source,target
 These objects (see Fig. A4)).," These objects (see Fig. \ref{oxspec}) ),"
 appear to be part of the population of red QSOs discussed e.g. by and?.. which on average are absorbed by columns below Nj=109 em..," appear to be part of the population of red QSOs discussed e.g. by and, which on average are absorbed by columns below $N_H=10^{23}$ ."
 On the contrary. VIO selected their objects from the sample of?.. in which strict eriteria on the line width have been adopted. producing an ensamble of pure type-2 objects.," On the contrary, V10 selected their objects from the sample of, in which strict criteria on the line width have been adopted, producing an ensamble of pure type-2 objects."
 As a simple check. when considering only those [Ne V]-selected objects which look like pure type-2 spectra(e.g.," As a simple check, when considering only those [Ne V]-selected objects which look like pure type-2 spectra(e.g."
 Mell FWHM x2000 km s7!) the fraction of CT candidates increases to 50% (2/4)., MgII FWHM $\lesssim2000$ km $^{-1}$ ) the fraction of CT candidates increases to $\approx$ (2/4).
 Despite the very low statistics. this fraction is consistent with what has been found by VIO. suggesting that. when the search is restricted to pure type-2 objects. [Ne V] selection may be an efficient way to pick up CT AGN at =~I.," Despite the very low statistics, this fraction is consistent with what has been found by V10, suggesting that, when the search is restricted to pure type-2 objects, [Ne V] selection may be an efficient way to pick up CT AGN at $z\sim 1$."
 Synthesis models predict that from to about of the XRB at 30 keV is not accounted for by the integrated emission of Compton-Thin AGN., Synthesis models predict that from to about of the XRB at 30 keV is not accounted for by the integrated emission of Compton-Thin AGN.
 This “missing” background is expected to be produced by Compton-Thick AGN. and most of it is expected to be produced by CT AGN with Seyfert-like intrinsic luminosities at a redshift of z~1.," This “missing” background is expected to be produced by Compton-Thick AGN, and most of it is expected to be produced by CT AGN with Seyfert-like intrinsic luminosities at a redshift of $z\sim1$."
 The [Ne V]-selected CT QSOs in the SDSS represent the high-luminosity. low space density tail of the distribution of CT AGN at z I. and are expected to provide only a minor contribution to the missing XRB.," The [Ne V]-selected CT QSOs in the SDSS represent the high-luminosity, low space density tail of the distribution of CT AGN at $z\sim1$ , and are expected to provide only a minor contribution to the missing XRB."
 Selection of lower-luminosity CT AGN at zo1 is therefore needed. which can in principle be done by applying the X/NeV diagnosties to objects in sky areas with deep spectroscopic surveys and deep X-ray coverage.," Selection of lower-luminosity CT AGN at $z\sim 1$ is therefore needed, which can in principle be done by applying the X/NeV diagnostics to objects in sky areas with deep spectroscopic surveys and deep X-ray coverage."
 As an example. the combination between the zCOSMOS-bright spectroscopic survey and the Chandra--COSMOS X-ray survey in the COSMOS field would be able to identify CT AGN at z~1 down to intrinsic Ly~I0Pere s7!.. i.e. the population which is thought to produce a large fraction of the," As an example, the combination between the zCOSMOS-bright spectroscopic survey and the -COSMOS X-ray survey in the COSMOS field would be able to identify CT AGN at $z\sim 1$ down to intrinsic $L_X\sim10^{43}$ , i.e. the population which is thought to produce a large fraction of the"
component.,.
".. To estimate the region of the star probed by the observed g-modes, we first examined a propagation diagram of the asteroseismological model of0"," To estimate the region of the star probed by the observed $g$ -modes, we first examined a propagation diagram of the asteroseismological model of."
122+200., In Fig.
". In Fig. 1 we plot the logarithm of the squared Brunt-Vaiisalla and the Lamb frequencies, along with the location of the nodes corresponding to g-modes (the zeros of the radial eigenfunctions) marked with (blue) plus symbols."," \ref{propa} we plot the logarithm of the squared Brunt-Väiisällä and the Lamb frequencies, along with the location of the nodes corresponding to $g$ -modes (the zeros of the radial eigenfunctions) marked with (blue) plus symbols."
 The nodes associated to the eigenmodes exhibited by aare emphasized with black dots., The nodes associated to the eigenmodes exhibited by are emphasized with black dots.
" Note that these modes have nodes in the region 0.1<r/R.x1, implying that they have an oscillatory character in almost the whole star."," Note that these modes have nodes in the region $0.1 \lesssim r/R_* \lesssim 1$, implying that they have an oscillatory character in almost the whole star."
 We also examined the rotational kernels computed from our asteroseismological model for, We also examined the rotational kernels computed from our asteroseismological model for.
01224-20, In Fig.
"0.. In Fig. 2 we show the normalized K,,(r) for k=12 and k=24, corresponding to the shortest and the longest pulsation periods observed in0122--200."," \ref{kernel} we show the normalized $K_{k\ell}(r)$ for $k= 12$ and $k= 24$, corresponding to the shortest and the longest pulsation periods observed in."
". As can be seen, the rotation kernels have the largest amplitudes at the outer regions of the model, but have also appreciable amplitudes (up to = 0.3) throughout thefull model of0122+200,, implying that the observed g-modes are sensitive to the entire rotation profile."," As can be seen, the rotation kernels have the largest amplitudes at the outer regions of the model, but have also appreciable amplitudes (up to $\approx 0.3$ ) throughout the model of, implying that the observed $g$ -modes are sensitive to the entire rotation profile."
" T'his is in contrast to the case of DBV or DAV stars, in which rotational kernels sample only the outer regions of the star — see Kawaler et al. ("," This is in contrast to the case of DBV or DAV stars, in which rotational kernels sample only the outer regions of the star — see Kawaler et al. ("
1999) — because of the larger degeneracy of the core.,1999) — because of the larger degeneracy of the core.
" First, we assumed that rrotates as a rigid body, that is, the rotation rate €) is constant throughout the star."," First, we assumed that rotates as a rigid body, that is, the rotation rate $\Omega$ is constant throughout the star."
" We variated the value of 2 from 1.15x10"" Hz (P~100 days) to 2.77x10 Hz (P~1 minutes) and for each value of 2 we computed* the theoretical frequency splittings (dvge,) by means of Eq. (2)),"," We variated the value of $\Omega$ from $1.15 \times 10^{-7}$ Hz $P \sim 100$ days) to $2.77 \times 10^{-4}$ Hz $P \sim 1$ minutes) and for each value of $\Omega$ we computed the theoretical frequency splittings $\delta \nu_{k \ell m}^{\rm T}$ ) by means of Eq. \ref{rota-rigid}) ),"
" where the coefficients Cy, were assessed for each mode through Eq. (3))", where the coefficients $C_{k \ell}$ were assessed for each mode through Eq. \ref{coefi-c1}) )
" and not by means of the asymptotic relation, Cr,©1/£(£4-1)."," and not by means of the asymptotic relation, $C_{k \ell} \approx 1 / \ell(\ell+1)$."
" The results of this optimization procedure are shown in Fig. 3,,"," The results of this optimization procedure are shown in Fig. \ref{rigid},"
 that shows the x? function versus the rotation rate., that shows the $\chi^2$ function versus the rotation rate.
 The best-fit solution corresponds to a rotation rate of Q=6.915 µΗΖ., The best-fit solution corresponds to a rotation rate of $\Omega= 6.915$ $\mu$ Hz.
" It corresponds to a rotation period of P—40.17 hours, in good agreement with the approximate value of P—37.2 hours quoted by Fu et al. ("," It corresponds to a rotation period of $P= 40.17$ hours, in good agreement with the approximate value of $P= 37.2$ hours quoted by Fu et al. ("
2007).,2007).
" Note that the rotation period (of the order of 10° s) is much longer than the longest pulsation period exhibited by (~600 s), thus justifying the use of the perturbative theory to a first order in the calculation of óv,,."," Note that the rotation period (of the order of $10^5$ s) is much longer than the longest pulsation period exhibited by $\sim 600$ s), thus justifying the use of the perturbative theory to a first order in the calculation of $\delta\nu_{k \ell
m}^{\rm T}$."
" Here, we lift the assumption of solid-body rotation."," Here, we lift the assumption of solid-body rotation."
" Because the exploratory nature of this study, we try very simplified functional forms for Q(r)."," Because the exploratory nature of this study, we try very simplified functional forms for $\Omega(r)$."
" Specifically, we adopt a family of differential rotation profiles defined as: where € and Ως are the rotation rates at the stellar surface and center,respectively’."," Specifically, we adopt a family of differential rotation profiles defined as: where $\Omega_{\rm s}$ and $\Omega_{\rm c}$ are the rotation rates at the stellar surface and center,."
. This family of linear profiles includes rotation rates that decrease and increase linearly with r and also “flat” rotation profiles (when Ὡς= Ὡς) that represent the case of rigid rotation already examined in Sect. 3.1.., This family of linear profiles includes rotation rates that decrease and increase linearly with $r$ and also “flat” rotation profiles (when $\Omega_{\rm s}= \Omega_{\rm c}$ ) that represent the case of rigid rotation already examined in Sect. \ref{rig}.
" We performed our optimization procedures varying the parameters Ως and €, in the range 0—20 wHz.", We performed our optimization procedures varying the parameters $\Omega_{\rm s}$ and $\Omega_{\rm c}$ in the range $0-20$ $\mu$ Hz.
" We computed the theoretical frequency splittings by means of Eq. (4)),"," We computed the theoretical frequency splittings by means of Eq. \ref{rota-diff}) ),"
 where the rotation kernels are computed by using Eq. (5))., where the rotation kernels are computed by using Eq. \ref{rot-kernel}) ).
" The results are shown in Fig. 4,,"," The results are shown in Fig. \ref{linear-pg0122},"
" where we prefer to plot 1/x? instead of x? to emphasize the location of the values (Ως, Ως) providing good agreement between observed and theoretical frequency splittings."," where we prefer to plot $1/\chi^2$ instead of $\chi^2$ to emphasize the location of the values $\Omega_{\rm
 c},\Omega_{\rm s}$ ) providing good agreement between observed and theoretical frequency splittings."
" The region of good solutions (that is, the smallest values of x?) has an elongated shape."," The region of good solutions (that is, the smallest values of $\chi^2$ ) has an elongated shape."
" As can be seen, there exists a unique, well-localized best-fit solution at (Q-,Qs)=(10.62,4.41) wHz, marked with a black dot in the plot."," As can be seen, there exists a unique, well-localized best-fit solution at $(\Omega_{\rm c},\Omega_{\rm s})= (10.62, 4.41)\, \mu$ Hz, marked with a black dot in the plot."
" This solution is substantially different from rigid-rotation, which should fall at some point along the green dashed line."," This solution is substantially different from rigid-rotation, which should fall at some point along the green dashed line."
 The existence of the best fit solution suggests that the central regions of ccould be rotating more than twice faster than the surface., The existence of the best fit solution suggests that the central regions of could be rotating more than twice faster than the surface.
 We studied the sensitivity of our result to each of, We studied the sensitivity of our result to each of
detailed analysis by Burkert&Odell(1993).. and ODelletal.(2000).,"detailed analysis by \cite{burkert98}, and \cite{odell00}."
. The emereine optical picture of the cometary knots reveals (hat thev are neutral gas condensations Chat appear as comet like structures with rims bright in Ha. and tails that appear as shadows in [OI] and that point away [rom the central star., The emerging optical picture of the cometary knots reveals that they are neutral gas condensations that appear as comet like structures with rims bright in $\alpha$ and tails that appear as shadows in [OIII] and that point away from the central star.
 The rim of low-excitation ionize gas has a steep temperature eradient indicating that the knots are photo-evaporating and that ionization fronts are advancing into the knots (O'Delletal.2000)., The rim of low-excitation ionize gas has a steep temperature gradient indicating that the knots are photo-evaporating and that ionization fronts are advancing into the knots \citep{odell00}.
