact, as in the formation of asteroid belt families \citep[e.g., ][]{Nesvorny2006,Michel2004}."571" In a catastrophic disruption event, a parent body is disrupted and dispersed such that the largest remnant is less than or equal to half the original mass."," In a catastrophic disruption event, a parent body is disrupted and dispersed such that the largest remnant is less than or equal to half the original mass."572" In the gravity regime, the fragments have initial velocities relative to the largest remnant comparable to the escape speed (Vesc) of the disrupted parent body (?).."," In the gravity regime, the fragments have initial velocities relative to the largest remnant comparable to the escape speed $V_{\rm esc}$ ) of the disrupted parent body \citep{Benz1999}."573" Thus, the observed magnitude of the velocity dispersion (Vs) of asteroid belt families is significant with respect to Vesc of the largest remnant; in other words, Vas. of the parent body was much greater than Ves. of the largest remnant in gravity dominated disruption events."," Thus, the observed magnitude of the velocity dispersion $V_{\infty}$ ) of asteroid belt families is significant with respect to $V_{\rm esc}$ of the largest remnant; in other words, $V_{\rm esc}$ of the parent body was much greater than $V_{\rm esc}$ of the largest remnant in gravity dominated disruption events."574" Unlike most asteroid belt families, the velocity dispersion among Haumea family members is a small fraction of the escape velocity from Haumea (Va~900 m s-!)."," Unlike most asteroid belt families, the velocity dispersion among Haumea family members is a small fraction of the escape velocity from Haumea $V_{\rm esc} \sim575900$ m $^{-1}$ )."576" Based on the current models of family formation via catastrophic disruption, the Haumea family could not have formed by catastrophic disruption of a much larger parent body."," Based on the current models of family formation via catastrophic disruption, the Haumea family could not have formed by catastrophic disruption of a much larger parent body."577 Two impact scenarios have been proposed for the formation of the Haumea system., Two impact scenarios have been proposed for the formation of the Haumea system.578" ? proposed an impact event that falls in the catstrophic disruption category, which does not agree with the observed velocity dispersion among family members."," \citet{Brown2007} proposed an impact event that falls in the catstrophic disruption category, which does not agree with the observed velocity dispersion among family members."579" To explain the small velocity dispersion, ? suggest the breakup of a single large moon in orbit around Haumea."," To explain the small velocity dispersion, \cite{Schlichting2009} suggest the breakup of a single large moon in orbit around Haumea."580" However, they do not provide an explanation for the initial state: a large moon in close orbit around a fast-spinning, elongated planet."," However, they do not provide an explanation for the initial state: a large moon in close orbit around a fast-spinning, elongated planet."581" To date, no known impact scenario explains all of the unusual characteristics of the Haumea system."," To date, no known impact scenario explains all of the unusual characteristics of the Haumea system."582" In this work, we quantitatively model the formation of the Haumea system."," In this work, we quantitatively model the formation of the Haumea system."583" We propose that the Haumea family formed via a novel type of giant collision: a impact between two comparably sized bodies resulting in high angular momentum, which spun off icyfragments that became satellites and family members."," We propose that the Haumea family formed via a novel type of giant collision: a impact between two comparably sized bodies resulting in high angular momentum, which spun off icyfragments that became satellites and family members."584 'The analytic and numerical methods are described in 82.., The analytic and numerical methods are described in \ref{sec:method}.585" The results are presented in 83,, and the implications for giant impacts in the Kuiper Belt are discussed in §4.."," The results are presented in \ref{sec:results}, and the implications for giant impacts in the Kuiper Belt are discussed in \ref{sec:disc}."586" To reduce the parameter space of possible collisions that produce a Haumea-like system, we used a three step process: derive an analytic prediction of plausible impact parameters1) (§??)); 2) conduct low-resolution simulations over a broad parameter space based on the results of the analytic prediction (§2.2)); and simulate the most promising impact scenarios in high 3)resolution (§2.3))."," To reduce the parameter space of possible collisions that produce a Haumea-like system, we used a three step process: 1) derive an analytic prediction of plausible impact parameters \ref{sec:ana}) ); 2) conduct low-resolution simulations over a broad parameter space based on the results of the analytic prediction \ref{sec:lowres}) ); and 3) simulate the most promising impact scenarios in high resolution \ref{sec:gadget}) )."587 The next three sections outline the method used in each step., The next three sections outline the method used in each step.588" Following ?,, using the conservation of energy and momentum, we derived an expression for the impact parameter and projectile-to-target mass ratio needed to obtain the observed angular momentum of Haumea via a giant impact."," Following \cite{Canup2001}, using the conservation of energy and momentum, we derived an expression for the impact parameter and projectile-to-target mass ratio needed to obtain the observed angular momentum of Haumea via a giant impact."589" Because Haumea is rotating near its spin instability limit and the observed velocity dispersion among family members is small, we consider the case where all of the angular momentum from the collision is retained in the remaining body."," Because Haumea is rotating near its spin instability limit and the observed velocity dispersion among family members is small, we consider the case where all of the angular momentum from the collision is retained in the remaining body."590" Assuming that the relative velocity between the projectile and target was zero at infinity, the impact parameter, b, is givenby where b is in units of the sum of the radii of the projectile and target, L is the angular momentum, and Le=kM*/5gVP?(31/6, where k is the inertial constant (2/5 for a sphere), M is the total mass, and p is the bulk density."," Assuming that the relative velocity between the projectile and target was zero at infinity, the impact parameter, $b$, is givenby where $b$ is in units of the sum of the radii of the projectile and target, $L$ is the angular momentum, and $L_{crit} = k M^{5/3} G^{1/2} (\frac{3}{4 \pi \rho})^{1/6}$, where $k$ is the inertial constant $2/5$ for a sphere), $M$ is the total mass, and $\rho$ is the bulk density."591" L..;; is, therefore, the critical spin angular momentum that a spherical body with constant density can sustain."," $L_{crit}$ is, therefore, the critical spin angular momentum that a spherical body with constant density can sustain."592" The mass ratio of projectile to the total mass, 7=ui: enters Eq."," The mass ratio of projectile to the total mass, $\gamma = \frac{M_P}{M_T+M_P}$, enters Eq."593 1 through f(y)=ία—3)(1?+(151/))17sin0 where 0 is the impact angle., \ref{eq:final} through $f(\gamma) = \gamma(1-\gamma)(\gamma^{1/3} + (1 - \gamma^{1/3}))^{1/2} \sin \theta$ where $\theta$ is the impact angle.594" However, if we assume that the impact velocity is greater than ος, the total energy equation will no longer equal zero B3of?).."," However, if we assume that the impact velocity is greater than $V_{\rm esc}$, the total energy equation will no longer equal zero \citep[Eq.~B3 of][]{Canup2001}."595" In this case, the impact parameter is constrained(Eq. by where V; is the impact velocity and Vege is the mutual escape velocity 1of?).."," In this case, the impact parameter is constrained by where $V_i$ is the impact velocity and $V_{\rm esc}$ is the mutual escape velocity \citep[Eq.~1 of][]{Canup2005}."596 For Haumea we(Eq. assume a mass of 4.2x10?! kg and a spin period 3.92 hr from ?.., For Haumea we assume a mass of $4.2\times 10^{21}$ kg and a spin period 3.92 hr from \citet{Rabinowitz2006}.597" Using these values, τος ranges between 1.1 and 0.8 for a plausible range of bulk densities of the colliding bodies (1.5 to 2.5 g cm~3)."," Using these values, $\frac{L}{L_{\mathrm crit}}$ ranges between 1.1 and 0.8 for a plausible range of bulk densities of the colliding bodies (1.5 to 2.5 g $^{-3}$ )."598 The results from Eq., The results from Eq.599 1 and 2 are shown in Fig. 1.., \ref{eq:final} and \ref{eq:bvi} are shown in Fig. \ref{fig:analytic}.600" If the impact velocity equals the mutual escape velocity of the projectile and target, Eq."," If the impact velocity equals the mutual escape velocity of the projectile and target, Eq."601 1 requires an impact parameter close to one (> 0.8) and a projectile close to the mass of the target in order to attain the angular momentum in Haumea (Fig. 1)).," \ref{eq:final}602 requires an impact parameter close to one $> 0.8$ ) and a projectile close to the mass of the target in order to attain the angular momentum in Haumea (Fig. \ref{fig:analytic}) )."603 Increasing the bulk density of the bodies broadens the range of impact parameters that could transfer the observed angular momentum., Increasing the bulk density of the bodies broadens the range of impact parameters that could transfer the observed angular momentum.604" Similarly, when V;>Voge, there is a larger range of possible projectile-to-target mass ratios that could produce the angular momentum of Haumea (Eq. 2,,"," Similarly, when $V_i >605V_{{\rm esc}}$, there is a larger range of possible projectile-to-target mass ratios that could produce the angular momentum of Haumea (Eq. \ref{eq:bvi},"606 dotted line in Fig., dotted line in Fig.607 1 assumes the mean bulk density for large KBOs of 2 g , \ref{fig:analytic} assumes the mean bulk density for large KBOs of 2 g $^{-3}$ ).608This work assumes no initial spin in the target and cm?).projectile., This work assumes no initial spin in the target and projectile.609 Initial spin in the same sense as the spin angular momentum would potentially increase the range of mass ratio that could produce a Haumea-like remnant., Initial spin in the same sense as the spin angular momentum would potentially increase the range of mass ratio that could produce a Haumea-like remnant.610" As the impact velocity increases, the remaining body does not retain most of the angular momentum of the encounter, as is assumed in the equations above."," As the impact velocity increases, the remaining body does not retain most of the angular momentum of the encounter, as is assumed in the equations above."611" When the impact velocity is large enough to begin to disrupt the target (3—3.5kms!, 7), a significant amount of angular momentum will be carried away by the smallest fragments (seeFig.2in ?).."," When the impact velocity is large enough to begin to disrupt the target \citep[3 -- 3.5 km s$^{-1}$ , a significant amount of angular momentum will be carried away by the smallest fragments \citep[see Fig.~2 in][]{Leinhardt2000}. ."612 Compensating for the partial loss of angular momentum by further increasing the impact velocity will lead to the catastrophic disruption regime., Compensating for the partial loss of angular momentum by further increasing the impact velocity will lead to the catastrophic disruption regime.613 Recall that the catastrophic disruption regime, Recall that the catastrophic disruption regime614"where /; and /;, are the model times and mm;4, and ms are the mass-loss rates at the corresponding times.",where $t_i$ and $t_{i+1}$ are the model times and $\dot{m}_{i+1}$ and $\dot{m}_i$ are the mass-loss rates at the corresponding times.615 The total mass-loss is determined by summing all of the AAJ;s. ‘Table 1. shows the values of Y and Z for which mass- was computed., The total mass-loss is determined by summing all of the $\Delta M_{i}$ s. Table \ref{padovamodels} shows the values of $Y$ and $Z$ for which mass-loss was computed.616 For all available masses the niass-loss on both the EAGB and ROB was computed., For all available masses the mass-loss on both the EAGB and RGB was computed.617 Z is the value of Z on the ZAAIS and Y is the value of Y on the ZAMS., $Z$ is the value of $Z$ on the ZAMS and $Y$ is the value of $Y$ on the ZAMS.618 The mass-loss on the ROB as a function of the ZAXMS mass for all available values of Y and Z is shown in figure L.., The mass-loss on the RGB as a function of the ZAMS mass for all available values of $Y$ and $Z$ is shown in figure \ref{rgbmassloss}.619 In all panels it is evident the amount of mass-loss decreases as Y increases., In all panels it is evident the amount of mass-loss decreases as $Y$ increases.620 This occurs because stars with higher values of Y means the RGB star will have smaller racii and higher surface gravity due to the lower opacity in the outer layers., This occurs because stars with higher values of $Y$ means the RGB star will have smaller radii and higher surface gravity due to the lower opacity in the outer layers.621 These factors lower the mass-Ioss rates and the total mass-OSS., These factors lower the mass-loss rates and the total mass-loss.622 The RGB mass-loss was ft using two linear [fits [or vigher and lower ZAMS masses., The RGB mass-loss was fit using two linear fits for higher and lower ZAMS masses.623 The transition point rchween the fits was determined. by visually estimating he mass where the slope appears to change., The transition point between the fits was determined by visually estimating the mass where the slope appears to change.624 This. mass is typically found. around a ZAATS mass ΕΣ..., This mass is typically found around a ZAMS mass of 0.8-0.9 $_{\sun}$.625 The higher mass fit was terminated where the high mass ine crosses the horizontal axis., The higher mass fit was terminated where the high mass line crosses the horizontal axis.626 Εις termination point was also estimated: visually., This termination point was also estimated visually.627 For masses larger the mass where he higher mass [it crosses the axis the mass-loss is 0., For masses larger the mass where the higher mass fit crosses the axis the mass-loss is 0.628 The equations of the linear fits for low and high masses are given w ANMpcpase and AMais.," The equations of the linear fits for low and high masses are given by $\Delta{\rm M}_{\rm RGB,low}$ and $\Delta{\rm M}_{\rm RGB,high}$."629 To make the fits work at the wo highest metallicities (Z=0.008 and 0.017) the fitting was done by excluding the M=0.6NE; models.," To make the fits work at the two highest metallicities $Z=0.008$ and 0.017) the fitting was done by excluding the ${\rm M}=0.6\,{\rm M}_{\sun}$ models."630 These can »e safely excluclecl since the mass-loss for these very low mass stars eliminates their envelope before the tip of the UGD is reached and such models will not be considered in his paper., These can be safely excluded since the mass-loss for these very low mass stars eliminates their envelope before the tip of the RGB is reached and such models will not be considered in this paper.631 Visual inspection indicates the fits are in. good agreement to the mass-Ioss calculations., Visual inspection indicates the fits are in good agreement to the mass-loss calculations.632 The equations for z;NMpconaos and: AApownian are eiven by Phe mass-loss is found by caleulating the value of both AAIs and finding the maximum value.," The equations for $\Delta{\rm M}_{\rm RGB,low}$ and $\Delta{\rm633 M}_{\rm RGB,high}$ are given by The mass-loss is found by calculating the value of both $\Delta{\rm634 M}$ s and finding the maximum value."635 Lo the mass-loss is ound to be negative then the value of the mass-loss is set to V., If the mass-loss is found to be negative then the value of the mass-loss is set to 0.636 The coellicients of these equations for the different values of Y and Z are shown in table 2.., The coefficients of these equations for the different values of $Y$ and $Z$ are shown in table \ref{tab:masslosscoes}.637 No attempt has been mace vet to calibrate this which will be done in a later paper.," No attempt has been made yet to calibrate this mass-loss, which will be done in a later paper."638 Lowever. the mass- values from these equations appear to be reasonable.," However, the mass-loss values from these equations appear to be reasonable."639 For example a 1.0M.; Y—0.26 Z=0.017 star would experience 28M.;. of mass-loss on the RGB which is typical of other niocdels.," For example a $1.0\,{\rm M}_{\sun}$ $Y=0.26$ $Z=0.017$ star would experience $\,{\rm M}_{\sun}$ of mass-loss on the RGB which is typical of other models."640 A typical turn-olf mass of Q.80M; with Y=0.245 and Z=0.0008 gives a ROB mass-loss of 81 which is reasonable giving a zero-age horizontal branch mass of approximately 0.58AL. which is similar to measured. values (c.g. Grattonetal. (2010))).," A typical turn-off mass of $0.80\,{\rm M}_{\sun}$ with $Y=0.245$ and $Z=0.0008$ gives a RGB mass-loss of $\,{\rm M}_{\sun}$ which is reasonable giving a zero-age horizontal branch mass of approximately $\,{\rm641 M}_{\sun}$ which is similar to measured values (e.g. \citet{grat10}) )."642 Lt should be noted. as suggested by the referee. that the method used to find the mass-Ioss is not consistent. with the stellar evolution models.," It should be noted, as suggested by the referee, that the method used to find the mass-loss is not consistent with the stellar evolution models."643 As the star loses mass its surface eravity would decrease causing the star to expand., As the star loses mass its surface gravity would decrease causing the star to expand.644 For the models used this would result in a higher mass-loss rate near the tip of the RGB and a greater amount of mass-loss on the RGB (and the E-ACGB) then is calculated here., For the models used this would result in a higher mass-loss rate near the tip of the RGB and a greater amount of mass-loss on the RGB (and the E-AGB) then is calculated here.645 However. this ellect should be relatively small since the ceviation will only be really significant at the tip of the RGB.," However, this effect should be relatively small since the deviation will only be really significant at the tip of the RGB."646 Although the method. used here is not strictly consistent the relative cillerencees in mass-Ioss due to the ellect of the ZAAIS helium abundances and the ZAMS metallicity should be correct., Although the method used here is not strictly consistent the relative differences in mass-loss due to the effect of the ZAMS helium abundances and the ZAMS metallicity should be correct.647 This is important since when all stars enter the RGB the convective envelope penetrates into regions of the star where partial LE burning has occurred. bringing these products up to the surface., This is important since when all stars enter the RGB the convective envelope penetrates into regions of the star where partial H burning has occurred bringing these products up to the surface.648 Loa PN is formed. this process will have mocified the surface abundances., If a PN is formed this process will have modified the surface abundances.649 This paper only considers the effects on Le and the CNO elements since these are what is observed in planetary. nebula., This paper only considers the effects on He and the CNO elements since these are what is observed in planetary nebula.650 The first clrecdge-up (EDU) prescription of Grocnewegen&deJong(1994). is used., The first dredge-up (FDU) prescription of \citet{gj94} is used.651 The same procedure was applied to the earbv-AGD (E-AGB) portions of the Padova tracks., The same procedure was applied to the early-AGB (E-AGB) portions of the Padova tracks.652 An additional condition of starting the mass-Ioss when the temperature was below 4500K was assumed. since this mass-Ioss law is applicable only to Ix and. M stars., An additional condition of starting the mass-loss when the temperature was below 4500K was assumed since this mass-loss law is applicable only to K and M stars.653 Figure 2. shows the caleulated mass-loss during the I-AGB anc the fits to these mass-osses., Figure \ref{eagbmassloss} shows the calculated mass-loss during the E-AGB and the fits to these mass-losses.654 The most. obvious trend is as Y increases so does the amount. of mass-Ioss., The most obvious trend is as $Y$ increases so does the amount of mass-loss.655 This is opposite to the trend on the RGB., This is opposite to the trend on the RGB.656 In this case the core mass on the AGB is increased. whieh also increases the luminosity., In this case the core mass on the AGB is increased which also increases the luminosity.657 This increase in the luminosity on the E-AGB results in greater mass-loss., This increase in the luminosity on the E-AGB results in greater mass-loss.658 This enhancement of mass-loss on the E-AGB is important since it means the higher the value of Y the more mass is lost on the E-AGB., This enhancement of mass-loss on the E-AGB is important since it means the higher the value of $Y$ the more mass is lost on the E-AGB.659 It means such a star has a higher probability to reach the horizontal branch but its envelope may not survive to reach the first thermal pulse., It means such a star has a higher probability to reach the horizontal branch but its envelope may not survive to reach the first thermal pulse.660 The mass-loss on the E-AGB is [fit using 4 fits in different: regions of mass., The mass-loss on the E-AGB is fit using 4 fits in different regions of mass.661 The lowest mass range 1.5N.z ) is fit via a cubic. the next mass range up (1.5AL.A0 M) is fit using a quadratic fit.," The lowest mass range ${\rm M}\la1.5\,{\rm M}_{\sun}$ ) is fit via a cubic, the next mass range up $1.5\,{\rm M}_{\sun}\la{\rm662 M}\la2.0\,{\rm M}_{\sun}$ ) is fit using a quadratic fit."663 Phe next mass range up (2.0NL;SsAls4.5 M5) is fit using a linear fit.," The next mass range up $2.0\,{\rm M}_{\sun}\la{\rm M}\la4.5\,{\rm M}_{\sun}$ ) is fit using a linear fit."664 Finally the highest masses are fit using a constant value of niss-loss., Finally the highest masses are fit using a constant value of mass-loss.665 The points of intersection between adjacent. fits were visually estimated., The points of intersection between adjacent fits were visually estimated.666 This procedure gives a good fit to the model mass-Iosses., This procedure gives a good fit to the model mass-losses.667 The equations for the E-ACGB mass-loss in the first. two mass regions are given by: and where AZ is the mass of the star on the ZAAIS., The equations for the E-AGB mass-loss in the first two mass regions are given by: and where $M$ is the mass of the star on the ZAMS.668 Only the coellicicnts of first. two regions have been included. in table 8 to save space and since no models of sullicicnt mass which need the fits for the upper regions are calculated in this paper., Only the coefficients of first two regions have been included in table \ref{tab:eagbco} to save space and since no models of sufficient mass which need the fits for the upper regions are calculated in this paper.669 The E-AGB mass-loss is calculated. by finding the intersection of the two regions and then choosing the appropriate region and plugeing into the corresponding equation., The E-AGB mass-loss is calculated by finding the intersection of the two regions and then choosing the appropriate region and plugging into the corresponding equation.670"Iu the previous section it was pointed out that there is a pinching effect only if D,, does not decrease faster than L/R.",In the previous section it was pointed out that there is a pinching effect only if $B_{\phi}$ does not decrease faster than $1/R$.671 However. this decay is untenable at laree Rin real astrophysical svstems as it will be shown in the next aud. therefore. it is inevitable that bevoud a certain radius. the magnetic tension produces a force pointing outwards (sce Fig.," However, this decay is untenable at large $R$ in real astrophysical systems as it will be shown in the next and, therefore, it is inevitable that beyond a certain radius, the magnetic tension produces a force pointing outwards (see Fig."672 1 for a visualization)., 1 for a visualization).673 In fact. the slowest radial magnetic decay occurs in the ideal case of having strict cvlndzrical ecometry with curreuts. J.. flowing from 2=x to.