. A recent anlavsis of knots over the whole Helix nebula by ODelletal.(2004) revealed a new 3-D picture for (he main ring of the ]lelix: it is composed of a disk structure and an outer ring tilted almost perpendicularly with respect to Che disk., A recent anlaysis of knots over the whole Helix nebula by \cite{odell04} revealed a new 3-D picture for the main ring of the Helix: it is composed of a disk structure and an outer ring tilted almost perpendicularly with respect to the disk.
 Within each of these components. they observed a similar. progressive evolution in the structure of the knots.," Within each of these components, they observed a similar, progressive evolution in the structure of the knots."
 The knots closest to the central star and clearly inside ol the ionization front were elegantly carved with the brightest rims., The knots closest to the central star and clearly inside of the ionization front were elegantly carved with the brightest rims.
 The knots furthest from the central star appeared slightly more amorphous in their structure wilh less well defined rims., The knots furthest from the central star appeared slightly more amorphous in their structure with less well defined rims.
 The culmination of these optical observations appear to support the theory that these knots were iniiallv formed earlier by instabilities at (he ionization Iront or perhaps bv the interaction of the last stellar wind ancl (hen have been sculpted by interaction with the harsh radiation field of the central star (Capriotti1973)., The culmination of these optical observations appear to support the theory that these knots were initially formed earlier by instabilities at the ionization front or perhaps by the interaction of the fast stellar wind and then have been sculpted by interaction with the harsh radiation field of the central star \citep{capriotti73}.
". In contrast to the high angular resolution (—0.01"")) optical studies of the ionized eas lines in the cometary knots. the molecular gas observations have had lower angular resolution 11"")) and sensitivity making it difficult to determine the detailed structure and excitation of the main gas component of the cometary knots."," In contrast to the high angular resolution $\sim$ ) optical studies of the ionized gas lines in the cometary knots, the molecular gas observations have had lower angular resolution ) and sensitivity making it difficult to determine the detailed structure and excitation of the main gas component of the cometary knots."
 These low resolution studies have revealed that the IIelix has retained a significant amount of molecular gas (Youngetal.Healy1986:Specketal.2002) ancl that the molecular gas appears to be very clumpy. and is probably confined {ο cometary knot structures (Speckllugeinsetal. 2002).," These low resolution studies have revealed that the Helix has retained a significant amount of molecular gas \citep{young99,huggins86,speck02} and that the molecular gas appears to be very clumpy and is probably confined to cometary knot structures \citep{speck02, huggins02}."
. The only detailed study of an isolated cometary knot. whieh is close to the central star. shows no evidence for large velocities in the molecular gas. ruling out a stellar wind shaping the knot. ancl reveals a stratified structure for the ionized aud molecular eas emissions (hat is expected in a photodissociation region (PDR) (IIugeinsetal.2002).," The only detailed study of an isolated cometary knot, which is close to the central star, shows no evidence for large velocities in the molecular gas, ruling out a stellar wind shaping the knot, and reveals a stratified structure for the ionized and molecular gas emissions that is expected in a photodissociation region (PDR) \citep{huggins02}."
. Ilowever. since recent optical studies show an evolution of the knot structure with radial distance from (he central star (ODelletal.2004)... it is not clear Chat this single knot study is representative of all (he knots in the nebula.," However, since recent optical studies show an evolution of the knot structure with radial distance from the central star \citep{odell04}, it is not clear that this single knot study is representative of all the knots in the nebula."
" Ii order to determine the structure and excitation of the Is emission in the cometary knots at comparable resolution to optical images across (he Helix. we pursued high angular resolution (70.2 ) NICMOS/NIC3 F212N II, images at several locations in the nebula. in parallel with the HST/ACS program recently published by O'Delletal.(2004)."," In order to determine the structure and excitation of the $_2$ emission in the cometary knots at comparable resolution to optical images across the Helix, we pursued high angular resolution $\sim$ 0.2 ) NICMOS/NIC3 F212N $_2$ images at several locations in the nebula, in parallel with the HST/ACS program recently published by \cite{odell04}."
. The remainder of this paper is organized as follows., The remainder of this paper is organized as follows.
 In section 2. we report the observation and data processing procedures.," In section 2, we report the observation and data processing procedures."
 In section 3. we discuss the major observational results ancl how these relate to the optical ionized gas line emissions imaged by ODelletal. (2004)..," In section 3, we discuss the major observational results and how these relate to the optical ionized gas line emissions imaged by \cite{odell04}. ."
tails themselves appear clearly brighter in the residual maps produced by subtraction of these models from the origina images.,tails themselves appear clearly brighter in the residual maps produced by subtraction of these models from the original images.
 TPhis shows that without masking. some of the lieh from the tails is included in the model. mocdifving the fi parameters.," This shows that without masking, some of the light from the tails is included in the model, modifying the fit parameters."
" 7? constructed a ""merger sequence! from. a sample of galaxies that are good. candidates for ongoing mergers anc remnants of mergers between two approximately equal mass disc galaxies.", \scite{keelwu95} constructed a `merger sequence' from a sample of galaxies that are good candidates for ongoing mergers and remnants of mergers between two approximately equal mass disc galaxies.
" Phey assigned a ""merger stage’ to each galaxy sed: upon dynamical crossing times. with zero age define o be the point of nuclear coalescence."," They assigned a `merger stage' to each galaxy based upon dynamical crossing times, with zero age defined to be the point of nuclear coalescence."
 They noted that the raction of galaxy starlight contained within the tails roughly anti-correlates with this merger stage., They noted that the fraction of galaxy starlight contained within the tails roughly anti-correlates with this merger stage.
 This allows us make a very rough estimate of the time-scale since the merger event hat created the tails within NGC 1700., This allows us make a very rough estimate of the time-scale since the merger event that created the tails within NGC 1700.
 This analvsis was performed. on the long exposure residual images., This analysis was performed on the long exposure residual images.
 As we wanted to include as much of the ail light in the residual images as possible. we used. the residual images produced. by excluding the tails from the elliptical fit of the galaxy.," As we wanted to include as much of the tail light in the residual images as possible, we used the residual images produced by excluding the tails from the elliptical fit of the galaxy."
 As mentioned. above. if the tails are not masked out during the fit. some of their light= is included. in the model. mocifving the fit. parameters and resulting in the subtraction of a significant amount of tail light from the galaxy image.," As mentioned above, if the tails are not masked out during the fit, some of their light is included in the model, modifying the fit parameters and resulting in the subtraction of a significant amount of tail light from the galaxy image."
 The total Dux contained within 300 small circular apertures positioned on the tails was measured using the utilityIMENAMINE., The total flux contained within $\sim300$ small circular apertures positioned on the tails was measured using the utility.
. This was used to derive a mean surface brightness for the tails. which was then multiplied by their total area (i6. including the area missed due to contaminating bright sources).," This was used to derive a mean surface brightness for the tails, which was then multiplied by their total area (i.e. including the area missed due to contaminating bright sources)."
 The resulting surface brightnesses were 26.6. 25.9 and 24.4 mag [or the B. V. and. { bands respectively.," The resulting surface brightnesses were 26.6, 25.9 and 24.4 mag for the $B$, $V$ and $I$ bands respectively."
 The total light. in the tails was divided by the total galaxy light to give the ‘tail fraction’., The total light in the tails was divided by the total galaxy light to give the `tail fraction'.
 We also roughly estimated the total tail light using polvgon-shaped apertures., We also roughly estimated the total tail light using polygon-shaped apertures.
 This method gave a similar result to the mean surface brightness method but included he light from contaminating point sources and was thus less reliable., This method gave a similar result to the mean surface brightness method but included the light from contaminating point sources and was thus less reliable.
 The tail fractions inthe D. V and { bands were found to o L84. 1.0 and 1.72 percent respectively.," The tail fractions in the $B$, $V$ and $I$ bands were found to be $1.84$ , $1.64$ and $1.72$ per cent respectively."
 Phe tail fractions in ? were derived in the V. band. with a few exceptions.," The tail fractions in \scite{keelwu95} were derived in the $V$ band, with a few exceptions."
 We hus use our V band tail fraction (which is similar to the D and 4 values) for NGC 1700 in the following analvsis., We thus use our $V$ band tail fraction (which is similar to the $B$ and $I$ values) for NGC 1700 in the following analysis.
 We fitted a linear least-square to the points obtained from he ? data., We fitted a linear least-square to the points obtained from the \scite{keelwu95} data.
 This fit is shown as a dashed line in Fig. 7.., This fit is shown as a dashed line in Fig. \ref{fig:TF}.
 The solid horizontal line represents the measured. V. band all fraction for NGC 1700., The solid horizontal line represents the measured $V$ band tail fraction for NGC 1700.
 ΠΕ we extrapolate the fit we ind that the V. band tail fraction measured for NGC 1700 corresponds to a merger stage of 8.13.8., If we extrapolate the fit we find that the $V$ band tail fraction measured for NGC 1700 corresponds to a merger stage of $8.1\pm3.8$.
 Ehe large error on his stage estimate is due to the scatter of the data points of ?.., The large error on this stage estimate is due to the scatter of the data points of \scite{keelwu95}.
 We also performed a quadratic fit on the heel Wu data., We also performed a quadratic fit on the Keel Wu data.
 Extrapolating this fit vielded a stage comparable with he result. using a linear least-square fit., Extrapolating this fit yielded a stage comparable with the result using a linear least-square fit.
 ὃν comparing the spectroscopic (1.0. central starburst) ages of several galaxies in the 7. sample with their assigned merger stage. we determined the time since nuclear coalescence.," By comparing the spectroscopic (i.e. central starburst) ages of several galaxies in the \scite{keelwu95} sample with their assigned merger stage, we determined the time since nuclear coalescence."
 For the stage of NGC 1700. the time since the central starburst and hence tail formation is approximately 3.2+1.5 Gvr.," For the stage of NGC 1700, the time since the central starburst and hence tail formation is approximately $3.2\pm1.5$ Gyr."
 A lower limit for the age of the ticaltails can be, A lower limit for the age of the tidaltails can be
conditions cnvisagecl here. there are two grain destruction mechanisms that must be considered.,"conditions envisaged here, there are two grain destruction mechanisms that must be considered."
 First. if the grains hemselves become too hot. they will rapidly sublime.," First, if the grains themselves become too hot, they will rapidly sublime."
 The eran temperature will be set by the thermal equilibrium oetween the AGN radiation incident on a given grain and the hermal raciation emitted by that grain (e.g. see Barvainis 1987)., The grain temperature will be set by the thermal equilibrium between the AGN radiation incident on a given grain and the thermal radiation emitted by that grain (e.g. see Barvainis 1987).
 For 6-30-15. the (1.0. the radius from the ACN within which dust. grains become so ιοί that they sublime) is ~101Tem.," For $-$ 6-30-15, the (i.e. the radius from the AGN within which dust grains become so hot that they sublime) is $\sim 10^{17}\cm$."
 Thus. any dust. &rains within the inner warm absorber would be rapidly sublimed ow the intense radiation field.," Thus, any dust grains within the inner warm absorber would be rapidly sublimed by the intense radiation field."
 Dust in the outer warn absorber would not be subject to significant sublimation., Dust in the outer warm absorber would not be subject to significant sublimation.
 The second. dust. destruction. mechanism that we must) consider is thermal sputtering., The second dust destruction mechanism that we must consider is thermal sputtering.
 Lf we make the standard: assumption that the (outer) warm. absorber is photoionized. then photoionization models suggest that the eas temperature is only Z—510Ix and thermal sputtering is negligible.," If we make the standard assumption that the (outer) warm absorber is photoionized, then photoionization models suggest that the gas temperature is only $T\sim 5\times 10^4\K$ and thermal sputtering is negligible."
" HL. instead. we suppose that the outer warm absorber is purely collisionallv-ionized. gas temperatures of Z10""Ix are required. in order to achieve 16 observed ionization states (Shull van Steenberg 1982)."," If, instead, we suppose that the outer warm absorber is purely collisionally-ionized, gas temperatures of $T\sim 10^6\K$ are required in order to achieve the observed ionization states (Shull van Steenberg 1982)."
 —_from. the expressions of Burke Silk (1974). the thermal sputtering timescale for this temperature is where n ids the electron. number censity in the gas.," From the expressions of Burke Silk (1974), the thermal sputtering timescale for this temperature is where $n$ is the electron number density in the gas."
 Suppose that r is the distance of the outer warm absorber from the central engine. and L is the (ionizing)luminosity of the central engine.," Suppose that $r$ is the distance of the outer warm absorber from the central engine, and $L$ is the (ionizing)luminosity of the central engine."
 Furthermore. define δριμάν822Ocrgems to be the ionization parameter of a photoionized plasma in which oxveen is ionized to the same degree às seen in the outer warm absorber of 6-30-15.," Furthermore, define $\xi_{\rm equiv}\approx 20\erg\cm\ps$ to be the ionization parameter of a photoionized plasma in which oxygen is ionized to the same degree as seen in the outer warm absorber of $-$ 6-30-15."
 Given our (temporary) hypothesis that the plasma is collisionallv-ionized. the density must. satisfy or else photoionization would dominate the ionization state.," Given our (temporary) hypothesis that the plasma is collisionally-ionized, the density must satisfy or else photoionization would dominate the ionization state."
 Evaluating the sputtering timescale for the parameters of 6-30-15 gives For comparison. the How timescale of the outer warn absorber is where we have acoptec a typical value of eg=1000kins for the velocity of the outer warm absorber. as indicated by UV. absorption line studies of other ACN (Alathur. Elvis Wilkes 1995).," Evaluating the sputtering timescale for the parameters of $-$ 6-30-15 gives For comparison, the flow timescale of the outer warm absorber is where we have adopted a typical value of $v_{\rm flow}=1000\kmps$ for the velocity of the outer warm absorber, as indicated by UV absorption line studies of other AGN (Mathur, Elvis Wilkes 1995)."
 It can be seen that. the low timescale of the warm absorber always exceeds the sputtering timescale unless rxLOOpe., It can be seen that the flow timescale of the warm absorber always exceeds the sputtering timescale unless $r\approxgt 100\pc$.
 LE the outer warm absorber was situated at such a laree distance. then either we would have to be viewing the AGN along a very special line of sight. or else the mass. A. and kinetic energy. Lic. associated with the outflow would both be huge.," If the outer warm absorber was situated at such a large distance, then either we would have to be viewing the AGN along a very special line of sight, or else the mass, $M$, and kinetic energy, $L_{\rm K}$, associated with the outflow would both be huge."
 From the expressions of Revnolds Fabian (1995). and. assuming a global covering fraction of f.=0.1. we get AZ~LO?M. and Ly~32107eresL.," From the expressions of Reynolds Fabian (1995), and assuming a global covering fraction of $f_{\rm c}=0.1$, we get $M\sim 10^6\Msun$ and $L_{\rm K}\sim 3\times 10^{42}\ergps$."
C The initial acceleration of this material would. be extremely problematic to. understand., The initial acceleration of this material would be extremely problematic to understand.
 We consider this possibility to be unphysical., We consider this possibility to be unphysical.
 Thus. in the absence of a viable. collisionally-ionizecl model. Whilst dust can survive in warn photoionizecl gas. it is extremely dillieult to form dust in such an environment: the grains could. never assemble at. such tempcratures.," Thus, in the absence of a viable, collisionally-ionized model, Whilst dust can survive in warm photoionized gas, it is extremely difficult to form dust in such an environment: the grains could never assemble at such temperatures."
 Furthermore. a comparison of the column density of the warm absorber with the cold column expected. to. be associated. with the reddening reveals that the warni-eas/dust ratio in the warm absorber must be very. similar to the cold-gas/dust. ratio in our Galaxy.," Furthermore, a comparison of the column density of the warm absorber with the cold column expected to be associated with the reddening reveals that the warm-gas/dust ratio in the warm absorber must be very similar to the cold-gas/dust ratio in our Galaxy."
 These two facts taken together suggest that the warm material. originates from cdusty. cold material. possibility via radiative heating. and that a substantial fraction. of the dust. survives the heating process.," These two facts taken together suggest that the warm material originates from dusty cold material, possibility via radiative heating, and that a substantial fraction of the dust survives the heating process."
 The putative cust’ molecular torus. of Sevlert unification schemes might be a possible progenitor of such a raciativelv-driven. warm. dusty outflow.," The putative dusty molecular torus of Seyfert unification schemes might be a possible progenitor of such a radiatively-driven, warm, dusty outflow."
 We have constructed photoionization models of dusty warm absorbers using the photoionization codeCLOUDY., We have constructed photoionization models of dusty warm absorbers using the photoionization code.
 Cirids of such models were constructed for various values of the column cdensitv Nw. ionization. parameter £ ancl X-ray whoton indices E.," Grids of such models were constructed for various values of the column density $N_{\rm W}$, ionization parameter $\xi$ and X-ray photon indices $\Gamma$."
 Since we are interested in the behaviour of the outer warm absorber. the distance of the absorber rom the primary source was fixed at ppc.," Since we are interested in the behaviour of the outer warm absorber, the distance of the absorber from the primary source was fixed at pc."
 Otherwise. these models are identical to those of Fabian et al. (," Otherwise, these models are identical to those of Fabian et al. ("
1994) and tevnolds et al. (,1994) and Reynolds et al. (
1995) except for the inclusion of dust grains.,1995) except for the inclusion of dust grains.
 The grain models used are described in (the manual o CLOUDY) pp., The grain models used are described in (the manual to ) pp.
 284., 284.
 Prompted by the observations of the »wevious paragraph. we have fixed the gas/clust ratio to Galactic value.," Prompted by the observations of the previous paragraph, we have fixed the gas/dust ratio to Galactic value."
 Two such grids were computed: one contains a standard (ic. local) mixture of silicate and graphite grains whereas the other contains only graphite grains., Two such grids were computed: one contains a standard (i.e. local) mixture of silicate and graphite grains whereas the other contains only graphite grains.
 These models were fitted to the data., These models were fitted to the data.
 Since we are interested in modeling fine details of the soft. spectrum. only cata from the best calibrated: solid-state imaging spectrometer (SISO) were used in the spectral fitting," Since we are interested in modeling fine details of the soft spectrum, only data from the best calibrated solid-state imaging spectrometer (SIS0) were used in the spectral fitting"
(seee.g.[T996)..,\citep[see e.g.][]{1996JOSAA..13.2266M}.
" Although this is in principle not impossible, for irregularly shaped constituents the computational demand of such an approach is very high, and at the moment not feasible."," Although this is in principle not impossible, for irregularly shaped constituents the computational demand of such an approach is very high, and at the moment not feasible."
" If the constituents themselves are very small while most of the interactions take place over relatively large distances, like in a large aggregate of many very small constituents, the dominant interaction is dipole-dipole interaction."," If the constituents themselves are very small while most of the interactions take place over relatively large distances, like in a large aggregate of many very small constituents, the dominant interaction is dipole-dipole interaction."
 The optical properties of such an aggregate of coupled dipoles can be computed using the Coupled Dipole Approximation (CDA)., The optical properties of such an aggregate of coupled dipoles can be computed using the Coupled Dipole Approximation (CDA).
 In this approximation each aggregate constituent is considered to interact as a single dipole with a given polarizability., In this approximation each aggregate constituent is considered to interact as a single dipole with a given polarizability.
" The difference with the well-known Discrete Dipole Approximation (DDA,seee.g.[[988) is that in DDA the volume of the constituents themselves have to be discretized using multiple dipoles."," The difference with the well-known Discrete Dipole Approximation \citep[DDA, see e.g.][]{1973ApJ...186..705P, 1988ApJ...333..848D} is that in DDA the volume of the constituents themselves have to be discretized using multiple dipoles."
 This has to be done in order to account for the shape of the aggregate constituents., This has to be done in order to account for the shape of the aggregate constituents.
 In the CDA we account for the shape of the constituents by using for each constituent a polarizability representative of an irregularly shaped grain., In the CDA we account for the shape of the constituents by using for each constituent a polarizability representative of an irregularly shaped grain.
 The mathematical formulation of both the CDA and the DDA is exactly the same; it describes the interaction of dipoles., The mathematical formulation of both the CDA and the DDA is exactly the same; it describes the interaction of dipoles.
" However, the numerical implementation might be slightly different."," However, the numerical implementation might be slightly different."
 In the DDA one can choose the dipoles to be located on a rectangular grid., In the DDA one can choose the dipoles to be located on a rectangular grid.
 This allows for the use of Fast Fourier Transform (FFT) methods to increase the numerical performance significantly [1991] [I998)..," This allows for the use of Fast Fourier Transform (FFT) methods to increase the numerical performance significantly \citep{Goodman1991, Hoekstra}."
" Since the constituents of an aggregate are usually not located on a rectangular grid, this is in general not possible when using the CDA."," Since the constituents of an aggregate are usually not located on a rectangular grid, this is in general not possible when using the CDA."
" In addition, the speedup in DDA using the FFT method requires one to fill a rectangular box circumscribing the aggregate with dipoles."," In addition, the speedup in DDA using the FFT method requires one to fill a rectangular box circumscribing the aggregate with dipoles."
" Since we wish to consider very fluffy grains with a low volume filling factor, this is very inefficient and would require many additional dipoles."," Since we wish to consider very fluffy grains with a low volume filling factor, this is very inefficient and would require many additional dipoles."
 A method providing a similar speedup as the FFT method is being developedMethod for the CDA computations using the Fast Multipole (Κος&Chew2001;[AminiProfi2003).," A method providing a similar speedup as the FFT method is being developed for the CDA computations using the Fast Multipole Method \citep{Koc2001, Amini2003}."
 As we mentioned above the approach of only considering the dipole-dipole interactions is valid if the constituents are small and the long range interactions between them dominate., As we mentioned above the approach of only considering the dipole-dipole interactions is valid if the constituents are small and the long range interactions between them dominate.
 This is the situation we are currently interested in., This is the situation we are currently interested in.
" Future computations, using a method taking into account the multipole interactions, like the superposition T-matrix method or large scale DDA simulations using multiple dipoles per constituent, can be employed to check the accuracy of the approximation we employ here."," Future computations, using a method taking into account the multipole interactions, like the superposition T-matrix method or large scale DDA simulations using multiple dipoles per constituent, can be employed to check the accuracy of the approximation we employ here."
" When we consider for each particle of the aggregate only dipole interactions we have [1988) where P; is the local dipole moment at the position of particle j, a; is the polarizability of particle j, Ej; is the incoming field at the location of particle j, and N is the total number of constituents in the aggregate."," When we consider for each particle of the aggregate only dipole interactions we have \citep{1988ApJ...333..848D}
 where $\vec{P}_j$ is the local dipole moment at the position of particle $j$, $\alpha_j$ is the polarizability of particle $j$, $\vec{E}_{\mathrm{inc},j}$ is the incoming field at the location of particle $j$, and $N$ is the total number of constituents in the aggregate."
 The matrix Ajx determines the electric field at the position of particle j due to the dipole field emitted by particle k (fordetails[[988).., The matrix $\matrix{A}_{jk}$ determines the electric field at the position of particle $j$ due to the dipole field emitted by particle $k$ \citep[for details see e.g.][]{1988ApJ...333..848D}.
 When Eq. (3)), When Eq. \ref{eq:DDA}) )
" is solved for the P; the mass absorption coefficient can be computed by where V is the total material volume of the aggregate, o is the average material density, and the asterisks denote the complex conjugates."," is solved for the $\vec{P}_j$ the mass absorption coefficient can be computed by where $V$ is the total material volume of the aggregate, $\rho$ is the average material density, and the asterisks denote the complex conjugates."