=x (otherwise. if currents are confined to a certain region. must decrease with radius at least as fast as a dipole field for large r: B.<W/r?. where WW is a constaut).," In fact, the slowest radial magnetic decay occurs in the ideal case of having strict cylindrical geometry with currents, $J_{z}$ , flowing from $z=-\infty$ to $z=\infty$ (otherwise, if currents are confined to a certain region, ${\mbox{\boldmath $ $}}$ must decrease with radius at least as fast as a dipole field for large ${\mbox{\boldmath $ $}}$: $B\leq K/r^{3}$, where $K$ is a constant)."674" Under strict evlindrical geometry ον, the condition of closed current loops is equivalent to inmposiug hsJRAR>0 at large P? (hereafter. this will be our definition of ina cvlindical svsteimi)."," Under strict cylindrical geometry , the condition of closed current loops is equivalent to imposing $\int_{0}^{R} J_{z} R'\,dR'\rightarrow 0$ at large $R$ (hereafter, this will be our definition of in a cylindrical system)."675" Frou Aaperre’s law. this requirement implies that D,,«C/R a laree R. being € a constant."," From Ampèrre's law, this requirement implies that $B_{\phi}< C/R$ at large $R$, being $C$ a constant."676" So there must exist a certain radius denoted by at which the maguetic field starts to decay as L/R or Rigg,faster.", So there must exist a certain radius denoted by $R_{\rm kep}$ at which the magnetic field starts to decay as $1/R$ or faster.677" is therefore tho radius a which the rotation speed of the Rig,eas coicides with the local Iseplerian velocity.", $R_{\rm kep}$ is therefore the radius at which the rotation speed of the gas coincides with the local Keplerian velocity.678 Tf Ry is the radius of the last poiut of detection. we require Rigg)>Rup diu order to have an anomalous faster rotation along the observed disk.," If $R_{\rm HI}$ is the radius of the last point of detection, we require $R_{\rm kep}>R_{\rm HI}$ in order to have an anomalous faster rotation along the observed disk."679 The system will be iu a configuration of equilibriu a Hom oulvdf the inward gravitational force is higher than the Rigoutward magnetic force If this condition is not fulfilled the disk will expaud racially due to the maeuetic forces., The system will be in a configuration of equilibrium at $R>R_{\rm kep}$ only if the inward gravitational force is higher than the outward magnetic force If this condition is not fulfilled the disk will expand radially due to the magnetic forces.680 This conditiou can be written as where {δω Is the magnetic feld strength at Zn.," This condition can be written as where $B_{\phi,{\rm kep}}$ is the magnetic field strength at $R_{\rm kep}$."681" Since a dependence B,,zC/R at lavee R is unphysical (see above). an upper limit to B, cau be established from Eq. (6)):"," Since a dependence $B_{\phi}\approx C/R$ at large $R$ is unphysical (see above), an upper limit to $B_{\phi,{\rm kep}}$ can be established from Eq. \ref{eq:atrest}) ):"682 where Rp is the radius where Dzc0., where $R_{B_{\phi}}$ is the radius where $B_{\phi}\approx 0$.683" Iu practice we wil take Rp»x to estimate. the maxinwi contribution,", In practice we will take $R_{B_{\phi}}\rightarrow \infty$ to estimate the maximum contribution.684" The imaxiumni value for D, corresponds to a situation iu which there is balauce at HBfü between gravitational and magnetic forces and thus the material outside the Rig, cirele las no rotation at all."," The maximum value for $B_{{\phi},{\rm kep}}$ corresponds to a situation in which there is balance at $R>R_{\rm kep}$ between gravitational and magnetic forces and thus the material outside the $R_{\rm kep}$ circle has no rotation at all."685 The upper limit derived above has απ casy interpretation., The upper limit derived above has an easy interpretation.686 In principle. one could achieve very large clifferences ee If one would male the cdeusity arbitrarily sinall than the Alfvóun speed would be arbitrarily laree.," In principle, one could achieve very large differences $v_{\phi}-v_{\rm c}$ if one would make the density arbitrarily small than the Alfvènn speed would be arbitrarily large."687" However, according to Eq. (5))."," However, according to Eq. \ref{eq:directbal}) ),"688 this is not possible elobally because the magnetic field has to be held iu by the radial weight of the plasma in the radial gravitational field since the net effect of magnetic fields is never coufiniug., this is not possible globally because the magnetic field has to be held in by the radial weight of the plasma in the radial gravitational field since the net effect of magnetic fields is never confining.689 It is customary and natural to discuss this kind of constraiuts using the virial theorem which savs that the ret nature of magnetic fields is expansive or null (but rever coufiniug) in both the radial aud vertical directions (Appendix D)., It is customary and natural to discuss this kind of constraints using the virial theorem which says that the net nature of magnetic fields is expansive or null (but never confining) in both the radial and vertical directions (Appendix B).690" More specifically, for toroidal magnetic fields aud strict cylindrical geometry. the total rotational energv of an isolated system should be the same with or without magnetic fields. keeping the mass distribution fixed (so that (R): see Appendix D for further details)."," More specifically, for toroidal magnetic fields and strict cylindrical geometry, the total rotational energy of an isolated system should be the same with or without magnetic fields, keeping the mass distribution fixed (so that $\Phi(R)$; see Appendix B for further details)."691" Dy iinposing that coustrait. a simular upper liuüt for Dy, is found (Appendix C). except by a factor (App). between 2. that takes iuto account possible threc-dinieusional effects."," By imposing that constraint, a similar upper limit for $B_{\rm kep}$ is found (Appendix C), except by a factor $\lambda_{\rho B}$ ), between $1$ $2$, that takes into account possible three-dimensional effects."692 It is convenient to consider first the extreme aud hypothetical case that spiral galaxies do not host dark matter halos., It is convenient to consider first the extreme and hypothetical case that spiral galaxies do not host dark matter halos.693 For a galaxy with a mass in gas and stars AM. @®(R)=GAL/R in the outer parts and The assumption that PLR)=GAL/R is satisfactory for many high surface deusitv galaxies (c.g.. van Albada et al.," For a galaxy with a mass in gas and stars $M$, $\Phi(R)\approx -GM/R$ in the outer parts and The assumption that $\Phi(R)\approx -GM/R$ is satisfactory for many high surface density galaxies (e.g., van Albada et al."694 1985) but it is not necessarily fulfilled im some low surface brightness galaxies (LSB) and cawarfs for which the eas surface density is not exponential aud its contribution to the potential may be comparable or even higher than that from the stellar component at radi —Aj for certain valuesof the adopted stellar iuass-to-Iunünositv. ratio., 1985) but it is not necessarily fulfilled in some low surface brightness galaxies (LSB) and dwarfs for which the gas surface density is not exponential and its contribution to the potential may be comparable or even higher than that from the stellar component at radii $\sim R_{\rm HI}$ for certain valuesof the adopted stellar mass-to-luminosity ratio.695" However, we are confident that our conclusious would uot chanee for these galaxies even adopting the most uufavorable assuniptious."," However, we are confident that our conclusions would not change for these galaxies even adopting the most unfavorable assumptions."696" Iu the optimistic aud rather uulikelv situation that £,, were constant with R out to fh. be. BG)=Bey at Π<Ryy. the characteristic variation οἳ οἳ would be UT,οςESD2(lip)."," In the optimistic and rather unlikely situation that $B_{\phi}$ were constant with $R$ out to $R_{\rm kep}$, i.e., $B_{\phi}(R)=B_{\rm cr}$ at $R<R_{\rm kep}$, the characteristic variation $v_{\phi}^{2}-v_{\rm c}^{2}$ would be $v_{\phi}^{2}-v_{\rm c}^{2}\approx B_{\rm cr}^{2}/(4\pi \rho)$."697 By using Eq. (8)).," By using Eq. \ref{eq:upperkep}) ),"698 it is possible to estimate the ιαππα relative variation of the circular speed of the gas at a radius ΠιοBy: where we have adopted a radial exponeutial decay for PpRO) with scale Re (es... Dlaud-IExwthoru. Freeman Quinn 1997).," it is possible to estimate the maximum relative variation of the circular speed of the gas at a radius $R<R_{\rm kep}$: where we have adopted a radial exponential decay for $\rho (R,0)$ with scale $R_{\rm g}$ (e.g., Bland-Hawthorn, Freeman Quinn 1997)."699 Note that (02ez)ος Is not sensitive to Pot because even though the deusitv at the midplane increases with Pog. equation (93) does not depend on the absolute value of the density but only on Ry.," Note that $(v_{\phi}^{2}-v_{\rm c}^{2})/v_{\rm c}^{2}$ is not sensitive to $P_{\rm ext}$ because even though the density at the midplane increases with $P_{\rm ext}$, equation \ref{eq:ten}) ) does not depend on the absolute value of the density but only on $R_{\rm g}$."700" The main source of πιοταπαν stems from the value of Rigg). but the most optimistic situation occurs when Rig,©Rip. so we will assunie for the discussion that both radii are identical. zz30 kpe for conunon spiral galaxies."," The main source of uncertainty stems from the value of $R_{\rm kep}$ , but the most optimistic situation occurs when $R_{\rm kep}\approx R_{\rm HI}$, so we will assume for the discussion that both radii are identical, $\approx 30$ kpc for common spiral galaxies."701 Iu order to estimate UTez from Eq. (9)).," In order to estimate $v_{\phi}^{2}-v_{\rm c}^{2}$ from Eq. \ref{eq:ten}) ),"702 we will assume that the mass of gas in the disk bevoud δι and within |:|«fy. beiug fy the characteristic scale height of the eas disk (see Appeudix C for further details). is 0.5 perceut the totalmass of the disk.," we will assume that the mass of gas in the disk beyond $R_{\rm HI}$ and within $|z|<h_{1}$, being $h_1$ the characteristic scale height of the gas disk (see Appendix C for further details), is $0.5$ percent the totalmass of the disk."703 This secius to bethe case of dwarf galaxies (van den Bosch et al., This seems to bethe case of dwarf galaxies (van den Bosch et al.704 2001). but it is probably a too ecuerous value for normal spiral galaxies.," 2001), but it is probably a too generous value for normal spiral galaxies."705 The latter assmuption corresponds to a radial scale leneth for the eas. Ry. of  kpe.," The latter assumption corresponds to a radial scale length for the gas, $R_{\rm g}$ , of $\sim 5.5$ kpc."706 Putting these values iuto Eq. (9)).," Putting these values into Eq. \ref{eq:ten}) ),"707 we obtain (e2oQe=ύλη at R=30kpc.," we obtain $(v_{\phi}^{2}-v_{\rm c}^{2})/v_{\rm c}^{2}=7080.36 \lambda_{\rho B}$ at $R=30$kpc."709 If we take for reference values te=100 Eni | at 30 kpe. the maximo," If we take for reference values $v_{\rm c}=100$ km $^{-1}$ at $30$ kpc, the maximum"710containing faint serendipitous sources with SCUBA sub-millimetre observations of the same lensing cluster. fields: onlv one source is common to both datasets. suggesting that if the SCUBA sources do host. powerful. GN. they must either contribute a small fraction of the sub-mim power. or be Compton-thick with X-ray scattering fractions of less than 1 per cent.,"containing faint serendipitous sources with SCUBA sub-millimetre observations of the same lensing cluster fields; only one source is common to both datasets, suggesting that if the SCUBA sources do host powerful AGN, they must either contribute a small fraction of the sub-mm power, or be Compton-thick with X-ray scattering fractions of less than 1 per cent."711 This result was confirmed by LLornschemoeier et al. (, This result was confirmed by Hornschemeier et al. (7122000). who detected none of the LO sub-nim sources in and around the Lubble Deep Field North in a 166-ks exposure.,"2000), who detected none of the 10 sub-mm sources in and around the Hubble Deep Field North in a 166-ks exposure."713 We stress. however. thatChandra has so [ar resolved the bulk of the SRB in the band. which is mainly due to Compton-thin sources: forthcoming deep surveys withVAZAZ will shed light on the more heavily obscured sources which are likely to contribute up tokeV.. but the bulk of the energy density of the SRB at ~30 which is likely to be dominated by Compton-thick sources will not be resolved untilConsfellalion-N is in light (see e.g. Valinia et al.," We stress, however, that has so far resolved the bulk of the XRB in the band, which is mainly due to Compton-thin sources; forthcoming deep surveys with will shed light on the more heavily obscured sources which are likely to contribute up to, but the bulk of the energy density of the XRB at $\sim 30$ – which is likely to be dominated by Compton-thick sources– will not be resolved until is in flight (see e.g. Valinia et al."714 1999)., 1999).715 The findings of Alushotzky et al. (, The findings of Mushotzky et al. (7162000) and Fabian et al. (,2000) and Fabian et al. (7172000) demonstrate that the newly-cdiscoverecl XB sources mav be quite dillerent. from established: classes of AGN. such as the quasars and. at low redshift. the Sevlert galaxies.,"2000) demonstrate that the newly-discovered XRB sources may be quite different from established classes of AGN, such as the quasars and, at low redshift, the Seyfert galaxies."718 Indeed. Fabian (1999) has argued that the new ARB sources represent the hitherto unobserved) phase associated with the major growth of massive black holes. whereas classical (optically-sclectecl) quasars ancl Sevfert galaxies represent a later. transient. phase during which the black hole acquires little additional mass.," Indeed, Fabian (1999) has argued that the new XRB sources represent the hitherto unobserved phase associated with the major growth of massive black holes, whereas classical (optically-selected) quasars and Seyfert galaxies represent a later, transient phase during which the black hole acquires little additional mass."719 In his model for the formation of galactic bulges and central black holes. voung spheroidal galaxies have a significant clistributec component of cold custy clouds which leads to absorption of X-ravs [rom the accreting black hole.," In his model for the formation of galactic bulges and central black holes, young spheroidal galaxies have a significant distributed component of cold dusty clouds which leads to absorption of X-rays from the accreting black hole."720 The accretion is terminated by winc-driven gas expulsion. when the mass of the black hole reaches a critical fraction of that in the surrounding spheroicl (see also Silk Rees 1998). thereby accounting for the observed correlation between the mass of the remnant black hole and its host spheroid (Magorrian et al.," The accretion is terminated by wind-driven gas expulsion when the mass of the black hole reaches a critical fraction of that in the surrounding spheroid (see also Silk Rees 1998), thereby accounting for the observed correlation between the mass of the remnant black hole and its host spheroid (Magorrian et al."721 1998: Van der Mare! 1999)., 1998; Van der Marel 1999).722 Following expulsion. the object shines brielly as an optically-sclectecd quasar.," Following expulsion, the object shines briefly as an optically-selected quasar."723 In this paper. we incorporate Fabian’s (1999) mocel for the obscured growth. of massive black holes into the semi-analvtic model for galaxy formation and quasar fuelling developed by Nulsen Fabian (1997. 2000) (hereafter NEOT and ΕΟΟ.," In this paper, we incorporate Fabian's (1999) model for the obscured growth of massive black holes into the semi-analytic model for galaxy formation and quasar fuelling developed by Nulsen Fabian (1997, 2000) (hereafter NF97 and NF00)."724 The result. is a physical model for the ARB which works forward in cosmic time from the epoch when 1¢ first massive bound objects were forming. in Contrast to 10 aforementioned svnthesis models which start with the ocally observed AGN Luminosity functions and extrapolate rem back to earlier epochs.," The result is a physical model for the XRB which works forward in cosmic time from the epoch when the first massive bound objects were forming, in contrast to the aforementioned synthesis models which start with the locally observed AGN luminosity functions and extrapolate them back to earlier epochs."725 We assume that quasars are ποΠο. bv Bondi accretion from. the dense. hot. cooling umospheres which form around. collapsing objects about 16 size of normal galaxies.," We assume that quasars are fuelled by Bondi accretion from the dense, hot cooling atmospheres which form around collapsing objects about the size of normal galaxies."726 Earlier attempts to incorporate AGN into the framework of semi-analvtic models were mace wv Jlxaulfmann Lachnelt (2000) and Cattaneo (2000). but rev assumed that black holes are fed hy cold. gas during major galaxy mergers and they did not use the ΧΙΟ as a constraint.," Earlier attempts to incorporate AGN into the framework of semi-analytic models were made by Kauffmann Haehnelt (2000) and Cattaneo (2000), but they assumed that black holes are fed by cold gas during major galaxy mergers and they did not use the XRB as a constraint."727 We use the semi-analytic galaxy formation model and associated scheme for quasar Luclling developed. by NE97 and NEO0. the salient features of which we outline here.," We use the semi-analytic galaxy formation model and associated scheme for quasar fuelling developed by NF97 and NF00, the salient features of which we outline here."728 The Cole Ixaiser (1988) block mocel is used to simulate the hicrarchical erowth of clustering. while the behaviour of the eas in collapsed regions is simulated using the model of Nulsen Fabian (1995).," The Cole Kaiser (1988) block model is used to simulate the hierarchical growth of clustering, while the behaviour of the gas in collapsed regions is simulated using the model of Nulsen Fabian (1995)."729 In short. the gas in the collapsed halo is split into two regions. according to the value of laus. Hae ratio of the cooling time of the gas to its time to the centre of the halo.," In short, the gas in the collapsed halo is split into two regions, according to the value of $\tau=t_{\rm{cool}}/t_{\rm{grav}}$ , the ratio of the cooling time of the gas to its free-fall time to the centre of the halo."730 Within a radius &=Rep where 7< the gas cools rapidly ancl forms stars.," Within a radius $R=R_{\rm{CF}}$ where $\tau<1$, the gas cools rapidly and forms stars."731 Any eas at Ro»Roy has ollo ancl is assumed to participate in a cooling How (Fabian 1994)., Any gas at $R>R_{\rm{CF}}$ has $\tau>1$ and is assumed to participate in a cooling flow (Fabian 1994).732 Collapses with and without the cooling Dow atmosphere are identified as normal galaxies ancl clhwarl galaxies. respectively.," Collapses with and without the cooling flow atmosphere are identified as normal galaxies and dwarf galaxies, respectively."733 The burst of star formation in 2<Rep Leads quickly to supernovae. which can expel some or all of the remaining eas from the svstem: some gas is always expelled: from dwarl galaxies. and in normal protogalaxies hot gas which is not cjected is heated ancl enriched by the supernovae.," The burst of star formation in $R<R_{\rm{CF}}$ leads quickly to supernovae, which can expel some or all of the remaining gas from the system; some gas is always expelled from dwarf galaxies, and in normal protogalaxies hot gas which is not ejected is heated and enriched by the supernovae."734 A normal galaxy is a spiral galaxy if the hot gas cools completely before. the present or the next hierarchical collapse. otherwise it is an elliptical. galaxy.," A normal galaxy is a spiral galaxy if the hot gas cools completely before the present or the next hierarchical collapse, otherwise it is an elliptical galaxy."735 Any collapse with at most one infalling normal galaxy forms a normal ealaxy. so that dwarl galaxies are assumed to be destroved in à collapse. with their stars contributing to the spheroid of the resulting svstem.," Any collapse with at most one infalling normal galaxy forms a normal galaxy, so that dwarf galaxies are assumed to be destroyed in a collapse, with their stars contributing to the spheroid of the resulting system."736 A svstem containing more than one normal galaxy is assumed to form a group or cluster. as mergers between normal galaxies are ignored.," A system containing more than one normal galaxy is assumed to form a group or cluster, as mergers between normal galaxies are ignored."737 Any collapse that is followed less than one dvnamical time later bv further collapse is ignored., Any collapse that is followed less than one dynamical time later by further collapse is ignored.738" We use an open CDM cosmology. with Ly=50kms density parameter Q)=0.3. barvon density parameter QO1,=0.075 and as=1."," We use an open CDM cosmology, with $H_{\rm{0}}=50$ , density parameter $\Omega=0.3$, baryon density parameter $\Omega_{\rm{b}}=0.075$ and $\sigma_{8}=1$."739 NEOO proposed that quasars ave formed. ancl [ed largely bv the accretion of hot gas from the atmospheres which form around normal galaxies., NF00 proposed that quasars are formed and fed largely by the accretion of hot gas from the atmospheres which form around normal galaxies.740 Phev showed that if such an atmosphere forms a nearly “maximal” cooling How. then a central black hole can accrete at close to its Edclington limit. leacing to the exponential growth of a seed black hole.," They showed that if such an atmosphere forms a nearly “maximal” cooling flow, then a central black hole can accrete at close to its Eddington limit, leading to the exponential growth of a seed black hole."741 They also incorporated. this model into the above semi-analvtic galaxy formation model. which we adopt here with some modifications.," They also incorporated this model into the above semi-analytic galaxy formation model, which we adopt here with some modifications."742 Each of the smallest. block model units has a mass of 1.5«101AL... and contains at its contre a seed. black hole of mass Ausg.," Each of the smallest block model units has a mass of $1.5\times 10^{10}$, and contains at its centre a seed black hole of mass $M_{\rm{h(seed)}}$."743 When a block collapses. the black holes associated with all merging. sub-blocks are assumed to merge into a single. black hole.," When a block collapses, the black holes associated with all merging sub-blocks are assumed to merge into a single black hole."744 The resulting nuclear black hole grows exponentially by Bondi aceretion from, The resulting nuclear black hole grows exponentially by Bondi accretion from745"choice of 02. is arbitrary and is made in such a wav (hat its amplitude is of the order of the amplitudes of 0b, and οἱ.",choice of $\delta B_z$ is arbitrary and is made in such a way that its amplitude is of the order of the amplitudes of $\delta B_x$ and $\delta B_y$.746 We have run several simulations with different values for the slopes a ancl 9 of the spectra and the restuts seem not to be significantly allected by Chose parameters. For simplicity. we will show the resulis when a—ο=0. As a further check on the soundness of the results we have also initialized some simulations with a speetrmm of waves with an Alfvenie velocity perturbation imposed. and the results are qualitatively similar. for the leneth ancl time scales investigated here.," We have run several simulations with different values for the slopes $\alpha$ and $\beta$ of the spectra and the results seem not to be significantly affected by those parameters, For simplicity, we will show the results when $\alpha=\beta=0$ As a further check on the soundness of the results we have also initialized some simulations with a spectrum of waves with an Alfvenic velocity perturbation imposed, and the results are qualitatively similar, for the length and time scales investigated here."747 The first results Chat we show are for benchmark cases. where we have initialised the perturbation (0.8/Dy~ 1) with a single wavenunmber and not wilh a spectrum of waves.," The first results that we show are for benchmark cases, where we have initialised the perturbation $\delta B/B_0\sim 1$ ) with a single wavenumber and not with a spectrum of waves."748 Figure 14. shows the developed spectrum of magnetic [Iuctuations 05/By in wavenunmber space. at the end of the sinulation.," Figure \ref{fig1} shows the developed spectrum of magnetic fluctuations $\delta B/B_0$ in wavenumber space, at the end of the simulation."749 The only mode initially perturbed was the mode m=ion=3. which is indicated with an arrow.," The only mode initially perturbed was the mode $m=1,n=3$, which is indicated with an arrow."750 The result indicates that the harmonics of the initial mode eet predominantly excited according to a 3-wave resonant interaction (A=hy the)., The result indicates that the harmonics of the initial mode get predominantly excited according to a 3-wave resonant interaction $k=k_1+k_2$ ).751 Clearly one cannot speak of turbulent cascade in this case. but the purpose of {his simulation is to check whether the code is able to treat in a consistent ancl satisfactory manner injections of enerev αἱ small scales.," Clearly one cannot speak of turbulent cascade in this case, but the purpose of this simulation is to check whether the code is able to treat in a consistent and satisfactory manner injections of energy at small scales."752 An issue with PIC codes is indeed the unavoidable presence of noise at small scales due to the discreteness of computational particles., An issue with PIC codes is indeed the unavoidable presence of noise at small scales due to the discreteness of computational particles.753 This noise could result in the spurious effect of an inverse cascade of energy [rom large wavenumbers which is completely iumnerically generated., This noise could result in the spurious effect of an inverse cascade of energy from large wavenumbers which is completely numerically generated.754 One can see that (his effect is not important in Figure 1H.. where the modes at large  that get excited are only the higher harmonics of the initial mode.," One can see that this effect is not important in Figure \ref{fig1}, where the modes at large $k$ that get excited are only the higher harmonics of the initial mode."755 The price to pav in order (ο avoid spurious effects at small scales is (he use of an unusually large number of particles (6400 particles per A confirmation of the fact that 3-wave resonant interactions are well described in the code is shown in Figure 15.., The price to pay in order to avoid spurious effects at small scales is the use of an unusually large number of particles (6400 particles per A confirmation of the fact that 3-wave resonant interactions are well described in the code is shown in Figure \ref{fig2}.756 In this case we have excited. along with the mode m.Ξ1.η=3. ils counter-propagaling mode nm=—1.» 3.," In this case we have excited, along with the mode $m=1,n=3$, its counter-propagating mode $m=-1,n=3$ ."757 The modes initially excited are circled., The modes initially excited are circled.758 The resulting distribution of energy sadislies again the relation A=Ay+fy. giving rise to that Checkerboard As we have said. these results should only be considered asbenchmark runs.," The resulting distribution of energy satisfies again the relation $k=k_1+k_2$, giving rise to that checkerboard As we have said, these results should only be considered asbenchmark runs."759 However.," However,"760The evolution of a planet created with J=Jy at /—0 cau be represeuted by solving Eq. (5)),The evolution of a planet created with $J=J_S$ at $t=0$ can be represented by solving Eq. \ref{diffusion}) )761 with a source term 0(/)5(4—Js)., with a source term $\delta(t)\delta(J-J_S)$.762 The Laplace trausform reduces the tiiie-dependeut problem to Unfortunately. although Eq. (18))," The Laplace transform reduces the time-dependent problem to Unfortunately, although Eq. \ref{eq:odes}) )"763 is just an ordinary differeutial equation in of. we canuot solve it completely even for power law disks described by Eq. (12)).," is just an ordinary differential equation in $J$, we cannot solve it completely even for power law disks described by Eq. \ref{eq:powers}) )."764 The difficulty is in part tliat physically interesting cases have a—9< —1. which is precisely the condition for Eq. (18))," The difficulty is in part that physically interesting cases have $\alpha-\beta<-1$ , which is precisely the condition for Eq. \ref{eq:odes}) )"765 to have au irregular singular point at =0., to have an irregular singular point at $J=0$.766" However. a formal solution cau be obtained in powers of s. Replacing exp(—5/) by its Taylor series iu the Laplace trausform (17)) shows that f/4,(7) is the iP moment of fü.J) with respect to /. More interesting than the moments of f are the moments of the correspoucing flux: The probabilitythat the planet survives longer thau / before accretion. P(/). is related to the flux at the origin by dP/di=Fj(f.0)."," However, a formal solution can be obtained in powers of $s$, Replacing $\exp(-st)$ by its Taylor series in the Laplace transform \ref{eq:laplace}) ) shows that $f_n(J)$ is the $n^{\rm th}$ moment of $f(t,J)$ with respect to $t$, More interesting than the moments of $f$ are the moments of the corresponding flux: The probabilitythat the planet survives longer than $t$ before accretion, $P(t)$, is related to the flux at the origin by $dP/dt=F_J(t,0)$."767" Therefore. is the i!"" moment of the lifetime. ancl in particular. —F(0) is the mean lifetime."," Therefore, is the $n^{\rm th}$ moment of the lifetime, and in particular, $-F_1(0)$ is the mean lifetime."768 Thus we are motivated to find the £67)., Thus we are motivated to find the $f_n(J)$ .769 Substituting Eq. (19)), Substituting Eq. \ref{eq:expans}) )770 into Eq. (18)), into Eq. \ref{eq:odes}))771 leads to, leads to772profiles aud He; lin absorption.,profiles and $\sc i$ in absorption.773 The probable high binary mass ratio im 1U21271119 leads to unstable mass transfer from the secondary star. resulting in a common envelope (Dailvu Caindlav 1987).," The probable high binary mass ratio in 4U2127+119 leads to unstable mass transfer from the secondary star, resulting in a common envelope (Bailyn Grindlay 1987)."774 Tn 121271119 the Mer absorption line is blue shifted with respect to the mean velocity of the system believed to arise in a stream of gas leaving the outer Lagrangian poiut (Bailvn et al.," In 4U2127+119 the $\sc i$ absorption line is blue shifted with respect to the mean velocity of the systemm believed to arise in a stream of gas leaving the outer Lagrangian point (Bailyn et al.,"775 1989)., 1989).776 Tf the mass transfer iu 25092)630 is wustable. then we would also expect the Tes ines to be bluc-shüfted aud have low nou-sinusoidal velocity variations.," If the mass transfer in 2S0921–630 is unstable, then we would also expect the $\sc i$ lines to be blue-shifted and have low non-sinusoidal velocity variations."777 It is interesting to uote the similaritics between 250921630 and Οτο X2., It is interesting to note the similarities between 2S0921–630 and Cyg X–2.778 Both systems are long period binaries in the halo of the Galaxy. they are at high inclination angles with evolved secondaries and both contain neutron stars. [," Both systems are long period binaries in the halo of the Galaxy, they are at high inclination angles with evolved secondaries and both contain neutron stars. ["779Cyg. N-2 unust contain a neutron star because of the observed types X-ray bursts.,Cyg X-2 must contain a neutron star because of the observed $\sc i$ X-ray bursts.780 For 250921630 we cannot unequivocally state that it contains a neutron as no bursts have been secu., For 2S0921–630 we cannot unequivocally state that it contains a neutron as no bursts have been seen.781 However. this may be a result of the natural couseuqueuce of ADC sources.," However, this may be a result of the natural consenquence of ADC sources."782" It should also be noted that our upper lint to M, suggests that it is a neutron star.|", It should also be noted that our upper limit to $M_{1}$ suggests that it is a neutron star.]783 Also 630 has a binary mass ratio q~1l. which is a factor of 3 higher than that of Cve X2 (q—0.31: Casares οἳ al.," Also 2S0921--630 has a binary mass ratio $q\sim 1$, which is a factor of 3 higher than that of Cyg X–2 $q$ =0.34; Casares et al.,"784 1997). sugeestingOO that if the neutron stars in both svstenis have sinular masses. then the secoudary star in 280921630 is more massive.," 1997), suggesting that if the neutron stars in both systems have similar masses, then the secondary star in 2S0921--630 is more massive."785 However.it should be noted that the secoudary star in 250921630 is much cooler (INO: Lo ~5h0L..4) aud hence less luminous than the secondary star iu Cvg N2 (A9//: Lo ~200 L..)). contrary to what we miel have expected eiven their interred masses.," However,it should be noted that the secondary star in 2S0921–630 is much cooler $\sc iii$ ; $L_{2}\sim$ 50 ) and hence less luminous than the secondary star in Cyg X–2 $\sc iii$; $L_{2}\sim$ 200 ), contrary to what we might have expected given their inferred masses."786 This discrepency cui be recouciled if we postulate that we are seeiue 250921630 and το X.2 at very different pliases in their evolution., This discrepency can be reconciled if we postulate that we are seeing 2S0921–630 and Cyg X–2 at very different phases in their evolution.787 In (νο X.2 we are probably sccing the secoudary star which is high up on the eiaut brauch aud has lost its outer evelvope due to mass transfer aud/or radiation. leaving just the hot inner core of what had been initially a more massive star.," In Cyg X–2 we are probably seeing the secondary star which is high up on the giant branch and has lost its outer evelvope due to mass transfer and/or irradiation, leaving just the hot inner core of what had been initially a more massive star."788 Whereas. iu 630 the secondary star is not as evolved aud so 1s jear the base of the eiut. brauch.," Whereas, in 2S0921--630 the secondary star is not as evolved and so is near the base of the giant branch."789 Ouly detailed stellar evolution calculations will resolve this., Only detailed stellar evolution calculations will resolve this.790 Using high resolution optical spectra. we estimate the spectral type of the companion star in 250921630 (=V395 Car) to be a IK0/7/ star.," Using high resolution optical spectra, we estimate the spectral type of the companion star in 2S0921–630 (=V395 Car) to be a $\sc791iii$ star."792 By optimally subtracting differcut broadened versions of the conmipanion star spectrum from the average V395 Car spectrum we determine the rotational broadeniug of the companion star to be 6149 (1-0) coutributiug  to the observed flux at 6500À., By optimally subtracting different broadened versions of the companion star spectrum from the average V395 Car spectrum we determine the rotational broadening of the companion star to be $\pm$ 9 $\sigma$ ) contributing $\sim$ to the observed flux at .793. J.C. ackuowlegdessupport by the Spanish Ministerio de Educacion y Cultura through the exaut FPEQOT0-97., J.C. acknowlegdessupport by the Spanish Ministerio de Educacion y Cultura through the grant FPI-070-97.794From Figure 6.. the photometrically derived mass and distance of NACIIO-LMC-5 are consistent with the values of these properties derived by combining (he astrometric and microlensing data.,"	From Figure \ref{fig:massdist2}, the photometrically derived mass and distance of MACHO-LMC-5 are consistent with the values of these properties derived by combining the astrometric and microlensing data."795 The error bars for both determinations could be improved significantly by obtaining additional data and by improving the analvsis., The error bars for both determinations could be improved significantly by obtaining additional data and by improving the analysis.796 On (he photometric side. both (he mass and the Iuminositv of the M cwarl are inferred [rom its color.," 	On the photometric side, both the mass and the luminosity of the M dwarf are inferred from its color."797 Apart [rom the error in measuring this quantity. these inferences suffer [rom {he intrinsic clispersions of mass and Duminositv at fixed color.," Apart from the error in measuring this quantity, these inferences suffer from the intrinsic dispersions of mass and luminosity at fixed color."798 A substantial part of this dispersion is due to metallicity., A substantial part of this dispersion is due to metallicity.799 Drakeοἱal.(2004) have argued that the kinematic data are consistent with either a disk or a Chick-disk star. and therefore a range of metallicities of about 1 dex.," \citet{drake} have argued that the kinematic data are consistent with either a disk or a thick-disk star, and therefore a range of metallicities of about 1 dex."800 Hence. spectroscopic determination of the M dwarl’s metallicity would go a long wav toward shrinking the photometry-based mass/cdistance error bars.," Hence, spectroscopic determination of the M dwarf's metallicity would go a long way toward shrinking the photometry-based mass/distance error bars."801 On the astrometric/microlensing side. (here are three paths to improvement.," 	On the astrometric/microlensing side, there are three paths to improvement."802 First. of course. the distance determination could be improved by a better trisonometric parallax measurement.," First, of course, the distance determination could be improved by a better trigonometric parallax measurement."803 Moreover. because (he mass and distance measurements are highly correlated (see eq. (10]]).," Moreover, because the mass and distance measurements are highly correlated (see eq. \ref{eqn:errellipse2}] ]),"804 a more accurate distance would also improve the mass determination., a more accurate distance would also improve the mass determination.805 Unfortunately. significantlv better. parallax measurements will not come cheaply.," Unfortunately, significantly better parallax measurements will not come cheaply."806 From a comparison of equations (8)) and (9)). the 185µας error from the AC'S astrometry is about larger (han the distance estimate achieved. [rom microlensing (ancl the proper-notion measurement) alone.," From a comparison of equations \ref{eqn:trigpi}) ) and \ref{eqn:errellipse1}) ), the $185\,\muas$ error from the ACS astrometry is about larger than the distance estimate achieved from microlensing (and the proper-motion measurement) alone."807 A plausible target for a significant improvement would be a 100pias. or better vel 50rs measurement.," A plausible target for a significant improvement would be a $100\,\muas$, or better yet $50\,\muas$ measurement."808 These would vield mass determinations with fractional precisions of and.LOW... respectively.," These would yield mass determinations with fractional precisions of and, respectively."809 Note that even if the distance were known exactly. the microlens mass measurement error could only be reduced to7.," Note that even if the distance were known exactly, the microlens mass measurement error could only be reduced to."8105%... If it were only necessary to consiler (he statistical errors. such improvements could be achieved by multiplving the total length of ACS observations by 3 and 14 respectively.," If it were only necessary to consider the statistical errors, such improvements could be achieved by multiplying the total length of ACS observations by 3 and 14 respectively."811 llowever. svslematic errors may become important. ancl the discrepancy between the F606 and E814 measurements implies that caution is warranted.," However, systematic errors may become important, and the discrepancy between the F606 and F814 measurements implies that caution is warranted."812 A parallax measurement by$737 might also prove feasible., A parallax measurement by might also prove feasible.813 This seems impossible at first sight because the M dwarf has V=22.7 whereas the magnitude limit ofS/S is often said to be V.«20., This seems impossible at first sight because the M dwarf has $V=22.7$ whereas the magnitude limit of is often said to be $V<20$.814" IIowever. what fundamentally limits573 at faint magnitudes is the number of skv photons that enter its 1"" radius stop."," However, what fundamentally limits at faint magnitudes is the number of sky photons that enter its $1''$ radius stop."815 If we ignore this sky noise for the moment. a 50yas measurement al V.—22.7 would require an observation of only about 1 hour.," If we ignore this sky noise for the moment, a $50\,\muas$ measurement at $V=22.7$ would require an observation of only about 1 hour."816 An additional 30-minute observation of the V.