 The dipole polarizability of a homogeneous spherical particle is given by where m is the complex refractive index of the particle material., The dipole polarizability of a homogeneous spherical particle is given by where $m$ is the complex refractive index of the particle material.
 The polarizability of irregularly shaped particles depends on the particle shape., The polarizability of irregularly shaped particles depends on the particle shape.
" However, a reasonable approximation for the average polarizability of an ensemble of highly irregular particles is given by the Continuous Distribution of Ellipsoids (CDE;see[BohrenHuffman| [2006b).."," However, a reasonable approximation for the average polarizability of an ensemble of highly irregular particles is given by the Continuous Distribution of Ellipsoids \citep[CDE; see][]{BohrenHuffman, 2006JQSRT..97..161M}."
 The CDE polarizability is& given by More realistic polarizabilities can be computed using the method of (2006b).., The CDE polarizability is given by More realistic polarizabilities can be computed using the method of \citet{2006JQSRT..97..161M}.
" However, here we wish to study only the effects of using irregularly shaped particles as monomers so we employ the frequently used CDE polarizability for the aggregate constituents."," However, here we wish to study only the effects of using irregularly shaped particles as monomers so we employ the frequently used CDE polarizability for the aggregate constituents."
 In the following subsections we will first define two quantities we use for the analysis of the emission spectra of the aggregates., In the following subsections we will first define two quantities we use for the analysis of the emission spectra of the aggregates.
 Then we will discuss how the aggregates are constructed and what composition we will assume., Then we will discuss how the aggregates are constructed and what composition we will assume.
 The mass absorption coefficient as given by Eq. (4), The mass absorption coefficient as given by Eq. \ref{eq:total kappa}) )
 is basically the sum over the absorption contributions of each component of the aggregate., is basically the sum over the absorption contributions of each component of the aggregate.
 We can thus easily compute the effective mass absorption coefficient of a part of the aggregate by summing over only that part of the components., We can thus easily compute the effective mass absorption coefficient of a part of the aggregate by summing over only that part of the components.
 In this way we can create an for each, In this way we can create an for each
where Q(I) is given bv (27). F; and /; are the place and time of injection. repectivelv.,"where $Q(E_0)$ is given by , $\vec{r_i}$ and $t_i$ are the place and time of injection, repectively."
 We note. that the energv. 2 of a particle al time / is linked (ο ils οποιον Ey al injection by ).," We note, that the energy $E$ of a particle at time $t$ is linked to its energy $E_0$ at injection by )."
 The anisotropy in the CR flux can be calculated in the context of diffusion as where V.N denotes the gradient of ./N.," The anisotropy in the CR flux can be calculated in the context of diffusion as \citep{1964ocr..book.....G}
 where $\nabla N$ denotes the gradient of $N$."
 The expected anisotropy in the positron LIS was calculated. assuming the contribution of a nearby source. as given by(35).. on top of an isotropic background.," The expected anisotropy in the positron LIS was calculated assuming the contribution of a nearby source, as given by, on top of an isotropic background."
 For the background we assumed a power law [it given by (1998).., For the background we assumed a power law fit given by \citet{1998ApJ...498..779B}.
 The calculated anisotropies are given in the right panels of Figs., The calculated anisotropies are given in the right panels of Figs.
 1 and 2 (thin lines)., \ref{fig:geminga} and \ref{fig:bo656} (thin lines).
 To get an estimate of the maximum expected anisotropy. we also calculate the anisotropy assumine (hat the whole CR positron {lux originates [rom a point source (thick lines in the rightpanels of Figs.," To get an estimate of the maximum expected anisotropy, we also calculate the anisotropy assuming that the whole CR positron flux originates from a point source (thick lines in the rightpanels of Figs."
 1 aud 2)).For energy-independent diffusion. Mao&Shen(1972) derived (he simple relation," \ref{fig:geminga} and \ref{fig:bo656}) ).For energy-independent diffusion, \citet{1972ChJPh..10...16M} derived the simple relation"
can be traced back to pioneeding works by Giovanelli (1946) and Dungey (1953).,can be traced back to pioneeding works by Giovanelli (1946) and Dungey (1953).
 The uncertainties with understanding of fast reconnection were one of the impediments for applying the process to energetic particle acceleration (see Lazarian Opher 2009)., The uncertainties with understanding of fast reconnection were one of the impediments for applying the process to energetic particle acceleration (see Lazarian Opher 2009).
" We appeal to the model of reconnection of weakly stochastic field in Lazarian Vishniac (1999), which was identified as a cause of First Order Fermi acceleration (see de Gouveia dal Pino Lazarian 2005, Lazarian 2005)."," We appeal to the model of reconnection of weakly stochastic field in Lazarian Vishniac (1999), which was identified as a cause of First Order Fermi acceleration (see de Gouveia dal Pino Lazarian 2005, Lazarian 2005)."
" In what follows we present the observational evidence for the existence of the cosmic ray excess in the direction of the solar system magnetotail in §2,, discuss existing explanations of this excess in §3.."," In what follows we present the observational evidence for the existence of the cosmic ray excess in the direction of the solar system magnetotail in \ref{sec:obs}, discuss existing explanations of this excess in \ref{sec:interp}."
 The structure of the magnatotail with magnetic field reversals arising from the solar cycle is presented in §4 and the mechanism of acceleration of cosmic rays in the magnetotail is outlined in §5.., The structure of the magnatotail with magnetic field reversals arising from the solar cycle is presented in \ref{sec:magfi} and the mechanism of acceleration of cosmic rays in the magnetotail is outlined in \ref{sec:magrec}.
" The discussion of the results and a short summary are given by 86 and §7,, respectively."," The discussion of the results and a short summary are given by \ref{sec:disc} and \ref{sec:summ}, respectively."
 The observation of the large angular scale anisotropy of sub-TeV cosmic rays (Nagashimaetal.1998;Halletal. revealed the evidence of a superposition of two 1999)different modulations in arrival direction.," The observation of the large angular scale anisotropy of sub-TeV cosmic rays \citep{nagashima,hall} revealed the evidence of a superposition of two different modulations in arrival direction."
 One with a sidereal variation identified with an extended deficit centered around 12 hours that seems to extend mostly across the northern hemisphere (the so-called loss cone)., One with a sidereal variation identified with an extended deficit centered around 12 hours that seems to extend mostly across the northern hemisphere (the so-called loss cone).
" And one with sidereal variation identified with a broad excess centereda around 6 hours, with half opening angle of about 68° that comprises the direction of the heliotail, and extended across part of the northern and the southern hemispheres (the tail-in excess)."," And one with a sidereal variation identified with a broad excess centered around 6 hours, with half opening angle of about $^{\circ}$ that comprises the direction of the heliotail, and extended across part of the northern and the southern hemispheres (the tail-in excess)."
 Figure 1 shows the combined observations of the anisotropy of sub-TeV cosmic rays from telescopes at different latitudes., Figure \ref{fig:nagashima} shows the combined observations of the anisotropy of sub-TeV cosmic rays from telescopes at different latitudes.
" 'The global anisotropy amplitude is found to increase with energy up to about 5-10 TeV, however while the loss-cone structure seems to maintain a similar shape up to the multi-TeV range, the tail-bin excess is still somewhat persistent in the multi-TeV range, but its broad structure appears to dissolve to smaller angular scale spots (Amenomorietal."," The global anisotropy amplitude is found to increase with energy up to about 5-10 TeV, however while the loss-cone structure seems to maintain a similar shape up to the multi-TeV range, the tail-in excess is still somewhat persistent in the multi-TeV range, but its broad structure appears to dissolve to smaller angular scale spots \citep{amenomori}."
"2006).. The apparent seasonal modulation of the tail-in excess, with a minimum amplitude in summer and a maximum (a factor of four in winter, provides a compelling connection to the larger)heliotail."," The apparent seasonal modulation of the tail-in excess, with a minimum amplitude in summer and a maximum (a factor of four larger) in winter, provides a compelling connection to the heliotail."
" Figure 2 shows the multi-TeV cosmic ray arrival direction map, from the MILAGRO collaboration, obtained by eliminating anisotropies with angular structures wider than ~30°."," Figure \ref{fig:milagromap} shows the multi-TeV cosmic ray arrival direction map, from the MILAGRO collaboration, obtained by eliminating anisotropies with angular structures wider than $\sim$ $^{\circ}$."
 The small scale structure is evidenced in this map and it shows two highly significant than 12 localized excess regions in the cosmic rays (morearrival direction., The small scale structure is evidenced in this map and it shows two highly significant (more than 12 $\sigma$ ) localized excess regions in the cosmic rays arrival direction.
"σ) Both regions are inconsistent with gamma, ray emission with high confidence and therefore are claimed to be dominated by cosmic rays.", Both regions are inconsistent with gamma ray emission with high confidence and therefore are claimed to be dominated by cosmic rays.
" They are found to have a constant yearly excess over the seven year period of collected data, however both of them were lowest in summer and highest in winter, with a x? probability relative to a constant fractional excess of only in each region."," They are found to have a constant yearly excess over the seven year period of collected data, however both of them were lowest in summer and highest in winter, with a $\chi^2$ probability relative to a constant fractional excess of only in each region."
" The strongest and more localized of them (called region A, with a fractional excess of ~6x 1072) coincides with the direction of the heliotail (the black dot in Figure 2,, with right ascension aez74? and declination 6z+17° in equatorial coordinates)."," The strongest and more localized of them (called region A, with a fractional excess of $\sim 6\times 10^{-4}$ ) coincides with the direction of the heliotail (the black dot in Figure \ref{fig:milagromap}, with right ascension $\alpha \approx 74^{\circ}$ and declination $\delta \approx +17^{\circ}$ in equatorial coordinates)."
 The corresponding energy spectrum was de-convoluted using the energy-dependent experimental observables., The corresponding energy spectrum was de-convoluted using the energy-dependent experimental observables.
 Figure 3 shows the result of the χ fit to the excess in region A, Figure \ref{fig:regiona} shows the result of the $\chi^2$ fit to the excess in region A
 (Ryuοἱal.2003).. T>10* 7—10°I0* 2005).. forareview)..," \citep{rkhj03}, $T > 10^7$ $T = 10^5 - 10^7$ \citep{co99,krcs05}. \citep[see][for a review]{car02}."
 ~iG 10 (Iximοἱal.1990)., $\sim\mu$ $\sim 10$ \citep{kim90}.
. 100—200radm7 ~5 μα (Clarkeοἱal.2001:Clarke2004).. (Vogt&EnBlin2005).," $\sim100 -200\ {\rm rad\ m^{-2}}$ $\sim 5$ $\mu$ \citep{cla01,cla04}. \citep{vog05},"
. (Guiclettiοἱal.2008) (Bonaledeetal.2010).., \citep{gmgp08} \citep{bfmg10}.
stellaar X-ray and EUV radiation.,ar X-ray and EUV radiation.
"Fiewre ον shows the Afoyya, relation.",Figure \ref{msigma} shows the $M_{200} - \sigma _p$ relation.
 The tieht relation indicates that the caustic asses are well correlated with velocity dispersion estimates., The tight relation indicates that the caustic masses are well correlated with velocity dispersion estimates.
 The eood correlation is perhaps not surprising because both parameters depend on the galaxy velocity distribution., The good correlation is perhaps not surprising because both parameters depend on the galaxy velocity distribution.
 The best-fit slope is Mog)Xο... with the uucertaintv estimated frou jackkuife resampling., The best-fit slope is $M_{200}\propto\sigma_p^{3.18\pm0.19}$ with the uncertainty estimated from jackknife resampling.
 We compare the caustic masses to virial mass estimates iu 512.., We compare the caustic masses to virial mass estimates in $\S$ \ref{virial}.