—21 source would vield a 30pras ," An additional 30-minute observation of the $V=21$ source would yield a $30\,\muas$ "817aud From (2.1)). (2.6)) and (2.8)). the comparison principle for ODEs eives in particular Tf we suppose TZ 1. we obtain from (2.7)) that τιT7 and hence (using (2.9))): Direct computations give whore. from (2.8)) aud (2.103). we deduce that (e(7|P).etz(ατὶ1T).etz!))12[gx.,"and From \ref{ergo_eq}) ), \ref{eqn_w}) ) and \ref{2}) ), the comparison principle for ODEs gives in particular If we suppose $T\geq 1$ , we obtain from \ref{1}) ) that $\t^{+}+T\geq \widetilde{\t}^{-}$ and hence (using \ref{chiWs}) )):Direct computations give where, from \ref{2}) ) and \ref{3}) ), we deduce that $818(v(\t^{-}+T)-v(\t^{-}))-(v(\t^{+}+T)-v(\t^{+}))\geq819-1-2\|g\|_{\infty}$."820" This inequality. together with (2.19) show that 0<AIT)ας1]2|20, and since this is true for anv à>0. we obtain ILlowever. iu the case where P<1. we always have Wilt)n<αςxa= and therefore theu First. if we compute A!GPT) for PCES (05. we get: Similarly. we get A(PT)>(D)."," This inequality, together with \ref{deltaest}) ) show that $ 0\leq \l^{+}(T)-\l^{-}(T)\leq821\frac{1+2\|g\|_{\infty}}{T}+2\delta, $ and since this is true for any $\delta>0$, we obtain However, in the case where $T\leq 1$, we always have $\frac{|v(\t+T)-v(\t)|}{T}\leq \|g\|_{\infty} \leq \frac{\|g\|_{\infty}}{T}$ and therefore then First, if we compute $\l^{+}(PT)$ for $P\in\N\setminus\{0\}$ , we get: Similarly, we get $\l^{-}(PT)\geq \l^{-}(T)$."822 Cousider Tj. To>0 such that νο=T2Q for some PQCE (0].," Consider $T_{1}$, $T_{2}>0$ such that $T_{1}P=T_{2}Q$ for some $P, Q\in \N\setminus\{0\}$ ."823 Using this and (2.11)). we have similarly we have AP(T5)ACP)x=. then By the same arguments as above we can ect Recall that (2.12)) aud (2.13)) ave true when Ti/To is rational.," Using this and \ref{fin_est_lam}) ), we have similarly we have $\l^{+}(T_{2})-\l^{+}(T_{1})\leq824\frac{\xi}{T_{2}},$ then By the same arguments as above we can get Recall that \ref{lambda+}) ) and \ref{lambda-}) ) are true when $T_{1}/T_{2}$ is rational."825 By an approximation argument. joint with the continuity of AT. it is casy to see that this is still πο when T/T is any positive real umber.," By an approximation argument, joint with the continuity of $\l^{\pm}$, it is easy to see that this is still true when $T_{1}/T_{2}$ is any positive real number."826 Moreover. the identities (2.12)) and (2.13)) eive that the sequence (A (D))gp is a Cauchy sequenceas Toy x and henceithas a lint:," Moreover, the identities \ref{lambda+}) ) and \ref{lambda-}) ) give that the sequence $(\l^{\pm}(T))_{T}$ is a Cauchy sequenceas $T\rightarrow827\infty$ , and henceithas a limit:"828"equation for the monochromatic intensity at level zy in the direction (p.6) can be written2002):: where the monochromatic notation has been changed to J, and 2=0 corresponds to a bounding region for the atmosphere (e.g... the bulk interior). with a one-sided radiative boundary condition specified as Z,(0:4.0).","equation for the monochromatic intensity at level $z_0$ in the direction $(\mu, \phi)$ can be written: where the monochromatic notation has been changed to $I_\nu$ and $z=0$ corresponds to a bounding region for the atmosphere (e.g., the bulk interior), with a one-sided radiative boundary condition specified as $I_\nu(0; \mu, \phi)$."829 The first term on the RIIS of eq. (2)), The first term on the RHS of eq. \ref{eq:two}) )830" describes the cumulative absorption of £,(0:44.6) from z=0 to zo along the optical path. while the second term describes the cumulative Planck emission. and its absorption. integrated over all lavers along the optical path. from z—0 to τη."," describes the cumulative absorption of $I_\nu(0; \mu, \phi)$ from $z=0$ to $z_0$ along the optical path, while the second term describes the cumulative Planck emission, and its absorption, integrated over all layers along the optical path, from $z=0$ to $z_0$."831 The monochromatic transmissivity encapsulates the absorption (and emission) properties of the medium., The monochromatic transmissivity encapsulates the absorption (and emission) properties of the medium.832 It is (he integral of the mass absorption coefficient 7; weighted bv the amount of absorber (with mass density p). between vertical levels z and zo. along the optical path defined by the direction (ji.6).," It is the integral of the mass absorption coefficient $k_\nu$ weighted by the amount of absorber (with mass density $\rho$ ), between vertical levels $z$ and $z_0$, along the optical path defined by the direction $(\mu, \phi$ )."833" According to equation (1)). bulk Doppler shifts in a dynamic atmosphere modify. the raciative transfer by changing the monochromatic absorption coefficient (unit of cross section per unit mass). or equivalently by changing the monochromatic transmissivities. 7,(z.24:Jro). in equation (2))."," According to equation \ref{eq:one}) ), bulk Doppler shifts in a dynamic atmosphere modify the radiative transfer by changing the monochromatic absorption coefficient (unit of cross section per unit mass), or equivalently by changing the monochromatic transmissivities, ${\cal T}_\nu(z,z_0; \mu, \phi)$, in equation \ref{eq:two}) )."834 If bulk Doppler shifts are important and (he material velocity [ield is anisotropic. so is the radiative transfer.," If bulk Doppler shifts are important and the material velocity field is anisotropic, so is the radiative transfer."835 By property of isotropy of the Planck source function. a large fraction of the thermal atmospheric radiation field is carried along rays which are sienilicantly slantecl relative to the vertical. even though net flux exchange between atmospheric lavers occurs vertically.," By property of isotropy of the Planck source function, a large fraction of the thermal atmospheric radiation field is carried along rays which are significantly slanted relative to the vertical, even though net flux exchange between atmospheric layers occurs vertically."836 The next step in derivingvertical flux equations for the atmospheric radiation problem tvpically involves separate angular integrations for (he ascending (j> 0) and descending (ji< 0) fhixes 2002).. of the tvpe," The next step in derivingvertical flux equations for the atmospheric radiation problem typically involves separate angular integrations for the ascending $\mu >0$ ) and descending $\mu <0$ ) fluxes , of the type"837P-Cyent absorption in many other spectral lines formed at different wind regions. such as most of the Balmer lines.II.NIL 410830. among others.,"P-Cygni absorption in many other spectral lines formed at different wind regions, such as most of the Balmer lines, $\lambda$ 10830, among others."838 Analyses of these lines should lead to à much improved understanding of the mass-loss history of Interestingly. the morphology of the absorption-line profiles seen in Fig.," Analyses of these lines should lead to a much improved understanding of the mass-loss history of Interestingly, the morphology of the absorption-line profiles seen in Fig."839 4. closely resemble those found in the interacting SN 20056] (Trundleetal.2008)., \ref{fig3} closely resemble those found in the interacting SN 2005gj \citep{trundle08}.840. This strengthens the link between LBVs and SNe that based their assertions on the bi-stability mechanism during DDor cycles (Kotak&Vink2006;Trundleetal. 2008).. and the LBV/SN link in general (Smithetal.2007:Gal-Yam&Leonard2009)..," This strengthens the link between LBVs and SNe that based their assertions on the bi-stability mechanism during Dor cycles \citep{kv06,trundle08}, and the LBV/SN link in general \citep{smith07,galyam09}."841 We expect that our results will encourage further observational and modeling efforts to establish under which conditions LBVs explode as SNe., We expect that our results will encourage further observational and modeling efforts to establish under which conditions LBVs explode as SNe.842The contour map reveals strongly disturbed tsophotes due to underlying features (Soubeyranetal.1989:Hjorth1995).. which affect the SB profiles.,"The contour map reveals strongly disturbed isophotes due to underlying features \citep{SWB_89,HVS_95}, which affect the SB profiles."843 The unsharp masked residual image refTT r&120bdn20)wevealsablueknottyring(a andacoupleo farcsextendingtotheNoneithersideo Fthenucleusbthe Wonebeingmore pronounced.," The unsharp masked residual image \\ref{11_Ark120bdm2o}) ) reveals a blue knotty ring $a\,$$\times$$\,b\,$$\approx$$9\arcsec$$\times$$8\arcsec$ ) and a couple of arcs extending to the N on either side of the nucleus, the W one being more pronounced."844T hering producesanS Bbumpandabluec Rc profile.," The ring produces an SB bump and a blue dip on the $B\,$ $\,R_{\rm \scriptstyle C}$ profile."845 The unsharp masked residual image ref124 r&376rdmed2n)revealsabentbar., The unsharp masked residual image \\ref{12_Mrk376rdmed2n}) ) reveals a bent bar.846Itisencircledbyaring(a withknotsof star formationthatareoutstandingintheN —I¢ image ref12 yrk376vi)).," It is encircled by a ring $a\,$$\times$$\,b\,$$\approx$$5\arcsec$$\times$$3\arcsec$ ) with knots of star formation that are outstanding in the $V\,$ $\,I_{\rm \scriptstyle C}$ image \\ref{12_Mrk376vi}) )."847Thetwos piralarms getnoticeablynotasbrightand Forman , The two spiral arms get noticeably not as bright and form a weak outer pseudo-ring 848We have identified the X-ray source aas à now magnetic CV.,We have identified the X-ray source as a new magnetic CV.849 The combination of extreme soft A-ray spectrum. a strong magnetic field of B= 5044 MC (or possibly even z 10. ALG). an inverted. Balmer decrement and strong Hell lines provide strong evidence for the polar nature though no polarimetry has been obtained.," The combination of extreme soft X-ray spectrum, a strong magnetic field of B = $\pm$ 4 MG (or possibly even $\approx$ 70 MG), an inverted Balmer decrement and strong II lines provide strong evidence for the polar nature though no polarimetry has been obtained."850 The observed. values for 2 and. {μμ fice obey well the proportionality relation between these quantities found. for other polars (Beucrmann Burwitz 1995)., The observed values for $B$ and $F_{\rm thbr}$ $F_{\rm bbdy}$ obey well the proportionality relation between these quantities found for other polars (Beuermann Burwitz 1995).851 The period derived. from the optical ancl X-ray light curves is 119.9 min. right below the lower edge of the period gap.," The period derived from the optical and X-ray light curves is 119.9 min, right below the lower edge of the period gap."852" No other periodicities have been found. so that aappears to be svnchronised over the observed timescale,"," No other periodicities have been found, so that appears to be synchronised over the observed timescale."853 The coincidence in phase of the bright phase in X-ray and optical bands as well as the lack of X-ray emission during the optical faint. phase resemble the behaviour of sel-eclipsing polars like ST LAL or VV Pup (Cropper Warner (1986). Cropper (1986)) where the accretion region passes behind the limb of the white chwarl ancl is out. of sight.," The coincidence in phase of the bright phase in X-ray and optical bands as well as the lack of X-ray emission during the optical faint phase resemble the behaviour of self-eclipsing polars like ST LMi or VV Pup (Cropper Warner (1986), Cropper (1986)) where the accretion region passes behind the limb of the white dwarf and is out of sight."854 “Phe duration of the faint phase ~ gives a constraint on possible gcometries., The duration of the faint phase $\gamma$ gives a constraint on possible geometries.855 Assuming a point-like accretion spot the inclination 7 and the colatitude 3 are related. via The lack of eclipses implies /<το., Assuming a point-like accretion spot the inclination $i$ and the colatitude $\beta$ are related via The lack of eclipses implies $i < 78\degr$.856" The duration of the bright phase is x0.5 for most of the observations consistent with c907. Le. an accretion region located on the hemisphere of the white dwarf facing away from the observer (""southern hemisphere”)."," The duration of the bright phase is $\le0.5$ for most of the observations consistent with $\beta > 90\degr$, i.e. an accretion region located on the hemisphere of the white dwarf facing away from the observer (“southern hemisphere”)."857 The light curves obtained on June 19 and July 2 1994 show a much more extended bright phase., The light curves obtained on June 19 and July 2 1994 show a much more extended bright phase.858 This might indicate that the location of the accretion spot night have changed or a second accereting pole was active., This might indicate that the location of the accretion spot might have changed or a second accreting pole was active.859 The observed: X-ray. intensity during the HIA pointing in 1995 is considerably smaller than the intensity seen during the RASS 5 vears earlier. thus implying variable mass transfer to the white chwarl," The observed X-ray intensity during the HRI pointing in 1995 is considerably smaller than the intensity seen during the RASS 5 years earlier, thus implying variable mass transfer to the white dwarf."860 We note. however. that the observed count rate is an extremely sensitive function of the temperature: depending on the exact absolute temperature and the model used. the count rate is proportional to 27l6 (Meise 119904).," We note, however, that the observed count rate is an extremely sensitive function of the temperature: depending on the exact absolute temperature and the model used, the count rate is proportional to $T^{5-16}$ (Heise 1994)."861 Thus. a reduction. of the temperature. Z7 by about can account already for the observed. count rate dillerence.," Thus, a reduction of the temperature $T$ by about can account already for the observed count rate difference."862 It is therefore impossible to quantify the dillerence in mass transfer rates., It is therefore impossible to quantify the difference in mass transfer rates.863 Additional evidence for changes in the transfer rate comes from the discovery of substantial (21 mag) long-term optical variations using photographic patrol plates., Additional evidence for changes in the transfer rate comes from the discovery of substantial $>1$ mag) long-term optical variations using photographic patrol plates.864 iis covered by the 992. Ποιά (taken with the GB 40/190 cm instrument) of the Sonneberg Observatory. astrographic patrol (though very near the edge of the field. of view)., is covered by the 92 field (taken with the GB 40/190 cm instrument) of the Sonneberg Observatory astrographic patrol (though very near the edge of the field of view).865 A check of the available +100 plates reveals ssometimes (e.g. 1976 Apr. until Sep.. LOST June 30. 1993 Aug. 1315) as bright as comparison star D (labeled in Fig. 1:," A check of the available $\approx$ 100 plates reveals sometimes (e.g. 1976 Apr. until Sep., 1987 June 30, 1993 Aug. 13–15) as bright as comparison star B (labeled in Fig. \ref{chart};"866 note that due to its colour star D is notably fainter than star A in the blue band)., note that due to its colour star B is notably fainter than star A in the blue band).867 At other times it is invisible even on very deep plates (lainter than 17.5 ni.) such as 1982 Apr./May.. 1983 Jun. 6/7. 19841985 and 1992 (including the time of the spectroscopic observation)," At other times it is invisible even on very deep plates (fainter than 17.5 $_{\rm pg}$ ) such as 1982 Apr./May, 1983 Jun. 6/7, 1984–1985 and 1992 (including the time of the spectroscopic observation)."868 Unfortunately. the data are too spotty to derive a meanineful lighteurve.," Unfortunately, the data are too spotty to derive a meaningful lightcurve."869 Due to its clear variability this object is assigned the number S 10946 in the series of variable stars detected at Sonneberg Observatory., Due to its clear variability this object is assigned the number S 10946 in the series of variable stars detected at Sonneberg Observatory.870 The density of a Roche-lobe filling secondary with PH=2his2+05eem. only. weakly depending on the mass ratio d.," The density of a Roche-lobe filling secondary with is $28\pm 0.5$ g $^{-3}$, only weakly depending on the mass ratio $q$."871 Assuming that a masseradius relationship for main-sequence stars is valid for ((c.@. Patterson 1984) we find. Ado=0.16 M. and 0.2 It.., Assuming that a mass-radius relationship for main-sequence stars is valid for (e.g. Patterson 1984) we find $M_{2}=0.16$ $_{\odot}$ and $R_{2}=0.2 $ $_{\odot}$.872 The spectral type of a star with that. mass. is AL 44.5 (dIxirkpatrick AleCarthy 1994)., The spectral type of a star with that mass is M 4–4.5 (Kirkpatrick McCarthy 1994).873 We do not. see any spectral signature of the late-tvpe companion in our spectrum., We do not see any spectral signature of the late-type companion in our spectrum.874 Assuming a contribution of the secondary to the total mean optica light of S10% in the V band (V.2 2071) and using Ay —13.1 mag (Ixirkpatrick AleCarthy 1994) we find a lower lirnit on the cistance of ool dz 250 pe., Assuming a contribution of the secondary to the total mean optical light of $\lax$ in the $V$ band $V \gax 20\fm 1$ ) and using $M_{\rm V}$ =13.1 mag (Kirkpatrick McCarthy 1994) we find a lower limit on the distance of of $d \gax$ 250 pc.875 Tls is Consistent with the Ny found in the X-ray spectral fit and the galactic latitude of oof bt = 33233., This is consistent with the $N_{\rm H}$ found in the X-ray spectral fit and the galactic latitude of of $^{\rm II}$ = 3.876For more than a decade. the +-aremin radio source 334.47. associated with the z=0.206 QSO 17214343 (B1950). was known as the largest quasar (??)..,"For more than a decade, the 4-arcmin radio source 34.47, associated with the $z=0.206$ QSO 1721+343 (B1950), was known as the largest quasar \citep{Conway1977, Jagers1982}."877" Using a flat cosmology. with Ho=73 and Q,,=0.27"". its projected linear size is 0.84 Mpe (the scaling factor is 3.25 Kpe/aresec)."," Using a flat cosmology, with $H_0 =73$ and $\Omega_m = 0.27$, its projected linear size is 0.84 Mpc (the scaling factor is 3.25 kpc/arcsec)."878 That size record was taken over in 1989 by 774.26 (?).. measuring 1.1 Mpe.," That size record was taken over in 1989 by 74.26 \citep{Riley1989}, measuring 1.1 Mpc."879 Having a projected dimension of 2.3 Mpe. WENSS 00750+434 is the current record holder. although its discoverers (?) did not seem to be aware of the fact that their giant quasar is substantially larger than the then current recorc holder 11127-1304 (?)..," Having a projected dimension of 2.3 Mpc, WENSS 0750+434 is the current record holder, although its discoverers \citep{Schoen2001} did not seem to be aware of the fact that their giant quasar is substantially larger than the then current record holder $-$ 1304 \citep{Bhat1998}."880 With the aim to study the detailed properties of 334.47. à series of multi-frequency VLA observations was conductec in the mid 1980-s (co-E's Barthel. van Breugel. Kiggers).," With the aim to study the detailed properties of 34.47, a series of multi-frequency VLA observations was conducted in the mid 1980-s (co-I's Barthel, van Breugel, Jäggers)."881 Some initial radio images were obtained and published (?) but the full analysis of the radio morphological. spectral. anc polarization properties was never completed.," Some initial radio images were obtained and published \citep{Barthel1987} but the full analysis of the radio morphological, spectral, and polarization properties was never completed."882 In the meantime. the bright radio core of 334.47 was targeted by successive series of VLBI observations. from 1980 onwards (????)..," In the meantime, the bright radio core of 34.47 was targeted by successive series of VLBI observations, from 1980 onwards \citep{Breugel1981, Barthel1985, Barthel1989a, Hooi1992}."883 The detection of superluminal motion in the core of this giant radio source (?) obviously provided substantial support for the preferred orientation of the radio-loud quasar class., The detection of superluminal motion in the core of this giant radio source \citep{Barthel1989a} obviously provided substantial support for the preferred orientation of the radio-loud quasar class.884 The book not being closed on this remarkable object combined with renewed interest in giant radio sources. within both radio source unification and evolution models (e.g..??) led us to reexamine the original VLA data.," The book not being closed on this remarkable object combined with renewed interest in giant radio sources, within both radio source unification and evolution models \citep[e.g.,][]{Ishwara1999,885Machalski2006} led us to reexamine the original VLA data."886 Do its large-scale radio properties agree with the proposition that 334.47 — despite its giant projected dimension — is oriented relatively close to the line of sight. as inferred from its nuclear radio properties?," Do its large-scale radio properties agree with the proposition that 34.47 -- despite its giant projected dimension – is oriented relatively close to the line of sight, as inferred from its nuclear radio properties?"887 This is the prime question to be addressed in this paper., This is the prime question to be addressed in this paper.888 Radio observations of 122334.47 have been made with the VLA using its C-band (6em) and L-band (20cm) and at three different array configurations. yielding four data sets: two different resolutions at two different wavelengths.," Radio observations of 34.47 have been made with the VLA using its C-band (6cm) and L-band (20cm) and at three different array configurations, yielding four data sets: two different resolutions at two different wavelengths."889 All data were taken in 1984 by Barthel and Van Breugel., All data were taken in 1984 by Barthel and Van Breugel.890 Typical resolution parameters are listed in Table 1.., Typical resolution parameters are listed in Table \ref{tab:table1}.891 On-source integration times for the observations are in the range of 1.5 to 3 hours for each configuration/band combination., On-source integration times for the observations are in the range of 1.5 to 3 hours for each configuration/band combination.892 10 to 20 minutes scans on 334.47 covering a range of hour angles were interspersed with short observations of nearby phase and amplitude calibrator B17324389., 10 to 20 minutes scans on 34.47 covering a range of hour angles were interspersed with short observations of nearby phase and amplitude calibrator B1732+389.893 2286 served as absolute amplitude calibrator and also to correct for the phase difference of right and left polarization., 286 served as absolute amplitude calibrator and also to correct for the phase difference of right and left polarization.894 Coordinates of the radio sources are shown in Table 2.., Coordinates of the radio sources are shown in Table \ref{tab:table2}.895 Two intermediate frequencies (IFs) with bandwidths ranging from MMHz to MMHz were used., Two intermediate frequencies (IFs) with bandwidths ranging from MHz to MHz were used.896 The detailed observing parameters are listed in Table 3.., The detailed observing parameters are listed in Table \ref{tab:table3}.897 The array performed well: judged from the calibration sources. the antenna phase. amplitude. and polarization. calibration appeared stable to within a few percent.," The array performed well: judged from the calibration sources, the antenna phase, amplitude, and polarization calibration appeared stable to within a few percent."898 The radio data were of high quality. and there was no need for extensive flagging of discrepant points.," The radio data were of high quality, and there was no need for extensive flagging of discrepant points."899 Reduction of the data was performed using standard NRAO AIPS image processing routines. including several steps of self-calibratior (phase only. followed by amplitude self-calibration).," Reduction of the data was performed using standard NRAO AIPS image processing routines, including several steps of self-calibration (phase only, followed by amplitude self-calibration)."900 Several successive self-calibration and cleaning eycles with varying amplitude gain factors generally led to a rapid convergence towards the final images., Several successive self-calibration and cleaning cycles with varying amplitude gain factors generally led to a rapid convergence towards the final images.901 In order to uncover the weak diffuse emission. the final deep cleaning steps involve well over 100.000 iterations.," In order to uncover the weak diffuse emission, the final deep cleaning steps involve well over 100.000 iterations."902 Multi-resolution images were obtained by combining indatasets., Multi-resolution images were obtained by combining $uv$ -datasets.903 However. 334.47 is known to have a (strong) variable radio core.," However, 34.47 is known to have a (strong) variable radio core."904 Hence the multi-resolution images involve subtraction of the cores in both data sets. with subsequent calibrating. Imaging and cleaning of the coneatenated data set. and restoration of a core in the resulting multi-resolution image.," Hence the multi-resolution images involve subtraction of the cores in both data sets, with subsequent calibrating, imaging and cleaning of the concatenated data set, and restoration of a core in the resulting multi-resolution image."905cclus. have been detected.,"cluster, have been detected."906theoretical models of both tvpes of GRD share many similarities. (he most important of them being the Formation of an ultrarelativistic jet.,"theoretical models of both types of GRB share many similarities, the most important of them being the formation of an ultrarelativistic jet."907 SGRB jet models generally. probe a clilferent part of the possible parameter space for such jets than long GRBs. although some overlap exists will underluminous instances of the latter (e.g. GRB 100316D. Starlingetal.2011)).," SGRB jet models generally probe a different part of the possible parameter space for such jets than long GRBs, although some overlap exists with underluminous instances of the latter (e.g. GRB 100316D, \citealt{Starling2011}) )."908" The overall οποιον release lor SGRBs is of the order LO7"" eyes (rather than. 1077. ergs). the cireumburst particle densities of order 10—1 * (rather than | oE 7) and they are less collimated (although there is currently little observational confirmation of the latter. in hydrodynamical models for long GRBs. e.g. \lacFaclven&Woosley1999.. the jet becomeV. collimated by passing through a dense stellar interior."," The overall energy release for SGRBs is of the order $10^{48-50}$ ergs (rather than $10^{52}$ ergs), the circumburst particle densities of order $10^{-5} - 1$ $^{-3}$ (rather than 1 $^{-3}$ ) and they are less collimated (although there is currently little observational confirmation of the latter, in hydrodynamical models for long GRBs, e.g. \citealt{MacFadyen1999}, the jet becomes collimated by passing through a dense stellar interior."909 This mechanism is absent for SGRBs}., This mechanism is absent for SGRBs).910 Reviews of SGRB science can be found in Nakar(200).. Gehrelsetal.(2009) and a recent comparison to long GRBs in Nvsewanderοἱal.(2009).," Reviews of SGRB science can be found in \cite{Nakar2007}, \cite{Gehrels2009} and a recent comparison to long GRBs in \cite{Nysewander2009}."911. Like long GRBs. short and underluminous GRBs produce afterglows peaking al progressively longer wavelengths with time. although (hey are harder to detect because they are intrinsically fainter.," Like long GRBs, short and underluminous GRBs produce afterglows peaking at progressively longer wavelengths with time, although they are harder to detect because they are intrinsically fainter."912 Ánalviical models of SGRB afterelows suffer from the same simplifications and shortcomings as those of long GRBs Gnainiv with respect to jet decollimation and off-axis emission)., Analytical models of SGRB afterglows suffer from the same simplifications and shortcomings as those of long GRBs (mainly with respect to jet decollimation and off-axis emission).913 These can be addressed through combining high-resolution relativistic hydrodynamics (RIED) simulations with numerical radiative translIer for svuehrotron radiation., These can be addressed through combining high-resolution relativistic hydrodynamics (RHD) simulations with numerical radiative transfer for synchrotron radiation.914 Such simulations have already been performed for lone GRBs (e.g. Zhang&MacFEadyenelal. 2010a)).," Such simulations have already been performed for long GRBs (e.g. \citealt{Zhang2009, vanEerten2010}) )."915 A more accurate understanding of short GRB alterglows is currently especially interesting not only because (μον are actually being detected. starting a few νους ago. but also because a new generation of extremely sensitive detectors of SGRBs is becoming operational.," A more accurate understanding of short GRB afterglows is currently especially interesting not only because they are actually being detected starting a few years ago, but also because a new generation of extremely sensitive detectors of SGRBs is becoming operational."916 On the one hand there are instruments such as LOFAR or SIVA. that will detect SGRD (afterglow) emission through the traditional electromagnetic (EM) channel. but at unprecedented long wavelengths on the order of tens of MIIz rather than GllIz (The lower limit goal for SNA is GO MIIz. for SIXA pioneer project ASIXAP it is 300 MIIz. 2008..," On the one hand there are instruments such as LOFAR or SKA, that will detect SGRB (afterglow) emission through the traditional electromagnetic (EM) channel, but at unprecedented long wavelengths on the order of tens of MHz rather than GHz (The lower limit goal for SKA is 60 MHz, for SKA pioneer project ASKAP it is 300 MHz, \citealt{Johnston2008}."917 for LOFAR it is ~10 MlIz. Rottgering 2006)).," for LOFAR it is $\sim 10$ MHz, \citealt{Rottgering2006}) )."918 Transient monitoring campaigns with these instruments should be able to detect. afterglows even if the prompt emission remains unseen., Transient monitoring campaigns with these instruments should be able to detect afterglows even if the prompt emission remains unseen.919 On the other hand. completely new channels are becoming available [or GRB detection: multiple gravilational-wave (GW) detectors are currently in operation (e.g. LIGO. Abbottetal.2009 and Virgo. Acerneseetal. 2003)) ancl upgrades are anticipated.," On the other hand, completely new channels are becoming available for GRB detection: multiple gravitational-wave (GW) detectors are currently in operation (e.g. LIGO, \citealt{Abbott2009} and Virgo, \citealt{Acernese2008}) ) and upgrades are anticipated."920 The amount of information that can be obtained [rom GW detections can be significantly enhanced by information from their EM counterparts that can help break degeneracies in GW model fits (Nissankeetal.2010)., The amount of information that can be obtained from GW detections can be significantly enhanced by information from their EM counterparts that can help break degeneracies in GW model fits \citep{Nissanke2010}.921. Also. the expected observer time between the GW signal and the peak of the alterelow signal is expected to be on the order of several clays ab least. so a GW localization can be used to increase the odds of detecting an afterglow.," Also, the expected observer time between the GW signal and the peak of the afterglow signal is expected to be on the order of several days at least, so a GW localization can be used to increase the odds of detecting an afterglow."922 It is therefore important to accurately understand (he relationships between SGRB energy. collimation and observer angle and their observational implications (see also," It is therefore important to accurately understand the relationships between SGRB energy, collimation and observer angle and their observational implications (see also"923Sou = 80Jy and 54154 = 196 Jy (Wainscoat et al.,$S_{60}$ = 80 Jy and $S_{100}$ = 196 Jy (Wainscoat et al.924 1987: Rice et al., 1987; Rice et al.925 1988; Young et al., 1988; Young et al.926 1989). the infrared/submillimeter spectrum of NGC 891 is now well-determined.," 1989), the infrared/submillimeter spectrum of NGC 891 is now well-determined."927 Assuming a dust emissivity proportional to À?. we have fitted these flux-densities with various dust temperatures. (," Assuming a dust emissivity proportional to $\lambda^{-2}$, we have fitted these flux-densities with various dust temperatures. ("928i).,i).929 Longwards of 100j/m. a good fit is obtained with a dust temperature {η~ 21 K. However. this fit leaves the mid-infrared fluxes and most of the 60;:m flux to be explained.," Longwards of $\mu$ m, a good fit is obtained with a dust temperature $T_{\rm d} \approx$ 21 K. However, this fit leaves the mid-infrared fluxes and most of the $\mu$ m flux to be explained."930 The interstellar dust models by Déssert. Boulanger & Puget (1990) suggest that virtually all of the 12;/m flux and about 50% of the 255m flux is attributable to PAH particles.," The interstellar dust models by Déssert, Boulanger $\&$ Puget (1990) suggest that virtually all of the $\mu$ m flux and about $\%$ of the $\mu$ m flux is attributable to PAH particles."931 This implies a ratio Fo5/Fey = 0.1 for the remaining very-small grain (VSG) component which suggests an average VSG size somewhat larger than in the Solar Neighbourhood. t.e. about 10 nm instead of 7 nm (see Déssert et al.," This implies a ratio $F_{25}/F_{60}$ = 0.1 for the remaining very-small grain (VSG) component which suggests an average VSG size somewhat larger than in the Solar Neighbourhood, i.e. about 10 nm instead of 7 nm (see Déssert et al."932 1993)., 1993).933 We have used equation (2) from Guéllin et al. (, We have used equation (2) from Guéllin et al. (9341993) to calculate the total hydrogen mass associated with the radiating dust (assuming WZ/Z.=1.6)and find Mj=3« ΠΜ...,1993) to calculate the total hydrogen mass associated with the radiating dust (assuming $b(Z/Z_{\odot}$ = 1.6) and find $M_{\rm H} = 3 \times 10^{9}$ $_{\odot}$.935"Once the ePSF is known from bright stars, the non-uniformity of the PRF is immaterial.","Once the ePSF is known from bright stars, the non-uniformity of the PRF is immaterial."936" Of course if each pixel has a different PRF, then the template ePSFs will be incorrect, leading to magnitude errors."," Of course if each pixel has a different PRF, then the template ePSFs will be incorrect, leading to magnitude errors."937 But it is important to recall that only variations at spatial frequencies below 21D/A can make any difference., But it is important to recall that only variations at spatial frequencies below $2\pi D/\lambda$ can make any difference.938" Unless the PRF is grossly larger than the Airy disk (and the charge-diffusion scale), inter-pixel variations will be strongly damped in the ePSF."," Unless the PRF is grossly larger than the Airy disk (and the charge-diffusion scale), inter-pixel variations will be strongly damped in the ePSF."939 I plot in Figure 2 the relative accuracy for a pixellated Airy PSF as a function of pixel size and interlacing., I plot in Figure \ref{centrNyq} the relative accuracy for a pixellated Airy PSF as a function of pixel size and interlacing.940 The penalty for large pixels is more severe for astrometric observations than for photometry., The penalty for large pixels is more severe for astrometric observations than for photometry.941 Interlacing at N=2 approaches Nyquist centroiding errors for P<2 in all cases; likewise N=3 recovers all information up to P<3., Interlacing at $N=2$ approaches Nyquist centroiding errors for $P\lesssim2$ in all cases; likewise $N=3$ recovers all information up to $P\lesssim3$.942" For P>3 we see that N=3 interlacing recovers the Nyquist accuracy in the median case, but an unfavorably positioned star can have greatly degraded astrometric accuracy."," For $P>3$ we see that $N=3$ interlacing recovers the Nyquist accuracy in the median case, but an unfavorably positioned star can have greatly degraded astrometric accuracy."943" In contrast to the photometric measurement, an astrometric measurement of a bright star is degraded by large pixels."," In contrast to the photometric measurement, an astrometric measurement of a bright star is degraded by large pixels."944 But the dependence of o; on P is not as steep as in the faint case., But the dependence of $\sigma_x$ on $P$ is not as steep as in the faint (background-limited) case.945" For point-source measurements, therefore, I find it is typically necessary to interlace exposures"," For point-source measurements, therefore, I find it is typically necessary to interlace exposures"946Once the orbital distribution at the end of the main sequence has been determined. using the simulations of Sec. 23...,"Once the orbital distribution at the end of the main sequence has been determined using the simulations of Sec. \ref{sec:ms},"947 we ren studied evolution »vond the main sequence. including gacellar mass loss.," we then studied evolution beyond the main sequence, including stellar mass loss."948 Phe star loses mass on timescales that are long compared to the orbital timescales and. thus this should be an acliabatic process., The star loses mass on timescales that are long compared to the orbital timescales and thus this should be an adiabatic process.949" Indeed this is seen to be the case for all test particles not scattered. by the planet. and the planet itself,", Indeed this is seen to be the case for all test particles not scattered by the planet and the planet itself.950 As the stars mass decreases by a factor of 3. their orbital radii increase by the same factor. whilst their cecentricities anc inclinations remain constant.," As the star's mass decreases by a factor of 3, their orbital radii increase by the same factor, whilst their eccentricities and inclinations remain constant."951" ""This would happen for all particles and the planet itself: however as the stellar mass decreases and the ratio of the planets mass to the stellar mass increases. the zone of inlluence of the planet increases."," This would happen for all particles and the planet itself; however as the stellar mass decreases and the ratio of the planet's mass to the stellar mass increases, the zone of influence of the planet increases."952 For these simulations. where the stellar mass is decreased. by a [actor of 3. the size of the chaotic zone increases. by a factor⋅ of ⋅⋅⊐3 (see Ίσα. 3)).," For these simulations, where the stellar mass is decreased by a factor of 3, the size of the chaotic zone increases by a factor of $3^{2/7}$ (see Eq. \ref{eq:chaos}) )."953" Analytically a prediction for the amount of mass scattered can be found by assuming5 that all test particles inside of the chaotic zone post-miass loss. but outside of its smaller pre-mass loss value. are scattered. given by: where óa,45,4,,,€) 1s the initial size of the chaotic zone (Eq. 3))."," Analytically a prediction for the amount of mass scattered can be found by assuming that all test particles inside of the chaotic zone post-mass loss, but outside of its smaller pre-mass loss value, are scattered, given by: where $\delta a_{chaos}(0)$ is the initial size of the chaotic zone (Eq. \ref{eq:chaos}) ),"954 αν) is the planet's initial semi-major axis. @ is taken as 1.0 ancl A=My;say(OY(2°E1) is a constant determined. from the initial belt. mass.," $a_{pl}(0)$ is the planet's initial semi-major axis, $\alpha$ is taken as 1.0 and $K=M_{belt}/\pi a_{pl}(0)(2^{2/3}-1)$ is a constant determined from the initial belt mass."955 The right-hand. panel of Fig., The right-hand panel of Fig.956 5. compares the amount of mass scattered. following mass loss and liver of further evolution. ound in the numerical simulations. to the analytic increase in the size of the chaotic zone.," \ref{fig:prempl} compares the amount of mass scattered, following mass loss and 1Gyr of further evolution, found in the numerical simulations, to the analytic increase in the size of the chaotic zone."957 The numerical simulations show approximately the same dependence with planet mass as the analytic prescription., The numerical simulations show approximately the same dependence with planet mass as the analytic prescription.958 The simulation with Cae=OO and Pasa=0.0 is closest to the analytic prescription. whilst as anticipated the simulations with higher initial eccentricities and inclinations scatter more test. particles.," The simulation with $e_{max}=0.0$ and $i_{max}=0.0$ is closest to the analytic prescription, whilst as anticipated the simulations with higher initial eccentricities and inclinations scatter more test particles."959 The main cause of scattering post stellar mass loss in these simulations is the increase in the extent of the chaotic region close to the planet., The main cause of scattering post stellar mass loss in these simulations is the increase in the extent of the chaotic region close to the planet.960 This extent. can be estimated analytically from. Eq. 3..," This extent can be estimated analytically from Eq. \ref{eq:chaos},"961 giving Eq. 6...," giving Eq. \ref{eq:manal},"962 however this unclerestimates Mau; by a factor of a few if the belt is initially clynamically hot., however this underestimates $M_{scatt}$ by a factor of a few if the belt is initially dynamically hot.963 We investigated the fate of scattered. bodies as a function of planet mass., We investigated the fate of scattered bodies as a function of planet mass.964 This is shown in the left. hand. panel of Fig. 6.., This is shown in the left hand panel of Fig. \ref{fig:mpl}.965 Phe analytic formulation does not give the ultimate fate of bodies. so it is necessary to use N-bocky simulations.," The analytic formulation does not give the ultimate fate of bodies, so it is necessary to use N-body simulations."966" The majority of the mass that is scattered. by. the plane ends up in the inner planetary system. according to our definition of ""scattered in’."," The majority of the mass that is scattered by the planet ends up in the inner planetary system, according to our definition of `scattered in'."967 The fraction of the mass tha is ejected increases with planet mass., The fraction of the mass that is ejected increases with planet mass.968 This is because higher mass planets give test particles a much larger kick per encounter and thus are more likely to scatter. bodies ou of the system after fewer encounters., This is because higher mass planets give test particles a much larger kick per encounter and thus are more likely to scatter bodies out of the system after fewer encounters.969 Multiple. encounters are required however to raise the test particle's eccentricity high enough that it is ejected., Multiple encounters are required however to raise the test particle's eccentricity high enough that it is ejected.970 Assuming that the Tisserzux parameter is conserved. for a test particle encountering the planet with a semi-major axis equal to the planets and zero inclination. the condition ο0.405 must be satisfied. for it to be ejected.," Assuming that the Tisserand parameter is conserved, for a test particle encountering the planet with a semi-major axis equal to the planet's and zero inclination, the condition $e>0.405$ must be satisfied for it to be ejected."971 No test. particles in our simulations start with such a high eccentricity and hence several encounters. each of which increase the eccentricity are required before a particle is ejected.," No test particles in our simulations start with such a high eccentricity and hence several encounters, each of which increase the eccentricity are required before a particle is ejected."972 Lower mass planets. on the other hand. tend to scatter test particles many many times before they get. ejected.," Lower mass planets, on the other hand, tend to scatter test particles many many times before they get ejected."973 This leads to an increased. chance of a test. particle having α«coO; at some point before it is ejectecl ancl hence in our definition being scattered in., This leads to an increased chance of a test particle having $a<a_{in}$ at some point before it is ejected and hence in our definition being scattered in.974 “Phere is a general trend that higher mass planets scatter test particles on shorter timescales and therefore clear any bodies from the scattered disc before the end of the simulation. whereas lower mass planets end the simulations with a higher mass in the," There is a general trend that higher mass planets scatter test particles on shorter timescales and therefore clear any bodies from the scattered disc before the end of the simulation, whereas lower mass planets end the simulations with a higher mass in the"975Altlough our analvsisis largely analytic. we have found that dit is 1ecessary to do some direct numerica] simulatious to dete1uine if the initial invariant. probaπιty clisributio1 p (or rather its projeclion to Le»wer cimension) is ergodic.,"Although our analysis is largely analytic, we have found that it is necessary to do some direct numerical simulations to determine if the initial invariant probability distribution $\rho$ (or rather its projection to lower dimension) is ergodic."976 For some choices ο“il ial distribution ancl two-form. he dyuanics is not chaotic at all. in which case p has eretalOl as an iuvariant cistribution over perioic or quasi-periodic trajectories.," For some choices of the initial distribution and two-form, the dynamics is not chaotic at all, in which case $\rho$ has the interpretation as an invariant distribution over periodic or quasi-periodic trajectories."977 Du nlally (her inslances. chaotic trajecto‘ies do not visit all regious where p has support. althoug1ithe iuiial distributior cau be renderec ergodic »v restrictii& the domain of support and adjustie the 101nalization.," In many other instances, chaotic trajectories do not visit all regions where $\rho$ has support, although the initial distribution can be rendered ergodic by restricting