 The excellent agreement between the caustic masses and the N-ray masses frou previously determined scaling relation between nass and X-ray temperatures confinis the prediction of D99 that the caustic lass estimate is unbiased., The excellent agreement between the caustic masses and the X-ray masses from previously determined scaling relation between mass and X-ray temperatures confirms the prediction of D99 that the caustic mass estimate is unbiased.
 CAIRNS found similar agrecment between caustic masses and κταν and virial mass estimates (2): 7? show eood aerecinent between masses estimated from the caustics and weak Ieusiug., CAIRNS found similar agreement between caustic masses and X-ray and virial mass estimates \citep{cairnsi}; \citet{diaferio05} show good agreement between masses estimated from the caustics and weak lensing.
 We fit the mass profiles of the CAIRNS clusters. to three simple analytic models., We fit the mass profiles of the CAIRNS clusters to three simple analytic models.
 The simplest model of a selferavitating svstem is a sineular isothermal sphere (SIS)., The simplest model of a self-gravitating system is a singular isothermal sphere (SIS).
 The mass of the SIS increases linearly with radius., The mass of the SIS increases linearly with radius.
 7. aud ? propose tsvo-paraieter models based on CDAL simulations of haloes., \citet{nfw97} and \citet{hernquist1990} propose two-parameter models based on CDM simulations of haloes.
 We note that the caustic mass profiles mostly saluple large radi and are therefore not very scusitive to the inner slope of the mass profile., We note that the caustic mass profiles mostly sample large radii and are therefore not very sensitive to the inner slope of the mass profile.
 Thus. we do not consider alternative models which differ only in the iuner slope of the density profile (ee.?)..," Thus, we do not consider alternative models which differ only in the inner slope of the density profile \citep[e.g.,][]{moore99}."
 At lee radii. the best constraiuts on cluster iiass profiles come from galaxy dynamics aud weak lensing.," At large radii, the best constraints on cluster mass profiles come from galaxy dynamics and weak lensing."
 The caustic mass profiles of Coma (2).. À576 (2).. A2199 (7) and the rest of the CAIRNS clusters ο} provided stroug evidence against a sineular isothermal sphere (SIS) profile aud in favor of steeper mass density profiles predicted by 7. (NFA) and ?..," The caustic mass profiles of Coma \citep{gdk99}, A576 \citep{rines2000}, A2199 \citep{rines02} and the rest of the CAIRNS clusters \citep{cairnsi} provided strong evidence against a singular isothermal sphere (SIS) profile and in favor of steeper mass density profiles predicted by \citet{nfw97} (NFW) and \citet{hernquist1990}."
 Oulv recently have weak lensing mass estimates been able to distinguish between SIS and NEW density profiles at large racii (27).," Only recently have weak lensing mass estimates been able to distinguish between SIS and NFW density profiles at large radii \citep{clowe01,kneib03}."
 At large radii. the NEW aass profile increases as In(i) and the mass ofthe Hreruquist model converges.," At large radii, the NFW mass profile increases as $(r)$ and the mass ofthe Hernquist model converges."
 The NEW lass profile is Min) 7 where e6 ds the scale radius and Af(a) is the mass within e., The NFW mass profile is M(<r) = where $a$ is the scale radius and $M(a)$ is the mass within $a$.
" We ft the paramcter AZ(e) rather than the characteristic density à, (M(a)=Ιπὸ,ρ,a?{In(2)1| where p. is the critical deusitv) because Αα} aud « are mich less correlated than 3, and e (?).."," We fit the parameter $M(a)$ rather than the characteristic density $\delta_c$ ${M(a) = 4\pi \delta_c \rho_c a^3 [\mbox{ln}(2) -
\frac{1}{2}]}$ where $\rho_c$ is the critical density) because $M(a)$ and $a$ are much less correlated than $\delta_c$ and $a$ \citep{mahdavi99}."
 The IHeruquist lass profile is Mir) = MiUB where αμ is the scale radius aud A is the total mass., The Hernquist mass profile is M(<r) = M where $a_H$ is the scale radius and $M$ is the total mass.
 Note that ἁαμ)=ALL., Note that $M(a_H) = M/4$.
 The SIS mass profile is M(«ry)X orc.We minimize u and st the best-fit parameters a. Cogo. the couceutration ονε τουα. aud. ουν for the best-ft NEW model and indicate the best-fit profile type in Table 11..," The SIS mass profile is $M(<r)\propto r$ .We minimize $\chi ^2$ and list the best-fit parameters $a$, $r_{200}$, the concentration $c_{NFW}$ $r_{200}/a$, and $M_{200}$ for the best-fit NFW model and indicate the best-fit profile type in Table \ref{mpfitsci}."
 We also list the parameter eyyp=riyt/a: sole authors prefer to use r/4gj as the virial radius., We also list the parameter $c_{101}$ $r_{101}/a$; some authors prefer to use $r_{101}$ as the virial radius.
 We perform the fits on all data points within the maxima radial exteut of the caustics ων listed in Table ϱ aud with caustic amplitude Afr)>100kins," We perform the fits on all data points within the maximum radial extent of the caustics $r_{max}$ listed in Table \ref{radii} and with caustic amplitude $\mathcal{A}
\mathnormal{(r)} > 100~\kms$."
 Because the individual poiuts iu the mass profile are uot independent. the absolutc| values of20 4 are indicative⋅⋅⋅ onlv. mt it is clear that the NEW aud Heruquist profiles provide acceptable fits to he caustic mass profiles: the SIS is excluded. for nearly all clusters.," Because the individual points in the mass profile are not independent, the absolute values of $\chi ^2$ are indicative only, but it is clear that the NFW and Hernquist profiles provide acceptable fits to the caustic mass profiles; the SIS is excluded for nearly all clusters."
 The NEW. profile provides a better fit to the data than the Heruquist profile for 36of the 72 CIRS clusters 35 are better fit bv a IIleruquist profile aud one is bst fit by SIS., The NFW profile provides a better fit to the data than the Hernquist profile for 36of the 72 CIRS clusters; 35 are better fit by a Hernquist profile and one is best fit by SIS.
 A non-ngular isothermal spliere mass profile! vields results simular to the SIS: thus. we report only our results for the SIS.," A non-singular isothermal sphere mass profile yields results similar to the SIS; thus, we report only our results for the SIS."
 Figure ?7 shows the shapes of the caustic mass profiles sealed bv. ου and ALooy along with SIS. NEW. and IIeruquist model profiles.," Figure \ref{scalem} shows the shapes of the caustic mass profiles scaled by $r_{200}$ and $M_{200}$ along with SIS, NFW, and Hernquist model profiles."
 The colored lines show differeut inode mass profiles., The colored lines show different model mass profiles.
 The straight dashed line is the SIS the solid lines are NEW. profles with ¢=3.5. Γ aud 10. aud the curved dashed lines are Heruquist profiles with two cüffereu pacale radii.," The straight dashed line is the SIS, the solid lines are NFW profiles with $c$ =3,5, and 10, and the curved dashed lines are Hernquist profiles with two different scale radii."
 The best-fit average profile is au NEW profile with e2)9=7.2 (this lowers to c29925.2 when the fits are restricted to. irrogo). consistent with Table 11 and with the values expected from simulatious for massive clusters (NEW.?)..," The best-fit average profile is an NFW profile with $c_{200}$ =7.2 (this lowers to $c_{200}$ =5.2 when the fits are restricted to $r$$\leq$$r_{200}$ ), consistent with Table \ref{mpfitsci} and with the values expected from simulations for massive clusters \citep[NFW, ][]{bullock01}."
 All three moclel profiles agree. fairly well with the caustic nass profiles iu the range 7209., All three model profiles agree fairly well with the caustic mass profiles in the range $r_{200}$.
 The SIS ouly fails beyoud 71.579599: this is why leusiug has iad trouble distinguishing between SIS aud NEW profiles., The SIS only fails beyond $\sim$ $r_{200}$; this is why lensing has had trouble distinguishing between SIS and NFW profiles.
 As discussed in D99. the causic technique can be subject o large variations for iucdividial clusters due to projection effects.," As discussed in D99, the caustic technique can be subject to large variations for individual clusters due to projection effects."
" The best coustraints οu the shapes of cluster mass xofiles are obtained by averag""uus over many lines of sight. or for real observations. over nany different clusters."," The best constraints on the shapes of cluster mass profiles are obtained by averaging over many lines of sight, or for real observations, over many different clusters."
 The current sample is the largest saluple of nass profiles at arge radii to date aud thus pr'ovides the best possible test of the shapes of cluster mass xofiles., The current sample is the largest sample of mass profiles at large radii to date and thus provides the best possible test of the shapes of cluster mass profiles.
 The concentration parameCIS C299=rogo/0 for the NEW aodels are in the range 260. in good agrecineut with the predictions of numevical simulations (?77)..," The concentration parameters $c_{200}=r_{200}/a$ for the NFW models are in the range 2–60, in good agreement with the predictions of numerical simulations \citep{nfw97,bullock01}."
 The differences iu e should be μπα] (~20% 3) over our mass ranee compared to the scatter iu ο present iu simulated clusters (77)..," The differences in $c$ should be small $\sim$ ) over our mass range compared to the scatter in $c$ present in simulated clusters \citep{nfw97,bullock01}."
" Figure ?? indicates the average values aud Lo scatter of e491=rip,α 1n simniulatious (?)..", Figure \ref{cnfw} indicates the average values and $1\sigma$ scatter of $c_{101}=r_{101}/a$ in simulations \citep{bullock01}.
 The dynamic range of these simulations is uot laree enough to contain many massive clusters. but the CIRS clusters agree well with the extrapolation of the relation fouud in simmilations.," The dynamic range of these simulations is not large enough to contain many massive clusters, but the CIRS clusters agree well with the extrapolation of the relation found in simulations."
 We bin the CIRS clusters iuto six bius of 12 clusters and compute the mean aud median of loge491., We bin the CIRS clusters into six bins of 12 clusters and compute the mean and median of $\mbox{log}c_{101}$.
 There is a weak positive correlation of e with mass (Fieure ??)). but the values of e494 and the scatter (lin errorbars) aeree well with the model of ? (the scatter iu CIRS is huger. indicating that observational uncertainties likely coutribute to the observed scatter).," There is a weak positive correlation of $c$ with mass (Figure \ref{cnfw}) ), but the values of $c_{101}$ and the scatter (thin errorbars) agree well with the model of \citet{bullock01} (the scatter in CIRS is larger, indicating that observational uncertainties likely contribute to the observed scatter)."
" This result addresses one concern from the CAIRNS mass profiles: the concentrations eogy were iu the rauge 5-17 rather than the rauge 1-6 expected frou, nmunerical simulations for massive clusters (27).."," This result addresses one concern from the CAIRNS mass profiles: the concentrations $c_{200}$ were in the range 5-17 rather than the range 4-6 expected from numerical simulations for massive clusters \citep{nfw97,cairnsi}. ."
 Silly. recent mass profiles from weak leusiug similarly find evidence of high concentrations in ÀAl689 (27)..CLOO2 ολων and MS2137 (?)..," Similarly, recent mass profiles from weak lensing similarly find evidence of high concentrations in A1689 \citep{2005ApJ...619L.143B,2005ApJ...621...53B}, ,CL0024 \citep{kneib03}, , and MS2137 \citep{gavazzi05}. ."
 However. Figure ?7 shows that the CIRS clusters have mass profiles consistent with those predicted by simulations. although with large scatter.," However, Figure \ref{cnfw} shows that the CIRS clusters have mass profiles consistent with those predicted by simulations, although with large scatter."
 If this scatter is physical rather than due to projection effects in the caustic mass profiles. then the apparent discrepancies between simulations and observations can be explained by an uulucky. selectiou of clusters.," If this scatter is physical rather than due to projection effects in the caustic mass profiles, then the apparent discrepancies between simulations and observations can be explained by an unlucky selection of clusters."
The best fit parameters somewhat depends on the range of integration.,The best fit parameters somewhat depends on the range of integration.
 For instance. if we use the observed column cleusity profile eq.(2)) out to 42.8 Mpc. regardless of the streueth of weak lensing signals. the core radius in units of rp. aud power-law index. change to 1.25. aud -3.71. respectively.," For instance, if we use the observed column density profile \ref{cpl}) ) out to $\pm$ 2.8 Mpc, regardless of the strength of weak lensing signals, the core radius in units of $r_E$, and power-law index, change to 1.25, and -3.71, respectively."
 Note that the power-law iudex of our choice. -3.11. is closer to that of au NEW profile ol -3. than -3.71.," Note that the power-law index of our choice, -3.41, is closer to that of an NFW profile of -3, than -3.71."
 Since our interest is in the inuer region as we show later. aud since the coutribution of the outer region to the total mass is small. our choice should be justified.," Since our interest is in the inner region as we show later, and since the contribution of the outer region to the total mass is small, our choice should be justified."
 Before proceeding to imodeliue of mass profiles. we first show that at the center of AT689 with volume deusities of order of 1021 (g-cm 3) uourelativistic eV-1uass [ermious can become degenerate.," Before proceeding to modeling of mass profiles, we first show that at the center of A1689 with volume densities of order of $10^{-24}$ $\cdot$ $^{-3}$ ), nonrelativistic eV-mass fermions can become degenerate."
 Since amass of 1 eV corresponds to Lx10.5 e. the iunber density. V/V10H oE and the mean inter-particle spacing is. (V/V)Vs210.! em," Since a mass of 1 eV corresponds to $1.8\times10^{-33}$ g, the number density, $N/V \approx 10^{11}$ $^{-3}$, and the mean inter-particle spacing is, $(N/V)^{-1/3} \approx 2\times 10^{-4}$ cm."
 On the other hand. the de Broglie wavelength for a 1 eV particle with a relative velocity e dis. μυς=hf(poc)(efe)Acompion cur.," On the other hand, the de Broglie wavelength for a 1 eV particle with a relative velocity $v$ is, $h/\mu_0 v = h/(\mu_0c)(c/v)=\lambda_{Compton}\cdot(c/v) = 1.2\times10^{-4}(c/v)$ cm."
 Therefore lor nonrelativistic particles with e«c. the couditiou Lor high degeneracy. (N/V)E«ΑγάςBroglie): ts satisfied.," Therefore for nonrelativistic particles with $v \ll c$, the condition for high degeneracy, $(N/V)^{-1/3} \ll \lambda_{({\rm de \hskip 5pt Broglie})}$, is satisfied."
 We first formulate the modeling procedure oL matter distribution for the case that tle eutire matter cousists purely of fermionic dark matter aud then. modify the formulation for the case that the fractional contribution of fermionic dark matter deusity to the total matter deusity is coustaut.," We first formulate the modeling procedure of matter distribution for the case that the entire matter consists purely of fermionic dark matter and then, modify the formulation for the case that the fractional contribution of fermionic dark matter density to the total matter density is constant."
 First we provide our justification for introduciug au equation of state and assuming lyclrostatic equilibrium for the mixture of degenerate fermious aud non-degenerate Classical collisiouless particles., First we provide our justification for introducing an equation of state and assuming hydrostatic equilibrium for the mixture of degenerate fermions and non-degenerate classical collisionless particles.
 A sell-gravitatiug system composed purely of classical collisiouless particles such as cold dark matter particles may be thermocdyuamically anomalous (Lyudeun-Bell&Wood1968). aud the equation of state may be poorly defined.," A self-gravitating system composed purely of classical collisionless particles such as cold dark matter particles may be thermodynamically anomalous \citep{Lynden-Bell}
 and the equation of state may be poorly defined."
 However. the elfect of fermion degeneracy or introduction of repulsion due to Pauli's exclusion principle is to make the mixture of degenerate [ermious and classical οςlisiouless particles a thermoclyuamically normal system aud an analysis based on lyclrostatic equilibrium valid.," However, the effect of fermion degeneracy or introduction of repulsion due to Pauli's exclusion principle is to make the mixture of degenerate fermions and classical collisionless particles a thermodynamically normal system and an analysis based on hydrostatic equilibrium valid."
 To deal with the general situations in which particle temperature is finite aud degeneracy is partial. we need to know the equation of state (EOS). aud have to determine the temperature prolile along with the density. profile.," To deal with the general situations in which particle temperature is finite and degeneracy is partial, we need to know the equation of state (EOS), and have to determine the temperature profile along with the density profile."
 We adopt two major assumptions that simplify our analysis ol fermioute dark matter distribution., We adopt two major assumptions that simplify our analysis of fermionic dark matter distribution.
 First. we assume that the EOS. or the pressure law. las the following form.," First, we assume that the EOS, or the pressure law, has the following form,"
Accretion onto a central massive black bole (DII) in a galactic nucleus produces energy. in the form. of radiation. relativistic jets. and wider angle (less-collimated) non-relativistic (0~IO!kms+ ) outllows (?)..,"Accretion onto a central massive black hole (BH) in a galactic nucleus produces energy in the form of radiation, relativistic jets, and wider angle (less-collimated) non-relativistic $v \sim 10^4 \kms$ ) outflows \citep{krolik99}."
 The coupling of this energy output to gas in galaxies and in the intergalactie medium is believed to play an important role in. galaxy formation. potentially regulating the growth of massive galaxies and the thermal properties of the intracluster mecdium in galaxy groups and clusters (e.g. 2?)).," The coupling of this energy output to gas in galaxies and in the intergalactic medium is believed to play an important role in galaxy formation, potentially regulating the growth of massive galaxies and the thermal properties of the intracluster medium in galaxy groups and clusters (e.g., \citealt{silk98,croton06}) )."
 The impact of this ‘feedback’ on the gas galaxies is particularly uncertain. both because the interstellar (ISAT) σας is denser. and thus more clillicult to alfect cynamically. anc because much of the ISAT subtends a relatively modest solid angle relative to a central active ealactic nucleus. (AGN).," The impact of this `feedback' on the gas galaxies is particularly uncertain, both because the interstellar (ISM) gas is denser, and thus more difficult to affect dynamically, and because much of the ISM subtends a relatively modest solid angle relative to a central active galactic nucleus (AGN)."
 However. analytic estimates and numerical simulations have demonstrated that if a moclest fraction of the energy. produced by aceretion onto a central DII can couple to the surrounding gas. it can unbine the interstellar eas (e.g... 22).," However, analytic estimates and numerical simulations have demonstrated that if a modest fraction of the energy produced by accretion onto a central BH can couple to the surrounding gas, it can unbind the interstellar gas (e.g., \citealt{silk98,dimatteo05}) )."
 The physical processes most likely to produce such an cllect are winds (22).. radiation pressure (?7).. and/or Compton heating (?) from a central AGN.," The physical processes most likely to produce such an effect are winds \citep{king03, king11}, , radiation pressure \citep{murray05}, and/or Compton heating \citep{sazonov04} from a central AGN."
 Understanding how this works in detail is one of the major challenges in our understanding of the connection between AGN physics and galaxy. formation., Understanding how this works in detail is one of the major challenges in our understanding of the connection between AGN physics and galaxy formation.
 In this paper. we assess the influence of AGN winds on gas in the AGN's host galaxy using threc-dimoensional numerical simulations.," In this paper, we assess the influence of AGN winds on gas in the AGN's host galaxy using three-dimensional numerical simulations."
 Previous analytic work and one and two-dimensional simulations have demonstrated that AGN winds can in principle sweep up and drive gas out of galaxies. potentially explaining the Mgg—0 relation and the dearth of gas and ongoing star formation in massive. earlv-tvpoe. ealaxies (e.g. 27277. and references therein).," Previous analytic work and one and two-dimensional simulations have demonstrated that AGN winds can in principle sweep up and drive gas out of galaxies, potentially explaining the $M_{BH}-\sigma$ relation and the dearth of gas and ongoing star formation in massive, early-type, galaxies (e.g., \citealt{king05,king11,novak10,ostriker10} and references therein)."
 Observationallv. there is strong evidence that ACN indeed drive powerful outllows.," Observationally, there is strong evidence that AGN indeed drive powerful outflows."
 Broac-absorption dine (BAL) quasars. which show blue-shifted absorption lines in the rest-frame ultraviolet with inferred. outflow: velocities ~10.00040.000kins represent over ~40% of quasars in infrared selected samples (2)...," Broad-absorption line (BAL) quasars, which show blue-shifted absorption lines in the rest-frame ultraviolet with inferred outflow velocities $\sim 10,000-40,000 \kms$, represent over $\sim 40\%$ of quasars in infrared selected samples \citep{dai08}."
 similar fraction of racio-quict quasars show evidence for high velocity outllows in X-ray absorption line spectroscopy (τὸν., A similar fraction of radio-quiet quasars show evidence for high velocity outflows in X-ray absorption line spectroscopy \citep{tombesi10}.
 Lt is ikelv thatαἱ quasars possess such outllows but that they ave only observed. when the system is viewed. mocestIvy edegc-on (τι., It is likely that quasars possess such outflows but that they are only observed when the system is viewed modestly edge-on \citep{murray1995}.
 However. determining the mass-loss rate rom spatially unresolved absorption-line observations is notoriously cillicult given uncertainties in the radius of he absorbing gas.," However, determining the mass-loss rate from spatially unresolved absorption-line observations is notoriously difficult given uncertainties in the radius of the absorbing gas."
 In a handful of low-ionization BAL quasars (in particular. FeLoBALS) this degeneracy has been ooken. suggesting mass loss rates significantly larger than he black hole accretion rate (??777)..," In a handful of low-ionization BAL quasars (in particular, FeLoBALs) this degeneracy has been broken, suggesting mass loss rates significantly larger than the black hole accretion rate \citep{moe09, bautista10,dunn10,claude11}."
 These observations race absorbers at large distances from the BLL (~ kpe). in contrast to most of the high ionization UV. and X- absorption seen in BAL quasars. which arises at =1x.," These observations trace absorbers at large distances from the BH $\sim$ kpc), in contrast to most of the high ionization UV and X-ray absorption seen in BAL quasars, which arises at $\lesssim 1$pc."
 In addition to these wellkeharacterizecl outflows. it is," In addition to these well-characterized outflows, it is"
where Muse is the original crror-bar returned. by. the photometry pipeline.,where $\sigma_{\rm mag}$ is the original error-bar returned by the photometry pipeline.
 For all the LMC fields the mean values of the error- parameters were: (57?=1.2039. (ο)=0.0046. v)=0.9956. ici?=0.0035.," For all the LMC fields the mean values of the error-correction parameters were: $\langle\gamma_I\rangle = 1.2039$, $\langle\epsilon_I\rangle = 0.0046$, $\langle\gamma_V\rangle= 0.9956$, $\langle\epsilon_V\rangle = 0.0035$."
 As a side product of the error correction. study we obtained alsoa formula for calculating error-bars. of svnthetic Z-band. magnitudes. used. in. the light. curves’ simulations: where £a ds the simulated magnitude for which the error bar (GNL a) is required. fy. and Ades are the magnitude and the error bar of the reference star at a given epoch.," As a side product of the error correction study we obtained alsoa formula for calculating error-bars of synthetic $I$ -band magnitudes used in the light curves' simulations: where $I_{\rm sim}$ is the simulated magnitude for which the error bar $\Delta
I_{\rm sim}$ ) is required, $I_{\rm ref}$ and $\Delta I_{\rm ref}$ are the magnitude and the error bar of the reference star at a given epoch."
 Such caleulated error bars still need to be corrected with eq. (1)., Such calculated error bars still need to be corrected with eq. \ref{eq:errors}) ).
 Error corrections for £ and V passbancds for the first couple of fields are gathered in Table 2.., Error corrections for $I$ and $V$ passbands for the first couple of fields are gathered in Table \ref{tab:errorcor}. .