the domain of support and adjusting the normalization."978 When an analvlic expression Cal be giveu lor the restricted domail1 of suppor. which cal uever be doue with absolute certaiuy since these domains are deteEned tunerically. we cau make very well motivate conjectures [or exact equal time nomentSs," When an analytic expression can be given for the restricted domain of support, which can never be done with absolute certainty since these domains are determined numerically, we can make very well motivated conjectures for exact equal time moments."979 I1 he absence of an analytic expression for the restilως| domain. one can not imake staements about exact moments.," In the absence of an analytic expression for the restricted domain, one can not make statements about exact moments."980 However. we expec4 that p still determines the ratios of frequencies with whicl a chaotic trajectory visits regious of phase space within which t1ο Chaotic invariant set has equivaleut local geometry.," However, we expect that $\rho$ still determines the ratios of frequencies with which a chaotic trajectory visits regions of phase space within which the chaotic invariant set has equivalent local geometry."981 Tn the oresent work. we will [octs on dyamical systeus on E\. With polynomial velocity fields.," In the present work, we will focus on dynamical systems on $\mathbb{R}^N$, with polynomial velocity fields."982 However the iuverse mehod we cese‘ibe may be generalizale to dynamical systenis iu spaces witl other topologies. sich as classical spin systeius on Sg.," However the inverse method we describe may be generalizable to dynamical systems in spaces with other topologies, such as classical spin systems on $S^N \otimes\mathbb{R}^N$."983 The uxMivatiou for this wor& ls severaold., The motivation for this work is several-fold.984 Oue iutentio Lis to provide exact so]utions which can ye used as testing &‘ouuds for threewetical ideas. aud as beuchinarks for approxi1nate uethods to compute the statisties of non-lirear dynamical systems.," One intention is to provide exact solutions which can be used as testing grounds for theoretical ideas, and as benchmarks for approximate methods to compute the statistics of non-linear dynamical systems."985 Another intention in το orovkle a means to reverse engileer systelus very close to oues of plivsical interest. altlough we will make uo attempt to do so in this ititial study.," Another intention is to provide a means to reverse engineer systems very close to ones of physical interest, although we will make no attempt to do so in this initial study."986 The principe difficulty in coustitcling dhivsical systems seems to be the choice of two-form. which has no cirect physical interpretation.," The principle difficulty in constructing physical systems seems to be the choice of two-form, which has no direct physical interpretation."987 The orgauizatiou of this artic eis as folows., The organization of this article is as follows.988 In section 2 we briefly review the Fokker-Plauck and. Hopf equatioIs governing the statistics of stochastic ancl chaoic dynamical systeiis., In section 2 we briefly review the Fokker-Planck and Hopf equations governing the statistics of stochastic and chaotic dynamical systems.989 We introduce the inverse inethod in section 3. and glve exaiiples of chaotic systems witl three eerees ol [freedom aud invariaut probability distributions which are polyuomlal withi1 their omaiu of support.," We introduce the inverse method in section 3, and give examples of chaotic systems with three degrees of freedom and invariant probability distributions which are polynomial within their domain of support."990 lu section |l. we give au example with our degrees of [reeclom.," In section 4, we give an example with four degrees of freedom."991 The luverse —jethod. for distributions witl more Complicated analytic structure is discussed iu seclon 5. where we give ai example wit 3+) degrees. of freedom.," The inverse method for distributions with more complicated analytic structure is discussed in section 5, where we give an example with 3 degrees of freedom."992 Couclitious lor uniqueness of the invariaut istributiou iu thee coutext [9] he inve‘se method are cliscussecl in section 6., Conditions for uniqueness of the invariant distribution in the context of the inverse method are discussed in section 6.993 In seclon T. we describe the inverse metlod for dynamical systems vvith Gaussian noise and a cass of istributious which arise in tle context of quautuim field tleory.," In section 7, we describe the inverse method for dynamical systems with Gaussian noise and a class of distributions which arise in the context of quantum field theory."994 Section 8 contaius conc‘lucling remarks., Section 8 contains concluding remarks.995" Couskler au NV dimniensioual cdsnamical system of the form where f4,(/) is a Gaussian ranelom force for which and the brackets [---] indicate an average over the random variable.", Consider an $N$ dimensional dynamical system of the form where $f_n(t)$ is a Gaussian random force for which and the brackets $[\cdots]$ indicate an average over the random variable.996 The time evolution of, The time evolution of997Sextans A (DDO 75) is a dwarl irregular galaxy. which lies in a small group of galaxies including NGC! 3109. Sextans D. and the Antlia chwarl at a distance of approximately 1.4 Alpe.,"Sextans A (DDO 75) is a dwarf irregular galaxy, which lies in a small group of galaxies including NGC 3109, Sextans B, and the Antlia dwarf at a distance of approximately $1.4$ Mpc."998 The group appears to not be bound to the Local Group (vandenBergh1999).. making il (he nearest eroup of galaxies to us.," The group appears to not be bound to the Local Group \citep{van99}, making it the nearest group of galaxies to us."999" Cepheids were discovered in the galaxy by Sandage&Carlson(1982).. who calculated a distance modulus of jiu,=25.6+0.2."," Cepheids were discovered in the galaxy by \citet{san82}, who calculated a distance modulus of $\mu_0 = 25.6 \pm 0.2$."1000 Later work (Sandage&Carlson1935: improved the photometry aud adjusted the Cepheid magnitudes by over half a magnitude fainter. a change (hal was largely counteracted by revisions to the period-Iuminosity relation.," Later work \citep{san85,wal87} improved the photometry and adjusted the Cepheid magnitudes by over half a magnitude fainter, a change that was largely counteracted by revisions to the period-luminosity relation."1001 DPiotto.Capaccioli.&Pellegrini(1994). reobserved the five Sandage Carlson Cepheids and added. observations of five new Cepheids in Sextans A. Thev derived a distance modulus of jt=25.71£0.20 based on a distance modulus of 18.5 for the LMC., \citet{pio94} reobserved the five Sandage Carlson Cepheids and added observations of five new Cepheids in Sextans A. They derived a distance modulus of $\mu_0 = 25.71 \pm 0.20$ based on a distance modulus of 18.5 for the LMC.1002 Sakai.Madore. added new. single epoch photometry of the six Cepheids with periods between LO anc 25 days and calculated a distance modulus of fy=25.85+0.15 as well as an RGB tip distance modulus of ji=25.74+ 0.13.," \citet{sak96} added new, single epoch photometry of the six Cepheids with periods between 10 and 25 days and calculated a distance modulus of $\mu_0 = 25.85 \pm 0.15$ as well as an RGB tip distance modulus of $\mu_0 = 25.74 \pm 0.13$ ."1003projections of the simulation box. we ean crudely measure a kind of sample variance which we call anisotropic sample variance (ASV).,"projections of the simulation box, we can crudely measure a kind of sample variance which we call anisotropic sample variance (ASV)."1004 If the halo-mass correlation function were exactly isolropic. all (hree projections would agree precisely.," If the halo-mass correlation function were exactly isotropic, all three projections would agree precisely."1005 Since (his is only (rue in the infinite volume limit. there will be differences between the three projections of the simulation as well as small departures [rom isotropy in any real measurement.," Since this is only true in the infinite volume limit, there will be differences between the three projections of the simulation as well as small departures from isotropy in any real measurement."1006 On small scales. these differences arise [rom (he asphericity of halos: if halo orientations are not strongly correlated. (he residual ellipticity will result in a small random error that will decrease as ~ήνως:," On small scales, these differences arise from the asphericity of halos: if halo orientations are not strongly correlated, the residual ellipticity will result in a small random error that will decrease as $\sim 1/\sqrt{N_{halos}}$."1007 More. explicitly. we can define the halo ellipticity along the z-direction as σ”)/σ”. where o? is the second moment of the cluster density distribution along the projected direction. and 67>=o;+0;+07 delines+ the characteristic. cluster size.," More explicitly, we can define the halo ellipticity along the $z$ -direction as $e_z = (3 \sigma_z^2 - \sigma^2)/\sigma^2$ , where $\sigma_z^2$ is the second moment of the cluster density distribution along the projected direction and $\sigma^2 = \sigma_x^2 +1008\sigma_y^2 +\sigma_z^2$ defines the characteristic cluster size."1009. The ensemble average of e. is zero bv symmetry. but the rms for a finite sample will be zero within £y/<(22γω.," The ensemble average of $e_z$ is zero by symmetry, but the rms for a finite sample will be zero within $\pm \sqrt{<e_z^2>/N_{halos}}$."1010 One can show that this rms halo ellipticity induces a multiplicative correction factor in the projected density ancl all derived. quantities (p and M) of Ed«e22(Notes: this factor will vary randomly [rom realization to realization (or from projection to projection within a single5 N-body realization).," One can show that this rms halo ellipticity induces a multiplicative correction factor in the projected density and all derived quantities $\rho$ and M) of $1 \pm1011\sqrt{<e_z^2>/N_{halos}}$; this factor will vary randomly from realization to realization (or from projection to projection within a single N-body realization)."1012 The rms halo ellipticity VV«€(2> appears to be about 0.5 for the massive halos in the N-body simulation described above., The rms halo ellipticity $\sqrt{<e_z^2>}$ appears to be about 0.5 for the massive halos in the N-body simulation described above.1013 Since large survey samples will have very. many clusters. (his correction will usually be a very small effect.," Since large survey samples will have very many clusters, this correction will usually be a very small effect."1014 For example. in (he sample used in Chis study. there are 1226 halos above (he mass threshold in the simulation. resulting in an expected multiplicative variance of £1.4% in the inferred. profiles.," For example, in the sample used in this study, there are 1226 halos above the mass threshold in the simulation, resulting in an expected multiplicative variance of $\pm10151.4\%$ in the inferred profiles."1016 This estimate agrees verv well with the observed scatter between the three different projections on small ancl intermediate scales. as shown below in Figures 2 and 3.," This estimate agrees very well with the observed scatter between the three different projections on small and intermediate scales, as shown below in Figures 2 and 3."1017 The SDSS cluster samples are (vpically larger than this. so the effect. will be correspondingly reduced.," The SDSS cluster samples are typically larger than this, so the effect will be correspondingly reduced."1018" Lessmassive halos (these are M.=10111 ). being more common. will have a larger ;/N5,,,; and thus Chis will be reduced further."," Lessmassive halos (these are $M=10^{14} h^{-1}M_{\sun}$ ), being more common, will have a larger $N_{halos}$ and thus this will be reduced further."1019 On larger scales. where the halo-mass correlation Iunction is dominated by contributions from mass elements in halos different [rom the lens halo (i.e.. where. in halo model terms. the (wo-halo term dominates (Seljak2000;Mandelbaumetal. 2004))). the asymmetric sample variance arises predominantly Irom the shapes of larger-scale structures such as filaments aud superclusters.," On larger scales, where the halo-mass correlation function is dominated by contributions from mass elements in halos different from the lens halo (i.e., where, in halo model terms, the two-halo term dominates \citep{seljak:halos,mandelbaum:diss-v-halo}) ), the asymmetric sample variance arises predominantly from the shapes of larger-scale structures such as filaments and superclusters."1020 Since there are fewer structures contributing to this part of the ASV (fewer filaments than halos). aud since these large structures are more asvmmetric than the halos. the variance between projections is expected to be larger on large scales (han small scales. in qualitative agreement with Figure 2. below.," Since there are fewer structures contributing to this part of the ASV (fewer filaments than halos), and since these large structures are more asymmetric than the halos, the variance between projections is expected to be larger on large scales than small scales, in qualitative agreement with Figure \ref{fig:rho} below."1021 This large-scale asymmetric sample variance is expected to scale as Vv where V is the volume of the survey., This large-scale asymmetric sample variance is expected to scale as $1/\sqrt{V}$ where $V$ is the volume of the survey.1022 When the shot noise from galaxy shapes (i.e.. the shape noise) is sullicientlv small. (he large-scale errors will be dominated by the ASV.," When the shot noise from galaxy shapes (i.e., the shape noise) is sufficiently small, the large-scale errors will be dominated by the ASV."1023" Judging by the volume of our simulation and the scatter that we see al scales ol a few Mpc/h. we expect this large-scale multiplicative error to scale roughly as 24x(V/Gpe?)0.5 "". although it may vary with scale 2."," Judging by the volume of our simulation and the scatter that we see at scales of a few Mpc/h, we expect this large-scale multiplicative error to scale roughly as $2\% ~\times (V/Gpc^3)^{-0.5}$ , although it may vary with scale $R$ ."1024eenerally lies between the expected N from conversion of initial C to N and the value of N expected from conversion of initial C. O both to N. The minority stars (both groups and CCen) have N abundances less than that expected from full couvertion of C to N. Although the N abundance iu many RCBs aud ii some EHes tmply wholesale conversion of O to N via ON cycles. παν stars are not O deficient suggesting O is syuthesized along with C. ie. 3a -process was followed by I C(o.2)! O0. Most of the O-rich stars have an observed O/C about 1 implying equal production of C and O. Dramatic enhancement of Πο s-process elements Sr. Y. aud. Zr was first seeu iu cool RCB star AAqr (Bond et al.,"generally lies between the expected N from conversion of initial C to N and the value of N expected from conversion of initial C, O both to N. The minority stars (both groups and Cen) have N abundances less than that expected from full convertion of C to N. Although the N abundance in many RCBs and in some EHes imply wholesale conversion of O to N via ON cycles, many stars are not O deficient suggesting O is synthesized along with C, i.e., $\alpha$ -process was followed by $^{12}$ $(\alpha,\gamma)^{16}$ O. Most of the O-rich stars have an observed O/C about 1 implying equal production of C and O. Dramatic enhancement of light $s$ -process elements Sr, Y, and Zr was first seen in cool RCB star Aqr (Bond et al."1025 1979)., 1979).1026 Aspluud et al. (, Asplund et al. (10272000) have shown that most of the RCB stars show enhancements [Y/Fe] of about 0.8 and [Ba/Fe] of about 0.1. i.e.. the lighter s-process elements are more enhanced than the heavier oues.,"2000) have shown that most of the RCB stars show enhancements [Y/Fe] of about 0.8 and [Ba/Fe] of about 0.4, i.e., the lighter $s$ -process elements are more enhanced than the heavier ones."1028 However. there is a considerable dispersion iu the Y aud Ba," However, there is a considerable dispersion in the Y and Ba"1029characterized by Luge pairing eaps (A~100 MeV) iu quark cores of some neutron stars aud in QS and discuss different possible phases of quark matter.,characterized by large pairing gaps $\Delta \sim 100 $ MeV) in quark cores of some neutron stars and in QS and discuss different possible phases of quark matter.1030 Large gaps arise for quark-quark interactions motivated by iustautous (Diakonovct1999) aud bv nouperturbative gluou propagators (BlaschkeaudRoberts1998:Blochetal.1999:Pis-arskiandRischke 1999).," Large gaps arise for quark-quark interactions motivated by instantons \citep{DFL96,CD99,RSSV99} and by nonperturbative gluon propagators \citep{BR98,BRS99,PR99}."1031. To be specific in our predictions we will consider models of the canonical QS and QCNS of 1.1 solar masses (1.1 M.) at a constant density.," To be specific in our predictions we will consider models of the canonical QS and QCNS of 1.4 solar masses $1.4\, M_\odot$ ) at a constant density."1032 The constant density profile is actually a very good approximation for QS of the mass M.<LLAL... see Alcocketal.(1986).," The constant density profile is actually a very good approximation for QS of the mass $M\leq 1.4\, M_\odot$, see \citet{AFO86}."1033.. We consider the modelof QCNS with a crust of the mass Ma~10TAL... the model of QS with a tiuv crust mass (M&10 PAL.) aud the model of QS with no crust.," We consider the modelof QCNS with a crust of the mass $M_{\rm cr}\sim 10^{-1}M_\odot$, the model of QS with a tiny crust mass $M_{\rm cr}\lsim 10^{-5}M_\odot$ ) and the model of QS with no crust."1034" For QCNS we shall use the same T;/T ratio as for ordinary NS. see (Tsuruta1979:Maxwell 1983).. whereas for QS we use somewhat larger values for this ratio. uauicly T,—50?T fora tiny crust (Horvathl and Zi=T for a neglieible crust (Pizzochero 19913."," For QCNS we shall use the same $T_s/T$ ratio as for ordinary NS, see \citep{T79,M79,ST83}, whereas for QS we use somewhat larger values for this ratio, namely $T_s =5\cdot 10^{-2}T$ for a tiny crust \citep{HBV91} and $T_s =T$ for a negligible crust \citep{P91}."1035. In the latter case. however. we assume the existence of black body photon radiation from the surface as for the cases of more extended crusts.," In the latter case, however, we assume the existence of black body photon radiation from the surface as for the cases of more extended crusts."1036 We will estimate the cooling of QS and QCNS first in absence of color superconductivity and then iun presence of color supercouductivitv Or πια. quark gaps (A~ 0.1.21 MeV). as sugeested by BailinandLove(1981) and for aree gaps (A~100 MeV) as obtained in Refs. (Alfordctal.19908:Rappet1998:Schifter 1999b).," We will estimate the cooling of QS and QCNS first in absence of color superconductivity and then in presence of color superconductivity for small quark gaps $\Delta \sim$ 0.1...1 MeV), as suggested by \citet{BL84} and for large gaps $\Delta \sim 100$ MeV) as obtained in Refs. \citep{ARW98,RSSV98,S98,CD99,RSSV99,BR98,PR99,ARW99,SW99a,ABR99,SW99b}."1037. Iu the latter case we will consider two phases: the color-flavor-locked ads-phase (Alfordi1999:SchaferaudWilezek1999b) aud the Ny=2 color superconducting phase (AlfordctRischke| 1999).. iu which the s-quark is absent Hxd the vd-diquark condensate selects a direction iu color space whereby the color charge has to be conrpeusated by the remainiug uipaired quarks.," In the latter case we will consider two phases: the color-flavor-locked $uds$ -phase \citep{ARW99,SW99a,ABR99,SW99b} and the $N_f =2$ color superconducting phase \citep{ARW98,RSSV98,S98,BR98,CD99,RSSV99,BRS99,PR99}, in which the $s$ -quark is absent and the $ud$ -diquark condensate selects a direction in color space whereby the color charge has to be compensated by the remaining unpaired quarks."1038 Finally. we waut to discuss the question whether the hvpothesis of a color superconducting quark matter phase in compact star interiors is compatible with existing N-rav data.," Finally, we want to discuss the question whether the hypothesis of a color superconducting quark matter phase in compact star interiors is compatible with existing X-ray data."1039 A detailed discussion of the neutrino ciissivity of quark matter has first been given by Twamoto(1982) where the possibility of color supercouductivitv has not been discussed., A detailed discussion of the neutrino emissivity of quark matter has first been given by \citet{I82} where the possibility of color superconductivity has not been discussed.1040 Iu this work the quark direct Urea reactions (QDU) 4>cp ancl πο>de were sugecsted as the most efficicut processes., In this work the quark direct Urca reactions (QDU) $d\rightarrow ue\bar{\nu}$ and $ue\rightarrow d {\nu}$ were suggested as the most efficient processes.1041" Their cinissivities were estimated as where at barvon densities p;—2py the strong coupling constaut is a,c1. aud decreases logarithmically at still higher deusities (INissliungeraudMorley 1976).", Their emissivities were estimated as where at baryon densities $\rho_b \simeq 2 \rho_0$ the strong coupling constant is $\alpha_s \approx 1$ and decreases logarithmically at still higher densities \cite[]{KM76}.1042.. The unclear saturation deusitvis py=O.17fu 5. 3.—peofpy is the electron fraction. and 75 is the temperature i units of 10 K. The lavecr the density of the uds- system the smaller is its electron fraction.," The nuclear saturation densityis $\rho_0=0.17 {\rm fm}^{-3}$ , $Y_e =\rho_e /\rho_b$ is the electron fraction, and $T_9$ is the temperature in units of $10^9$ K. The larger the density of the $uds$ -system, the smaller is its electron fraction."1043 For a density py~Dyoue can expect a rather low electron fraction of strange quark iatter τινας 7 (Clercenniue1996) and eq. (1)), For a density $\rho_b \sim 3\rho_0$one can expect a rather low electron fraction of strange quark matter $Y_e \sim $ $^{-5}$ \citep{G96} and eq. \ref{neutr-DU}) )1044 vields ελuv103)TSoreenPsec ὃν seo (Duncan 1991)...," yields $\epsilon^{\rm QDU} _\nu \sim 10^{25}1045~T_{9}^6 ~ {\rm erg} ~{\rm cm}^{-3}~{\rm sec}^{-1}$ , see \citep{DSW83,HBV91}. ."1046 We did not vet discuss the strange quark contribution given by the direct Urea processes s>acp and we>sr., We did not yet discuss the strange quark contribution given by the direct Urca processes $s\rightarrow ue\bar{\nu}$ and $ue\rightarrow s {\nu}$.1047 Although these processes can occur. their contribution is suppressed compared to the corresponding ud- reactions (Duncan1983) by an extra factor sinc.Di~410.M 7. where 6c is. the Cabibbo. angle.," Although these processes can occur, their contribution is suppressed compared to the corresponding $ud$ -reactions \citep{DSW83} by an extra factor $\mbox{sin}^2 \theta_{\rm C} \sim 10^{-3}$ , where $\theta_{\rm C}$ is the Cabibbo angle."1048" If for somewhat larger density the clectrou fraction.: was foo snall (3.