 Phe full table is available on-line on the OGLE website., The full table is available on-line on the OGLE .
"each of the three energy loss processes, at the position of all the 23 regions.","each of the three energy loss processes, at the position of all the 23 regions."
" For each region, we plot the values of the normalised energy loss rate for the synchrotron (calculated using Breg), ICS and the bremsstrahlung processes."," For each region, we plot the values of the normalised energy loss rate for the synchrotron (calculated using $B_{\rm reg}$ ), ICS and the bremsstrahlung processes."
" All the values were evaluated on the plane of the disc (z= 0) and we used the frequency peak approximation Fe=\/BregXν/νο GeV, where Breg is measured in µία. Since the results were very similar for v—1.4 and v—4.8 GHz, we show only the results obtained for 1.4 GHz."," All the values were evaluated on the plane of the disc $z=0$ ) and we used the frequency peak approximation $E_e=\sqrt{B_{\rm reg}\times\nu/\nu_0}$ GeV, where $B_{\rm reg}$ is measured in $\mu$ G. Since the results were very similar for $\nu=1.4$ and $\nu=4.8$ GHz, we show only the results obtained for 1.4 GHz."
" While ICS is clearly the dominant process in all regions we are studying, the contribution of bremsstrahlung seems to be the the smallest one."," While ICS is clearly the dominant process in all regions we are studying, the contribution of bremsstrahlung seems to be the the smallest one."
" It is however, surely not negligible in at least 3 regions (10, 11 and 14)."," It is however, surely not negligible in at least 3 regions (10, 11 and 14)."
" These processes therefore, cannot be neglected."," These processes therefore, cannot be neglected."
" If we remember that the regions are numbered according to their galactocentric distance, we immediately notice in Fig."," If we remember that the regions are numbered according to their galactocentric distance, we immediately notice in Fig."
" 5 the apparent lack of correlation between the energy loss rates (and therefore of the magnetic field, the ISRF and the hydrogen distribution) and the galactocentric distance, which is clearly a consequence of the irregular nature of the LMC."," \ref{EnergyLoss} the apparent lack of correlation between the energy loss rates (and therefore of the magnetic field, the ISRF and the hydrogen distribution) and the galactocentric distance, which is clearly a consequence of the irregular nature of the LMC."
" We considered two possible WIMPs annihilation channels: XX—bb, in which electrons and positrons will be produced by decaying muons (u—e Ψενμ) and anti-muons DyVe) produced in pions decays (1>pv7, and yt v) and the leptophilic channel yy4μμ."," We considered two possible WIMPs annihilation channels: $\chi \chi \to b \overline{b}$, in which electrons and positrons will be produced by decaying muons $\mu^- \to e^-\, \overline{\nu}_{e} \nu_{\mu}$ ) and anti-muons $\mu^+ \to e^+\, \overline{\nu}_{\mu} \nu_{e}$ ) produced in pions decays $\pi^- \to \mu^- \overline{\nu}_{\mu}$ and $\pi^+ \to \mu^+ \nu_{\mu}$ ) and the leptophilic channel $\chi \chi \to \mu^+ \mu^-$."
 Leptophilic channels have recently raised interest in view of the experimental results on the electron/positron cosmic ray spectra., Leptophilic channels have recently raised interest in view of the experimental results on the electron/positron cosmic ray spectra.
" While Pamela observed an unexpected rise in the positron fraction (Adrianietal.2009),, Fermi-LAT observes a deviation from a simple power-law spectrum (Abdoetal.2009), thus confirming the previous results obtained by HESS (Aharonianetal.2009)."," While Pamela observed an unexpected rise in the positron fraction \citep{PAMELA}, Fermi--LAT observes a deviation from a simple power-law spectrum \citep{b1}, thus confirming the previous results obtained by HESS \citep{Hess}."
". If these results are to be interpreted as due to DM annihilation in the galactic halo, one needs to consider leptophilic channels and high mass scales."," If these results are to be interpreted as due to DM annihilation in the galactic halo, one needs to consider leptophilic channels and high mass scales."
" 'The synchrotron intensity at a frequency v due to DM annihilation coming from a region inside a solid angle dQ on the LMC's disc is: where i is the disc inclination, s is the distance along the line-of-sight and j,(r,2) is the synchrotron emissivity at a position in the LMC’s halo with galactocentric distance r along the disc and height z above or below the disc."," The synchrotron intensity at a frequency $\nu$ due to DM annihilation coming from a region inside a solid angle $d\Omega$ on the LMC's disc is: where $i$ is the disc inclination, $s$ is the distance along the line-of-sight and $j_{\nu}(r,z)$ is the synchrotron emissivity at a position in the LMC's halo with galactocentric distance $r$ along the disc and height $z$ above or below the disc."
 The term cos accounts for the fact that the line-of-sight is not parallel to z.," The term $\,i$ accounts for the fact that the line-of-sight is not parallel to $z$."
 The expression of the emissivity is derived in detail in Borrielloetal.(2009)., The expression of the emissivity is derived in detail in \citet{PaperMW}.
. We evaluated eq. (7)), We evaluated eq. \ref{SynFlux}) )
 for all 23 regions using v—1.4 and 4.8 GHz., for all 23 regions using $\nu=1.4$ and 4.8 GHz.
 The most constraining results were obtained for 1.4 GHz and can be seen in Fig., The most constraining results were obtained for 1.4 GHz and can be seen in Fig.
 6 for both annihilation channels considered., \ref{Results1} for both annihilation channels considered.
" For comparison, we show also the best constraint obtained in Borrielloetal.(2010) for M33 using an NFW profile and assuming equipartition between magnetic fields and cosmic rays, and the best constraint obtained in Borrielloetal.(2009) for the Milky Way using the yx—bb channel."," For comparison, we show also the best constraint obtained in \citet{PaperM33} for M33 using an NFW profile and assuming equipartition between magnetic fields and cosmic rays, and the best constraint obtained in \citet{PaperMW} for the Milky Way using the $\chi \chi \to b \overline{b}$ channel."
 For the yy—pty” channel we show the best constraint obtained for the Milky Way using the same formalism and observations described in Borrielloetal.(2009) and also the favoured region obtained when one attributes to DM annihilation the experimental results described above (Meadeetal.2010)., For the $\chi \chi \to \mu^+ \mu^-$ channel we show the best constraint obtained for the Milky Way using the same formalism and observations described in \citet{PaperMW} and also the favoured region obtained when one attributes to DM annihilation the experimental results described above \citep{Meade}.
". We have imposed constraints on the m,-(cAv) plane using radio observations at 1.4 GHz and 4.8 GHz of the LMC and analysing two different DM annihilation channels, a hadronic and a leptonic one."," We have imposed constraints on the $m_{\chi}$ $\langle\sigma_Av\rangle$ plane using radio observations at 1.4 GHz and 4.8 GHz of the LMC and analysing two different DM annihilation channels, a hadronic and a leptonic one."
" The existence of high resolution observations of the LMC in several frequency bands has allowed us to obtain most of the information needed to calculate the DM annihilation signal, making the least possible number of hypotheses in all the steps of the calculation."," The existence of high resolution observations of the LMC in several frequency bands has allowed us to obtain most of the information needed to calculate the DM annihilation signal, making the least possible number of hypotheses in all the steps of the calculation."
" Being able to escape from this problem and, when necessary, making"," Being able to escape from this problem and, when necessary, making"
thiu shell spherical capacitors at successive values of the radius r. cach of thickness A~O(Ly aud charge AQ(r) eiven by On a very short time scale Of) the QED vacua diclectric breakdown produces a number— deusity of pairs Hel(r) such that Er)ee€.,"thin shell spherical capacitors at successive values of the radius $r$, each of thickness $\lambda\sim O({\hbar\over mc})$ and charge $\Delta Q(r)$ given by On a very short time scale $O({\hbar\over mc^2})$, the QED vacuum dielectric breakdown produces a number density of pairs $n_{e^+e^-}(r)$ such that $E(r)\approx {\cal E}_{\rm c}$."
 This approximate equality sinply neans that the ο)« pair creation exponoenutiallv decreases when the initial electric field is screened to the critical value., This approximate equality simply means that the $e^+e^-$ pair creation exponentially decreases when the initial electric field is screened to the critical value.
 It is iuportaut to emphasize that the first laver of thickuess A outside the horizon produces a uber of pairs sufficient to reduce the charge of the EMDIT to Qe=&n. its critical value in the seuse of eiseuberg and Euler.," It is important to emphasize that the first layer of thickness $\lambda$ outside the horizon produces a number of pairs sufficient to reduce the charge of the EMBH to $Q_{\rm c}={\cal E}_{\rm c}r_+^2$, its critical value in the sense of Heisenberg and Euler."
 The total muuber of pairs actually created in the dvadosphere is verv uuch larger than the number captured by the black hole. since it is amplified by the factor (rasΓΕ]λ.," The total number of pairs actually created in the dyadosphere is very much larger than the number captured by the black hole, since it is amplified by the factor $(r_{\rm ds}-r_+)/\lambda $."
 The deusity of pairs as a function of the radius is then eiven by Tn Figs., 	The density of pairs as a function of the radius is then given by In Figs.
" 2 aud 3.. we plot the density of pais for 10A£.. and 10°AL,. EMBII or selected values of £."," \ref{fig.2} and \ref{fig.3}, we plot the density of pairs for $10M_{\odot}$ and $10^5M_{\odot}$ EMBH for selected values of $\xi$."
 These two values of the mass were chosen to be representative of objects typical of the galactic population or for the uuclei of galaxies compatible with our upper liuüt of the miaxinmui nass of 6:10AZ..., These two values of the mass were chosen to be representative of objects typical of the galactic population or for the nuclei of galaxies compatible with our upper limit of the maximum mass of $6\cdot 10^5M_{\odot}$.
" We are now im a position to compute the total number of pairs Nya created in the dvadosphere aud from a suoledee of the electrostatic energy deusitv iu each shell. ie enerev deusitv of created pairs as a function of the radial coordinate and the total energy ETT, iu the pairs."," We are now in a position to compute the total number of pairs $N_{\rm pair}$ created in the dyadosphere and from a knowledge of the electrostatic energy density in each shell, the energy density of created pairs as a function of the radial coordinate and the total energy $E^{\rm tot}_{e^+e^-}$ in the pairs."
 Finally we can estimate the total energv extracted by ie pair creation process in EMDITIs of different masses or selected values of© and courpare aud coutrast these values with the maxinnun extractable cnerey given by 1ο nass formula for black holes. (see Eqs. (1)), Finally we can estimate the total energy extracted by the pair creation process in EMBH's of different masses for selected values of $\xi$ and compare and contrast these values with the maximum extractable energy given by the mass formula for black holes (see Eqs. \ref{em}) )
 and (3)))., and \ref{s1}) )).
 This comparison shows that the effcieucy. sharply decreases as oue reaches the maxima value of the EMDII uass permitting vacuun polarization. while the efficicucy approaches LOOM iu the low mass Πα (Preparata et al. L998)}).," This comparison shows that the efficiency sharply decreases as one reaches the maximum value of the EMBH mass permitting vacuum polarization, while the efficiency approaches $100\%$ in the low mass limit (Preparata et al. \cite{prx}) )."
 Duc o the very large pair density given by Eq. (8)), Due to the very large pair density given by Eq. \ref{density}) )
 aud to the sizes of the cross-sections for the process €|<>~| +. the system is expected to thermalize to a plasma configuration for which aud reach an average teniperature where & is Boltzmaun’s coustaut.," and to the sizes of the cross-sections for the process $e^+e^-\leftrightarrow \gamma+\gamma$ , the system is expected to thermalize to a plasma configuration for which and reach an average temperature where $k$ is Boltzmann's constant."
" The average energy per pair p is shown as a fiction of the EXIBIT mass for selected values of the charge parameter © iu Fig. 1,", The average energy per pair ${ E^{\rm tot}_{e^+e^-}\over N_{\rm pair}}$ is shown as a function of the EMBH mass for selected values of the charge parameter $\xi$ in Fig. \ref{fig.4}.