-νι2YBadoonde(δανM2pp) ὃν for a,=OF aud py= Spy. m, ds the electron mass).then all theQDU processes would be completely switched off (Duncan1983) and theneutrino cussion would be governed by two-quark reactions like the quark modified Urea (QMU) dg ΕΕ the quark bremsstralihie (QD) processes «πο.> qiqoii."," If for somewhat larger density the electron fraction was too small $Y_e<Y_{ec}\simeq1049\sqrt{3}\pi m_e^{3}/(8\alpha_s^{3/2}\rho_b) 1050\leq 2\cdot 10^{-8}$ , for $\alpha_s \simeq 0.7$ and $\rho_b \simeq 5\rho_0$ , $m_e$ is the electron mass),then all theQDU processes would be completely switched off \citep{DSW83} and theneutrino emission would be governed by two-quark reactions like the quark modified Urca (QMU) $dq\rightarrow uqe\bar{\nu}$ and the quark bremsstrahlung (QB) processes $q_1 q_2 \rightarrow q_1 q_2 \nu\bar{\nu}$ ."1051 The emissivities, The emissivities1052 , 1053the integrated mass found through the direct reconstruction method will be consistent. with that of the input map: however. it is clear from Figure S that this method. will not allow one to determine with any confidence the true shape of the underlving mass profile.,"the integrated mass found through the direct reconstruction method will be consistent with that of the input map; however, it is clear from Figure \ref{fg:directrec} that this method will not allow one to determine with any confidence the true shape of the underlying mass profile."1054 Moreover. the choice of normalisation constant relies either on the presence. of data at large radii from the centre of the cluster. or on other external information.," Moreover, the choice of normalisation constant relies either on the presence of data at large radii from the centre of the cluster, or on other external information."1055 In the absence of either of these. the choice of normalisation. anc hence the cluster mass thus derived. is somewhat arbitrary.," In the absence of either of these, the choice of normalisation, and hence the cluster mass thus derived, is somewhat arbitrary."1056" As in LINWOO. the PAZ u-statistic was measured for /=5 and R=607.90"".1207]."," As in LKW09, the $\fmap$ -statistic was measured for $l=5$ and $R=[60'',90'',120'']$."1057" Hence. to test how well this profile might be identified. £AZ,, data for an SIS mocel and the full range of NEW models were obtained for A4. ancl added to our sample of test. profiles."," Hence, to test how well this profile might be identified, $\fmap$ data for an SIS model and the full range of NFW models were obtained for $M_{200}^\ast$, and added to our sample of test profiles."1058" The peak signal to noise in the reconstructions was found to be ὃ=2.5.3.0. and 3.3. in order of increasing aperture radius. and we assume an error on the zero-signal radius measurements of op.=10"". which corresponds to 5 pixels on the input convergence map."," The peak signal to noise in the reconstructions was found to be ${\cal S}=2.5, 3.0,$ and $3.3$, in order of increasing aperture radius, and we assume an error on the zero-signal radius measurements of $\sigma_{Ro}=10''$, which corresponds to $\sim 5$ pixels on the input convergence map."1059 We note that in each reconstruction shown in LIXN09. here is a significant peak seen at the top edge of the field of view.," We note that in each reconstruction shown in LKW09, there is a significant peak seen at the top edge of the field of view."1060" In the /?=60"" FAL, reconstruction. this feature actually obtains higher signal to noise than the central »ealkk."," In the $R=60''$ $\fmap$ reconstruction, this feature actually obtains higher signal to noise than the central peak."1061 This feature is believed. to arise due to edge effects. as the significance of this peak is reduced. in. subsequent reconstructions. and its position changes somewhat as the ilter is changed.," This feature is believed to arise due to edge effects, as the significance of this peak is reduced in subsequent reconstructions, and its position changes somewhat as the filter is changed."1062 This indicates a noise feature. rather than a true signal.," This indicates a noise feature, rather than a true signal."1063" As we are considering a racdiallv-averaged signal here centred on the centre of the PAZ, Field. and this xurticular feature is located far outside the zero-signal radius of the central mass peak. this feature will not contaminate our measurements substantially."," As we are considering a radially-averaged signal here centred on the centre of the $\fmap$ field, and this particular feature is located far outside the zero-signal radius of the central mass peak, this feature will not contaminate our measurements substantially."1064" Using the three PAZ, reconstructions of the N-bocky cluster. the data indicate that the radial profile of the cluster is well-lit bv an NEW mass profile with e=3 and Aloo=1.1.23062.10%1AL..."," Using the three $\fmap$ reconstructions of the N-body cluster, the data indicate that the radial profile of the cluster is well-fit by an NFW mass profile with $c=3$ and $M_{200}=1,\ 1.23\ {\rm or}\ 2\times 10^{15}h^{-1}\,M_\odot$."1065" Phe radial profiles for the ALG, signal from the cluster for cach aperture radius are plotted in Figure 10.. along with the racial profiles of the three best-fitting models."," The radial profiles for the $\fmap$ signal from the cluster for each aperture radius are plotted in Figure \ref{fg:radnbody}, along with the radial profiles of the three best-fitting models."1066 The effect of the eluster's cllipticity and associated substructure can be clearly seen in its racial profile. with a secondary. peak being seen around ro=1307 in cach reconstruction.," The effect of the cluster's ellipticity and associated substructure can be clearly seen in its radial profile, with a secondary peak being seen around $x_0=130''$ in each reconstruction."1067 Al three models show values of Z2) that are smaller han that seen in the cluster data. implying that the best it model might be one with an even smaller concentration xwameter (see Figure 6)).," All three models show values of $R_0$ that are smaller than that seen in the cluster data, implying that the best fit model might be one with an even smaller concentration parameter (see Figure \ref{fg:nfw_c}) )."1068 However. the peak signal does appear to be best fit across the three reconstructions by the xolile with Aou!=123«1075.1M. as expectecd.," However, the peak signal does appear to be best fit across the three reconstructions by the profile with $M_{200}=1.23\times10^{15}h^{-1}\,M_\odot$, as expected."1069 Furthermore. we can compare this best-fit models to he racial profile of the convergence map.," Furthermore, we can compare this best-fit models to the radial profile of the convergence map."1070 Figure 11. shows he measured. racial profile of the convergence of the lens., Figure \ref{fg:kapparad} shows the measured radial profile of the convergence of the lens.1071 The dotted curves show the convergence profile for the three xst-fitting mass models described above., The dotted curves show the convergence profile for the three best-fitting mass models described above.1072" Clearly the two ower-mass models olfer excellent. fits to the cluster data. hus demonstrating the power of this method to accurately characterise the mass profile of a lens using a relatively small number of PAZ, reconstructions."," Clearly the two lower-mass models offer excellent fits to the cluster data, thus demonstrating the power of this method to accurately characterise the mass profile of a lens using a relatively small number of $\fmap$ reconstructions."1073" In this paper. we have presented the expected. PAZ, signal from two common mass profiles: the Singular Isothermal Sphere model and the Navarro-Frenk-White. model."," In this paper, we have presented the expected $\fmap$ signal from two common mass profiles: the Singular Isothermal Sphere model and the Navarro-Frenk-White model."1074 This signal is characterised by a peak value. found: when the aperture location coincides with a mass concentration. and a zero-signal contour.," This signal is characterised by a peak value, found when the aperture location coincides with a mass concentration, and a zero-signal contour."1075" By simulating radial PAZ, profiles for a laree number of combinations of halo mass. NEW concentration. parameter. aperture radius and filter polynomial order. the behaviour of the peak signal and zero-signal contour has been characterised for both the SIS and NEW density profiles under the assumption of circular symmetry."," By simulating radial $\fmap$ profiles for a large number of combinations of halo mass, NFW concentration parameter, aperture radius and filter polynomial order, the behaviour of the peak signal and zero-signal contour has been characterised for both the SIS and NFW density profiles under the assumption of circular symmetry."1076 The behaviour of both these measures is seen to diverge rather sharply between cdilferent models with the same mass as the aperture properties are varied., The behaviour of both these measures is seen to diverge rather sharply between different models with the same mass as the aperture properties are varied.1077 This implies that one might be able to use the PAM -statistic to constrain the masses and mass profiles of structures detected: simply by varving the aperture parameters and. noting the change in the peak signal and the location of the zero-signal contour., This implies that one might be able to use the $\fmap$ -statistic to constrain the masses and mass profiles of structures detected simply by varying the aperture parameters and noting the change in the peak signal and the location of the zero-signal contour.1078 Indeed. it has been shown using simulated. data fron analytic models. that with modest. signal to noise and relatively laree errors on the measurement of the zero-signal radius. it ds possible to isolate an input model using a reasonable number of combinations of aperture size and filter polynomial order.," Indeed, it has been shown using simulated data from analytic models that with modest signal to noise and relatively large errors on the measurement of the zero-signal radius, it is possible to isolate an input model using a reasonable number of combinations of aperture size and filter polynomial order."1079 It also becomes easier to discriminate between masses at the high-mass end. of the spectrum considered here. with higher mass haloes requiring fewer combinations of/ and f? to reach convergence.," It also becomes easier to discriminate between masses at the high-mass end of the spectrum considered here, with higher mass haloes requiring fewer combinations of $l$ and $R$ to reach convergence."1080 This was further reinforced. by testing the method on PAL data using the simulated cluster of LIANWOO as the input lens., This was further reinforced by testing the method on $\fmap$ data using the simulated cluster of LKW09 as the input lens.1081" This lens has a virial mass of 1.23.107.1AL.. and the combination of three PAZ, measurements of the lens was able to recover this mass to within a [actor of «1.5. and to correctly identify the shape of the profile as an NEW with low concentration parameter."," This lens has a virial mass of $1.23\times10^{15}h^{-1}\,M_\odot$, and the combination of three $\fmap$ measurements of the lens was able to recover this mass to within a factor of $<1.5$, and to correctly identify the shape of the profile as an NFW with low concentration parameter."1082 This success. despite the eirceularisation of a clearly elliptical lens profile. demonstrates solichy the power of the PA -statistic to discriminate between haloes of different masses.," This success, despite the circularisation of a clearly elliptical lens profile, demonstrates solidly the power of the $\fmap$ -statistic to discriminate between haloes of different masses."1083 Aloreover. this method shows a dramatic improvement," Moreover, this method shows a dramatic improvement"1084three different angular sizes for the removal (i.e. 37. 6° and 9°).,"three different angular sizes for the removal (i.e. $3^{\circ}$ , $6^{\circ}$ and $9^{\circ}$ )."1085 Fig., Fig.1086 6 shows the result of such foreground subtraction technique on the normalized correlation function for the cosmological signal using the normalized estimator c., \ref{fig:cross_agv2} shows the result of such foreground subtraction technique on the normalized correlation function for the cosmological signal using the normalized estimator $\omega_{RM}$.1087 At small distances. this procedure leads to a significant suppression of the correlation signal. even up to a factor of ~2 for angular distances below 2. almost independently of the size of the removing radius.," At small distances, this procedure leads to a significant suppression of the correlation signal, even up to a factor of $\sim2$ for angular distances below $\sim2^{\circ}$, almost independently of the size of the removing radius."1088 At larger distances. the amplitude of the correlation function is slightly increased €1O — )) starting from scales larger than the smoothing radius.," At larger distances, the amplitude of the correlation function is slightly increased (10 – ) starting from scales larger than the smoothing radius."1089 Another problem for the observed RMs are the measurement errors by themselves., Another problem for the observed RMs are the measurement errors by themselves.1090 For example. since the data recenty published by is based on only two different frequency bands tlye resulting RMs will be affected by a significant uncertainty.," For example, since the data recently published by \citet{2009ApJ...702.1230T} is based on only two different frequency bands the resulting RMs will be affected by a significant uncertainty."1091 We also note that these errors are not reduced by the smoothing involvec when removing the foreground., We also note that these errors are not reduced by the smoothing involved when removing the foreground.1092 The typical error of the observational RMs (as inferred from comparison with a data subset which was observed at more frequency bands) turns out to be around 0 to 20 rad 7? (see?.Fig.2).., The typical error of the observational RMs (as inferred from comparison with a data subset which was observed at more frequency bands) turns out to be around 10 to 20 rad $^{-2}$ \citep[see][ Fig. 2]{2009ApJ...702.1230T}.1093 In order to estimate the effect of he observational errors. we added random values to our simulated RM signal. which were drawn from a Gaussiandistribution with a dispersion given by Arar.," In order to estimate the effect of the observational errors, we added random values to our simulated RM signal, which were drawn from a Gaussiandistribution with a dispersion given by $\sigma_{\rm RM}$."1094 We explored values of 0.001. 0.01. 0.1. 1.0 and 10 rad 2 for gar.," We explored values of $0.001$, $0.01$, $0.1$, $1.0$ and $10$ rad $^{-2}$ for $\sigma_{\rm RM}$."1095 Note that most of these values are much more optimistic than what is expected fromcurrent instruments., Note that most of these values are much more optimistic than what is expected fromcurrent instruments.1096 However. future instruments. like eg. SKA and ASKAP will achieve an RM accuracy of a few rad m7 (2)..," However, future instruments, like e.g. SKA and ASKAP will achieve an RM accuracy of a few rad $^{-2}$ \citep{2004NewAR..48.1289B}."1097 Fig., Fig.1098 7 shows the impact of such measurement errors onto the resulting correlation function., \ref{fig:cross_agv3} shows the impact of such measurement errors onto the resulting correlation function.1099 Even oa;=0.01 (e.g. a hundredth of the actual measurement error) leads to a sizable (ea. 50%), Even $\sigma_{\rm RM}=0.01$ (e.g. a hundredth of the actual measurement error) leads to a sizable (ca. )1100) reduction of the correlation signal., reduction of the correlation signal.1101 Furthermore. ση0.1 (e.g. ten percent of the actual measurement error) reduces the signal by a factor of ~5 and em;=1 (e.g. nearly the present measurement errors) makes the correlation very close to the one of the correspondingnul? signal.," Furthermore, $\sigma_{\rm RM}=0.1$ (e.g. ten percent of the actual measurement error) reduces the signal by a factor of $\sim5$ and $\sigma_{\rm RM}=1$ (e.g. nearly the present measurement errors) makes the correlation very close to the one of the corresponding signal."1102 From this it is clear that using the normalized estimator wyay(6) will be quite problematic., From this it is clear that using the normalized estimator $\omega_{RM}(\theta)$ will be quite problematic.1103 The presence of even small measurement errors (far smaller than what can be reached currently) will affect the shape and amplitude of the correlation function in a way that the information on the cosmic magnetization is basically lost., The presence of even small measurement errors (far smaller than what can be reached currently) will affect the shape and amplitude of the correlation function in a way that the information on the cosmic magnetization is basically lost.1104 In recent years. different models for the Galactic magnetic field were proposed (e.g.2222). ," In recent years, different models for the Galactic magnetic field were proposed \citep[e.g.][]{2006ApJ...642..868H, 2007ApJS..170..335P, 2008ICRC....2..223J, 2008A&A...477..573S}."1105To estimate the influence of the GF on the cosmological cross-correlations we produced a synthetic map of the RM signal expected for our galaxy using the publicly available code (?).. where we made use of the Galactic magnetic model given by ?..," To estimate the influence of the GF on the cosmological cross-correlations we produced a synthetic map of the RM signal expected for our galaxy using the publicly available code \citep{2009A&A...495..697W}, where we made use of the Galactic magnetic model given by \citet{2008A&A...477..573S}."1106 The original model was constructed to give a good representation of the synchrotron emission of the Milky Way but. by missing possible reversals within the model magnetic field. it overproduces the RM signal by a significant factor.," The original model was constructed to give a good representation of the synchrotron emission of the Milky Way but, by missing possible reversals within the model magnetic field, it overproduces the RM signal by a significant factor."1107 We therefore scaled the original model down to obtain a better representation of the observed RMs., We therefore scaled the original model down to obtain a better representation of the observed RMs.1108 We also note that such reversals could lead to significant small scale structures in the RM signal due to the GF. as shown by ?..," We also note that such reversals could lead to significant small scale structures in the RM signal due to the GF, as shown by \citet{2009A&A...507.1087S}."1109 Such fluctuations could significantly compromise the cosmological signal. as they would be present on scales smaller than the one used to filter the GF.," Such fluctuations could significantly compromise the cosmological signal, as they would be present on scales smaller than the one used to filter the GF."1110 However. we do not currently include this effect in our foreground model.," However, we do not currently include this effect in our foreground model."1111 In Fig., In Fig.1112 8 we show the obtained RM map models tleft column) compared to the observed RM signal right column) taken from ?.., \ref{fig:simulgalaxy} we show the obtained RM map models (left column) compared to the observed RM signal (right column) taken from \citet{2009ApJ...702.1230T}.1113 From top to bottom we show the original GF model with noise and the RM dataset. a smoothed version of the maps (within 8). and the residuals when applying theforeground subtraction as described above for 3°.," From top to bottom we show the original GF model with noise and the RM dataset, a smoothed version of the maps (within $^{\circ}$ ), and the residuals when applying theforeground subtraction as described above for $^{\circ}$ ."1114 All the synthetic maps are imprinted with an observational error of σ=LO rad >., All the synthetic maps are imprinted with an observational error of $\sigma=10$ rad $^{-2}$.1115 The last row shows the synthetic residual map when reducing the noise level oc=L rad 7? as expected for future instruments., The last row shows the synthetic residual map when reducing the noise level to $\sigma=1$ rad $^{-2}$ as expected for future instruments.1116 The close-ups show the remaining signal of prominent galaxy clusters in the residual maps., The close-ups show the remaining signal of prominent galaxy clusters in the residual maps.1117 Note that the signal of other prominent clusters. ying behind the Galactic plane. are not longer visible after the oreground subraction was applied.," Note that the signal of other prominent clusters, lying behind the Galactic plane, are not longer visible after the foreground subtraction was applied."1118 As expected. when adding such a large. plain foreground signal to the cosmological one. he cross-correliition function vanishes.," As expected, when adding such a large, plain foreground signal to the cosmological one, the cross-correlation function vanishes."1119 Therefore. we also applied he GF remova technique described before.," Therefore, we also applied the GF removal technique described before."1120 The results can be seen in Fig. 9..," The results can be seen in Fig. \ref{fig:cross_agv4},"1121 where the angular cross-correlation function of he combined maps for both estimators is shown., where the angular cross-correlation function of the combined maps for both estimators is shown.1122 For comparison. we showthe exected signal from the plain simulation (e.g. assuming a very small of 2= 0.033. the GF signal alone. and the combined with the GF signal for a large (e. >= 1.03. as well asfor a extreme," For comparison, we showthe expected signal from the plain simulation (e.g. assuming a very small of $z=0.03$ ), the GF signal alone, and the combined with the GF signal for a large (i.e. $z=1.03$ ), as well asfor a extreme"1123"Πολ). aud estimates the field-star wuuber-deusity. jy, (for Res,SRx Προ)","), and estimates the field-star number-density, $\eta_{fs}$ (for $R_{FS1}\la R\la R_{FS2}$ )."1124" Next. it colputes the expected mwmuber-density of member stars. ici,—hot Hye converts the wmuber-density yy. uto the estimated uunber of field stars. alc subtracts it from each cell."," Next, it computes the expected number-density of member stars, $\eta_{mem}=\eta_{tot}-\eta_{fs}$ , converts the number-density $\eta_{fs}$ into the estimated number of field stars, and subtracts it from each cell."1125 Finally. after subtraction of the field stars. the remaimine ANGUS stays du each coll aro ideutifed for further use (see below).," Finally, after subtraction of the field stars, the remaining $N^{cell}_{clean}$ stars in each cell are identified for further use (see below)."1126" Photometrie uncertünties (assumed to be Gaussian) are explicitly taken iuto account: we compute he probability of a star of eiven magnitude and colours o be found ina any cell (νο, the difference of the error Unetiou. computed at the cellsborders)"," Photometric uncertainties (assumed to be Gaussian) are explicitly taken into account: we compute the probability of a star of given magnitude and colours to be found in a any cell (i.e., the difference of the error function computed at the cell'sborders)."1127 Initially. cell dimensions ave AJ= {αμα ACSI)=ACL 1.2. but cell sizes half and twice those values are also used.," Initially, cell dimensions are $\Delta\jj=1.0$ and $\Delta\jh=\Delta\jk=0.2$ , but cell sizes half and twice those values are also used."1128" We also apply shifts iu the exid positiouiug bv 41/3 of he respective cell size iu the 2 colours aud maguitude axes,", We also apply shifts in the grid positioning by $\pm1/3$ of the respective cell size in the 2 colours and magnitude axes.1129 When all the differeut setups are used. the number of independent decoutamination outputs amounts to 729.Each setup results iu a total number of member stats νο=zoll?reedclean and the average of N44 over all setups produces the expected total umber of ieniber stars ONpea)," When all the different setups are used, the number of independent decontamination outputs amounts to 729.Each setup results in a total number of member stars $N_{mem}=\sum_{cell}N^{cell}_{clean}$, and the average of $N_{mem}$ over all setups produces the expected total number of member stars $\left<N_{mem}\right>$."1130 Each star (identified above) is vauked according to the number of times 1 survives after all runs (survival frequeney)., Each star (identified above) is ranked according to the number of times it survives after all runs (survival frequency).1131 Ouly tle UNnenjf lighest ranked stars are considered cluster 1nenubers and transposed to the respective decontaminated) CMD., Only the $\left<N_{mem}\right>$ highest ranked stars are considered cluster members and transposed to the respective decontaminated CMD.1132 The differeuce between the expected number of field stars (usually fractional) aud the actual uuuber of stars Guteger) subtracted from cach cell. sununed over all cells. is the subtraction efficiency (Further details on the decontamination statistics are in Bonatto&Bica 20073).," The difference between the expected number of field stars (usually fractional) and the actual number of stars (integer) subtracted from each cell, summed over all cells, is the subtraction efficiency (Further details on the decontamination statistics are in \citealt{BB07}) )."1133 The above setup. applied to the prescut targets. resulted in subtraction cfiiciencies higher than.," The above setup, applied to the present targets, resulted in subtraction efficiencies higher than."1134 The decontaminated CMDs are shown in the bottom panels of Figs, The decontaminated CMDs are shown in the bottom panels of Figs.1135l to L.,\ref{fig1} to \ref{fig4}.1136 Fundamental paramecters are derived with Padova isochrones (Girardietal. 2002))?.., Fundamental parameters are derived with Padova isochrones \citealt{Girardi2002}) .1137 The isochrones of, The isochrones of1138eeneral are unlikely to explain the slowly rotating. isotropic SAUBRON ellipticals.,"general are unlikely to explain the slowly rotating, isotropic SAURON ellipticals."1139" The data points cluster around e;,,20.57 and 920.43 which is close to the relationship between anisotropy and ellipticitv (dotted line) Found Lor disk-clisk mergers with star Formation.", The data points cluster around $\epsilon_{int} \approx 0.57$ and $\delta \approx 0.43$ which is close to the relationship between anisotropy and ellipticity (dotted line) found for disk-disk mergers with star formation.1140 From a dynamical point of view. these dry. merger remnants are similar (o gas-rich disk mergers with star formation.," From a dynamical point of view, these dry merger remnants are similar to gas-rich disk mergers with star formation."1141 ? had analvsed the structure of ellipticals. formed through dry of ellipcals that were generated Irom collisionless. 1:1 and 3:1 stellar disk mergers as discussed in section 3.," \citet{2006ApJ...636L..81N} had analysed the structure of ellipticals, formed through dry re-merging of ellipticals that were generated from collisionless, 1:1 and 3:1 stellar disk mergers as discussed in section 3."1142 Note (hat. as shown in Fig.," Note that, as shown in Fig."1143 2. the progenitor ellipticals do not lie on the SAURON relation.," 2, the progenitor ellipticals do not lie on the SAURON relation."1144" Nevertheless. it is interesting that re-mereing of these svstems places (hem nicely on (he d-e;,; relation described by Eq."," Nevertheless, it is interesting that re-merging of these systems places them nicely on the $\delta$ $\epsilon_{int}$ relation described by Eq."1145 7 (open circles in Fig., 7 (open circles in Fig.1146 3)., 3).1147 Sul. (hese merger remnants are faster rotating. more anisotropic and more ellipsoidal than the slowly rotating SAUBRON ellipticals.," Still, these merger remnants are faster rotating, more anisotropic and more ellipsoidal than the slowly rotating SAURON ellipticals."1148 Yet another possibility to generate spheroidal ellipticals are multiple mergers in cosmological high-densi(v regions., Yet another possibility to generate spheroidal ellipticals are multiple mergers in cosmological high-density regions.1149 ? investigated the formation of a mnunber of massive galaxies using hieh-resolution cosmological simulations in à ACDAM universe., \citet{2007ApJ...658..710N} investigated the formation of a number of massive galaxies using high-resolution cosmological simulations in a $\Lambda$ CDM universe.1150 The calculations were simple. including only photoionization aud cooling of the interstellar mecium as well as star formation.," The calculations were simple, including only photoionization and cooling of the interstellar medium as well as star formation."1151 AGN and supernova feedback was neglected., AGN and supernova feedback was neglected.1152 In these simulations ellicient cooling of gas eeneraled rapid gas infall into smaller dark halo density perturbations. followed by a burst ol star formation.," In these simulations efficient cooling of gas generated rapid gas infall into smaller dark halo density perturbations, followed by a burst of star formation."1153 At the same time. these substructures merged into massive spheroidal stellar galaxy. resembling a present-day. red giant elliptical.," At the same time, these substructures merged into massive spheroidal stellar galaxy, resembling a present-day, red giant elliptical."1154 Shock heating in the later phases eeneraled a surrounding hot gaseous halos (hat suppressed late star formation. leacling al the end (o a red. old galaxy (??)..," Shock heating in the later phases generated a surrounding hot gaseous halos that suppressed late star formation, leading at the end to a red, old galaxy \citep{2003MNRAS.345..349B,2007MNRAS.380..339B}."1155 The green points in Fig., The green points in Fig.1156 3 show the location of three spheroidal galaxies presented in ? and 7 additional galaxies of similar mass simulated in the same manner., 3 show the location of three spheroidal galaxies presented in \citet{2007ApJ...658..710N} and 7 additional galaxies of similar mass simulated in the same manner.1157 The distribution is in excellent agreement with the SAURON observations οἱ red. massive ellipticals.," The distribution is in excellent agreement with the SAURON observations of red, massive ellipticals."1158 Interestingly. (he simulations reproduce not only the observed low ellipticilies and anisotropies.," Interestingly, the simulations reproduce not only the observed low ellipticities and anisotropies."1159 They. also show the same trend of anisotropy. with ellipticity as observed., They also show the same trend of anisotropy with ellipticity as observed.1160 The numerical simulations. discussed in the previous sections. have shown that interstellar eas dvnanmies. star formation ancl stellar feedback plavs a crucial role in order to reproduce the observed kinematical and isophotal properties of fast rotating. earlv-tvpe galaxies.," The numerical simulations, discussed in the previous sections, have shown that interstellar gas dynamics, star formation and stellar feedback plays a crucial role in order to reproduce the observed kinematical and isophotal properties of fast rotating, early-type galaxies."1161 The final structure of the merger remnants depends on (he initial mass ratio and gas ΠΟΙΟΙ., The final structure of the merger remnants depends on the initial mass ratio and gas fraction.1162 The remnants are more round. less anisotropic and more rotationally supported the smaller the mass ratio M4/M»>1 of the progenitors and (he larger (he initial gas fraction.," The remnants are more round, less anisotropic and more rotationally supported the smaller the mass ratio $M_1/M_2 \geq 1$ of the progenitors and the larger the initial gas fraction."1163" The dependence of 9 on e;,; is in agreement with the observed (rend. found in the SAURON", The dependence of $\delta$ on $\epsilon_{int}$ is in agreement with the observed trend found in the SAURON1164space reddening of each Cepheid.,space reddening of each Cepheid.1165 Fig., Fig.1166 2. represcuts ouly a portion of each variahle-extinction diagram. aamcly the most lLeavily-populated regions associated with the expected paraiecters for cach Cepheid.," \ref{fig3} represents only a portion of each variable-extinction diagram, namely the most heavily-populated regions associated with the expected parameters for each Cepheid."1167" Alcan (B; aud (V5 inaguitudes are available for cach Cepheid from Berduikov(2007) and the preseut study. and rough estimates of reddening aud hWnuuinositv were made fom older. published period-color ίσιο,Feruie1990a.b) and period-luninosity (e.g.Turner1992) relations. which do not differ substautially from more recent results (Turner2001.2010)."," Mean $\langle B \rangle$ and $\langle V \rangle$ magnitudes are available for each Cepheid from \citet{bd07} and the present study, and rough estimates of reddening and luminosity were made from older, published period-color \citep[e.g.,][]{fe90a,fe90b} and period-luminosity \citep[e.g.,][]{tu92} relations, which do not differ substantially from more recent results \citep{tu01,tu10}."1168 It was then possible to establish roughly where in each variable-extinction diagram the parameters for the Cepheid should fall. keeping iu iuind that an extremely liberal iuterpretation of such “predictions” ds essential to avoid biasing the results.," It was then possible to establish roughly where in each variable-extinction diagram the parameters for the Cepheid should fall, keeping in mind that an extremely liberal interpretation of such “predictions” is essential to avoid biasing the results."1169 Some of the sample Cepheids are suspected Type II objects or overtoue pulsators. for example. which affects estimates of both reddening and luminosity.," Some of the sample Cepheids are suspected Type II objects or overtone pulsators, for example, which affects estimates of both reddening and luminosity."1170 Cenerous uucertaiuties of EO.1 or more in Epjq aud £1 in My: were therefore assumed in the analysis., Generous uncertainties of $\pm0.1$ or more in $E_{B-V}$ and $\pm 1$ in $M_V$ were therefore assumed in the analysis.1171 Note that the “predictions” for IO Cas. FO Cas. and Vise2 Ser are inconsistent with expectations for classical Cepheids (they have larger predicted distance moduli than those for surrounding stars of similar reddening). which means that they are potential Type II objects.," Note that the “predictions” for IO Cas, FO Cas, and V1882 Sgr are inconsistent with expectations for classical Cepheids (they have larger predicted distance moduli than those for surrounding stars of similar reddening), which means that they are potential Type II objects."1172 The situation for IZ Per. BD Pup. and OT Per is more ambiguous.," The situation for HZ Per, BD Pup, and OT Per is more ambiguous."1173 All such information is needed in order to establish what stars in the feld of cach Cepheid are useful for deriving its space reddening., All such information is needed in order to establish what stars in the field of each Cepheid are useful for deriving its space reddening.1174 Iu the case of UY Mou. for exaniple. the estimated distance aud reddening for the Cepheid associate it with the eroup of slightly reddened stars at Epyc OL ARDYzm Ll12 (dz 1.62.5 kpc). but less distaut and less reddened than stars of Ep20.5. ARSyz 12.513 (42 3.E kpc). in its vicinity.," In the case of UY Mon, for example, the estimated distance and reddening for the Cepheid associate it with the group of slightly reddened stars at $E_{B-V} \simeq 0.1$ , $_V)_0 \simeq$ 11–12 $d \simeq$ 1.6–2.5 kpc), but less distant and less reddened than stars of $E_{B-V} \simeq 0.5$, $_V)_0 \simeq$ 12.5–13 $d \simeq$ 3–4 kpc), in its vicinity."1175 The best match is therefore to the lL stars within 5' of UY Mon that are reddened by Ep(o70., The best match is therefore to the 4 stars within $5^\prime$ of UY Mon that are reddened by $E_{B-V} \simeq 0.1$.1176 Other cases are 110re Complex. because of the patchy reddening that permeates most fields. but have been resolved by considering only stars close to each Cepheid.," Other cases are more complex because of the patchy reddening that permeates most fields, but have been resolved by considering only stars close to each Cepheid."1177 What appears to be a continuous ruu of reddening with distance in some fields results from the patchy extinction in each field combined with larger-thau-average uncertainties i the inferred color excesses. Epv.," What appears to be a continuous run of reddening with distance in some fields results from the patchy extinction in each field combined with larger-than-average uncertainties in the inferred color excesses, $E_{B-V}$."1178 The extinction associated with most Calactic star fields is typically associated with iudividual dust clouds dispersed aloug the line of sight (Turner1991)., The extinction associated with most Galactic star fields is typically associated with individual dust clouds dispersed along the line of sight \citep{tu94}.1179. But large[m] uncertainties iu τοσοc» czi confuse the picture., But large uncertainties in reddening can confuse the picture.1180 Fie., Fig.1181 L|. preseuts the results of a simulation of such ciretuustances iu a field where the scatter in the color excesses is taken to be -cEQG.05. with associated uucertainties in absolute magnitude of -0.5. both quautities beiug applied. randomly to the test points.," \ref{fig4} presents the results of a simulation of such circumstances in a field where the scatter in the color excesses is taken to be $\pm0.05$, with associated uncertainties in absolute magnitude of $\pm0.5$, both quantities being applied randomly to the test points."1182" Star densifies were assunied constant as a fiction of distance. aud the input parameters iucluded specific anounts of reddening and extinction arising m discrete dust clouds located along the line of sight at distances of 0.5 pe. 0.9 pe. aud 1.1 pe. producing mea color excesses of Epy = 0.2. 0.5. and 0.7. respectively,"," Star densities were assumed constant as a function of distance, and the input parameters included specific amounts of reddening and extinction arising in discrete dust clouds located along the line of sight at distances of 0.5 pc, 0.9 pc, and 1.1 pc, producing mean color excesses of $E_{B-V}$ = 0.2, 0.5, and 0.7, respectively."1183 Au extinction law with R=3.0 is depicted for the last group., An extinction law with $R=3.0$ is depicted for the last group.1184 The parameters. in particular the adopted scatter. were chosen iu order to produce the greatest coniplexitv iu the resulting variable-extiuctiou diagram.," The parameters, in particular the adopted scatter, were chosen in order to produce the greatest complexity in the resulting variable-extinction diagram."1185 The resulting scatter produces results simular to some of the variable-extinction diagrams of Fig. 3.., The resulting scatter produces results similar to some of the variable-extinction diagrams of Fig. \ref{fig3}.1186 The large range of inferred reddeuiues for field stars near each Cepheid was reduced further through an analysis of 2MLASS observations (Cutretal.2003) for likely BAF-type stays in the same fields. analyzed in simular fashion to that cmploved by Turnerctal.(2008) and Turner(2011).," The large range of inferred reddenings for field stars near each Cepheid was reduced further through an analysis of 2MASS observations \citep{cu03} for likely BAF-type stars in the same fields, analyzed in similar fashion to that employed by \citet*{te08} and \citet{tu11}."1187. 2AMfASS observations were used separately without combination with the BV(RO¢ photometry in order to avoid potential zero- problems., 2MASS observations were used separately without combination with the $_C$ photometry in order to avoid potential zero-point problems.1188 The observed Mand AY colors for stars Iving within 5! of cach Cepheid are shown in Fie. 5..," The observed and $_{\rm s}$ colors for stars lying within $5^\prime$ of each Cepheid are shown in Fig. \ref{fig5},"1189 and were compared with the iutriusic relation for maiu-sequence stars in the 2\TASS system (Turner2011).. adjusted with a reddening slope Eyy/E;yo=0.19 from Turuer(2011).," and were compared with the intrinsic relation for main-sequence stars in the 2MASS system \citep{tu11}, adjusted with a reddening slope ${\rm E}_{H-K}/{\rm E}_{J-H} = 0.49$ from \citet{tu11}."1190". Multiple solutious iu some cases. e.g.. UY Mon aud IIZ Per. were resolved with reference to the variable-extinction diagrams and ""predicted? values. and best fits were made by trial aud error by establishing reddcnines for which likely BAF-type stars had colors distributed. randomly about the reddened intrinsic relation."," Multiple solutions in some cases, e.g., UY Mon and HZ Per, were resolved with reference to the variable-extinction diagrams and “predicted” values, and best fits were made by trial and error by establishing reddenings for which likely BAF-type stars had colors distributed randomly about the reddened intrinsic relation."1191" The JER, colors generate independent Lyy- reddcnings for the stars in the Cepheid fields. with the advantageof being more closely tied to B-type stars in the fields. stars that lie bluewud of the “kink” iu the intrinsic relation and that may share a common origin with the Cepheid."," The $_{\rm s}$ colors generate independent $E_{B-V}$ reddenings for the stars in the Cepheid fields, with the advantageof being more closely tied to B-type stars in the fields, stars that lie blueward of the “kink” in the intrinsic relation and that may share a common origin with the Cepheid."1192 The reddenines have slightly larger, The reddenings have slightly larger1193YNECESD y EU (ALB)awd The angular term for the tensor auto-correlation is extremely unwieldy and may be found in BOO.,"_q ) _q) _q) ) _p) ), ( _p _q _q) ), _q. The angular term for the tensor auto-correlation is extremely unwieldy and may be found in B06."1194" In the colinear limit 7;,-,-,B and 7;,.,;, reduce to", In the colinear limit $\FTsTsTs$ and $\FTtTtTt$ reduce to1195to be at Π>28 mag (ic. extremely faint) becomes large.,"to be at $R>28$ mag (ie, extremely faint) becomes large."1196 Quautitativelv. as the :>2.5 value of a ranges from 1.0 to. 1.75. Fo for the SFR.TSD.CCV models ranges from Έτος=031.0.19.0.17 to 0.:31.0.22.0.35.," Quantitatively, as the $z>2.5$ value of $\alpha$ ranges from $-1.0$ to $-1.75$, $F_{>28}$ for the SFR,TSD,CCV models ranges from $F_{>28}=11970.21,0.19,0.17$ to $0.34,0.22,0.35$."1198 Tf the fait cud of the ealaxv huuinositv function really is steep at high redshift. aud either the SFR or the CCV livpothesis is close to correct. it is possible that some of the cuvreut GRD host ealaxy ideutificatious or photometric neasurements are iu error. since very few optical observations are sensitive to 28 nae.," If the faint end of the galaxy luminosity function really is steep at high redshift, and either the SFR or the CCV hypothesis is close to correct, it is possible that some of the current GRB host galaxy identifications or photometric measurements are in error, since very few optical observations are sensitive to 28 mag."1199 Iu all these models. a large fraction of host galaxics lave extremely small iutriusie huuiuosities.," In all these models, a large fraction of host galaxies have extremely small intrinsic luminosities."1200 Even if such ealaxies are as common as the extrapolated ealaxy i1unuinositv fictions sugeest. they may uot host GRBs.," Even if such galaxies are as common as the extrapolated galaxy luminosity functions suggest, they may not host GRBs."

Showing the first 1,200 of 10296 lines. Download the file for the rest.