 As shown by Buffiui et al.(1998)) the further evolution of this plasina leads to a relativistic expausiou. ¢|( annihilation and au enormous pair-clectromaguctic-pulse “PEL pulse”.," As shown by Ruffini et \cite{rwx}) ) the further evolution of this plasma leads to a relativistic expansion, $e^+ e^-$ annihilation and an enormous pair-electromagnetic-pulse “P.E.M. pulse""."
 By introducing a variety of models based on relativistic bydrodvnamucal equations. it has," By introducing a variety of models based on relativistic hydrodynamical equations, it has"
Ultra-luminous X-ray sources (ULXs) are point-like objects with high. (107 erg 1) X-ray luminosities that are not associated with an active galactic nucleus (AGN) or. indeed. the central regions of a host galaxy. (see. Miller Colbert 2004: Roberts 2007: Gladstone 2011).,"Ultra-luminous X-ray sources (ULXs) are point-like objects with high $>$ $^{39}$ erg $^{-1}$ ) X-ray luminosities that are not associated with an active galactic nucleus (AGN) or, indeed, the central regions of a host galaxy (see Miller Colbert 2004; Roberts 2007; Gladstone 2011)."
 The nature of these objects has been the subject of. much speculation. with CCD resolution N-rav. spectroscopy plaving a major role in advancing our understanding.," The nature of these objects has been the subject of much speculation, with CCD resolution X-ray spectroscopy playing a major role in advancing our understanding."
 Although other missions iwe plaved an important part (e.g. detection. of »ossible state transitions in. ULNs. Ixubota ct al.," Although other missions have played an important part (e.g. detection of possible state transitions in ULXs, Kubota et al."
 2001). hese results have predominantly. come from the mission.," 2001), these results have predominantly come from the mission."
 Us first major advance was the detection of a soft excess in the spectra of many ULNs. with a cempcrature consistent with that expected. for the inner edge of an accretion disc around. an intermeciate-mass Xack hole (AAIBII: c.g. Miller ct al.," Its first major advance was the detection of a soft excess in the spectra of many ULXs, with a temperature consistent with that expected for the inner edge of an accretion disc around an intermediate-mass black hole (IMBH; e.g. Miller et al."
 2003: Miller. Fabian Aliller 2004).," 2003; Miller, Fabian Miller 2004)."
 However. later stuclies showed that the second. larder component in these spectra turns over within the bandpass. and so appears much cooler and optically thicker than the corresponding Comptonisation media in Galactic black holes (Stobbart et al.," However, later studies showed that the second, harder component in these spectra turns over within the bandpass, and so appears much cooler and optically thicker than the corresponding Comptonisation media in Galactic black holes (Stobbart et al."
 2006)., 2006).
 This is inconsistent with the identification of a sub-Ecelington state for an IMDBIILI. and more indicative of super-Eddington accretion onto a stellar-mass black hole (Clacstone. Done Roberts 2009).," This is inconsistent with the identification of a sub-Eddington state for an IMBH, and more indicative of super-Eddington accretion onto a stellar-mass black hole (Gladstone, Done Roberts 2009)."
 The apparent divergence of the spectra of more luminous ULXs into two components (see Fig., The apparent divergence of the spectra of more luminous ULXs into two components (see Fig.
 S of Gladstone et al., 8 of Gladstone et al.
 2009) can be interpreted. in terms of the emergence of a radiativelv-driven wind at super-Ecddington accretion rates. with the outllowing material thermalising he underlving disc emission to produce the soft. spectral component as predicted. by e.g. Wing (2004). Poutanen et al. (," 2009) can be interpreted in terms of the emergence of a radiatively-driven wind at super-Eddington accretion rates, with the outflowing material thermalising the underlying disc emission to produce the soft spectral component as predicted by e.g. King (2004), Poutanen et al. ("
2007).,2007).
 The hard component is then produced: within he photospheric radius. with its characteristic optically-hick Comptonisation signature either the result of a thick shroucl of Comptonising electrons around the hot inner disc. or perhaps a change in the opacity of the outer lavers of the jot inner accretion clise itself (Middleton et al.," The hard component is then produced within the photospheric radius, with its characteristic optically-thick Comptonisation signature either the result of a thick shroud of Comptonising electrons around the hot inner disc, or perhaps a change in the opacity of the outer layers of the hot inner accretion disc itself (Middleton et al."
 POLL)., 2011).
 Such a model can explain the startling lack of variability seen in many of these sources (Lleil et al., Such a model can explain the startling lack of variability seen in many of these sources (Heil et al.
 2009)., 2009).
 In those few cases, In those few cases
"combination of five reasons may provide an D) Higher than average rotation velocities in the progenitor stars of these supergiants on the MS may reconcile the situation for some 1) Evolution models for rotating stars that also account for the interaction of rotation and a magnetic dynamo (MM05) predict enhanced mixing signatures of the amount required (dotted r1)) Some stars may have evolved in a close binary, which can also lead to enhanced mixing associated with mass 1V)) Some objects may have been siblings to τ SSco on the MS, climbing up the N/O-N/C relation even further in their further v)) Supergiants may already have evolved through the red supergiant phase (e.g., on a blue loop) to expose first abundance ratios, which could quantitatively also explain the observations (dashed line).","combination of five reasons may provide an ) Higher than average rotation velocities in the progenitor stars of these supergiants on the MS may reconcile the situation for some ) Evolution models for rotating stars that also account for the interaction of rotation and a magnetic dynamo (MM05) predict enhanced mixing signatures of the amount required (dotted ) Some stars may have evolved in a close binary, which can also lead to enhanced mixing associated with mass ) Some objects may have been siblings to $\tau$ Sco on the MS, climbing up the $N/O$ $N/C$ relation even further in their further ) Supergiants may already have evolved through the red supergiant phase (e.g., on a blue loop) to expose first abundance ratios, which could quantitatively also explain the observations (dashed line)."
" More information may be derived from the helium content, which in the case of BA-type supergiants is determined here for a significant number of stars for the first time in a self-consistent analysis."," More information may be derived from the helium content, which in the case of BA-type supergiants is determined here for a significant number of stars for the first time in a self-consistent analysis."
 Our results are displayed in Fig. 6.., Our results are displayed in Fig. \ref{hemix}.
" On the MS no helium surface enrichment is observed, as predicted in the models for stars with masses below about Mo."," On the MS no helium surface enrichment is observed, as predicted in the models for stars with masses below about $M_\odot$."
" After the MS, the picture is blurred by the possible occurrence of a blue loop."," After the MS, the picture is blurred by the possible occurrence of a blue loop."
 Actually the interpretation of the blue supergiant can become really constraining only when we obtain additional hints to the previous evolution of the star., Actually the interpretation of the blue supergiant can become really constraining only when we obtain additional hints to the previous evolution of the star.
" Has the blue supergiant evolved directly from the MS, or has it evolved in that stage after going through a red supergiant stage?"," Has the blue supergiant evolved directly from the MS, or has it evolved in that stage after going through a red supergiant stage?"
" At the moment, from the models the situation would be the following: for models below Mo, He-enrichments at the level observed in the present supergiants are only compatible with models having undergone a dredge-up in the red supergiant phase."," At the moment, from the models the situation would be the following: for models below $M_\odot$, He-enrichments at the level observed in the present supergiants are only compatible with models having undergone a dredge-up in the red supergiant phase."
" This is true whether rotation is considered or not, or a magnetic field is accounted for or not."," This is true whether rotation is considered or not, or a magnetic field is accounted for or not."
 The present track for the magnetic Μο model was computed only up to the end of the MS phase and thus did not yet go through the dredge-up phase., The present track for the magnetic $M_\odot$ model was computed only up to the end of the MS phase and thus did not yet go through the dredge-up phase.
" Depending on the rotation velocity, the presence of a magnetic field or its absence, models, after the red supergiant phase, will populate diverse parts of the region in the plane Ys versus N/O, as illustrated e.g. by the dashed and dotted lines in Fig. 6.."," Depending on the rotation velocity, the presence of a magnetic field or its absence, models, after the red supergiant phase, will populate diverse parts of the region in the plane $Y_{\rm S}$ versus $N/O$, as illustrated e.g. by the dashed and dotted lines in Fig. \ref{hemix}."
" We note, however, that we cannot exclude at present the possibility that the observed helium abundances in the supergiants may be overestimated."," We note, however, that we cannot exclude at present the possibility that the observed helium abundances in the supergiants may be overestimated."
" A systematic downward shift by a mere (which is within the typical systematic uncertainties in our abundance determinations) would be sufficient, e.g., to bring the observations and the magnetic model in Fig."," A systematic downward shift by a mere (which is within the typical systematic uncertainties in our abundance determinations) would be sufficient, e.g., to bring the observations and the magnetic model in Fig."
 6 into agreement., \ref{hemix} into agreement.
 All observed lines arise from two energetically close levels only ?P)), All observed lines arise from two energetically close levels only ).
".Modelatomshortcoming s( suchasinsuficientab linelimitatthecooltemperatureborder, couldtheref ore"," Model atom shortcomings (such as insufficient collisional data), which may become important only in the weak-line limit at the cool temperature border, could therefore remain unnoticed and could give rise to systematics."
remainunnotice," It would not be the first time that uncertainties in atomic data complicate the statistic equilibrium and radiative transfer calculations needed to interpret the observed lines \citep[e.g.][]{przybilla05,najarro06}."
dan," Further investigations are required before firm conclusions on the evolutionary state of the supergiants are drawn from the helium abundances, and a fully coherent picture can be deduced."
order.,order.
 Finally. we add up the re-adjusted co-aligned versions of the copies of the object spectra and get an improved version of the superspectrum.," Finally, we add up the re-adjusted co-aligned versions of the copies of the object spectra and get an improved version of the superspectrum."
 Each of the original. unmodified object spectra is modeled using the improved superspectrum.," Each of the original, unmodified object spectra is modeled using the improved superspectrum."
 In this initial step. we ignore the presence of the faint planetary signal in the data.," In this initial step, we ignore the presence of the faint planetary signal in the data."
 First the superspectrum (model) is corrected for a general linear trend in flux., First the superspectrum (model) is corrected for a general linear trend in flux.
 Second. the model is shifted according to the barycentric velocity of the Earth. the radial velocity of the star. and the aforementioned shifts and stretches/contractions in the sub-pixel regime. so that the positions of absorption lines of the object spectrum and the model are matched.," Second, the model is shifted according to the barycentric velocity of the Earth, the radial velocity of the star, and the aforementioned shifts and stretches/contractions in the sub-pixel regime, so that the positions of absorption lines of the object spectrum and the model are matched."
 This is achieved using a chunk-Brent-spline-approach similar to that described in the previous paragraph., This is achieved using a chunk-Brent-spline-approach similar to that described in the previous paragraph.
 We note that in all analysis steps. modifications are exclusively applied to the model. but the object spectrum are used in their original version. ie. the data are unchangec.," We note that in all analysis steps, modifications are exclusively applied to the model, but the object spectrum are used in their original version, i.e. the data are unchanged."
 At the third stage. the model is sealed chunkwise with respect to the object spectrum.," At the third stage, the model is scaled chunkwise with respect to the object spectrum."
 As we now compare the scaled model with each object spectrum. we notice that the widths and depths of the absorption lines differ slightly.," As we now compare the scaled model with each object spectrum, we notice that the widths and depths of the absorption lines differ slightly."
 These differences originate most likely in the aforementioned effects of residuals wavelength calibration errors. guiding errors. and variations in the instrumental profile. and can be corrected by adding a scaled version of the second derivative of the object spectrum to the model.," These differences originate most likely in the aforementioned effects of residuals wavelength calibration errors, guiding errors, and variations in the instrumental profile, and can be corrected by adding a scaled version of the second derivative of the object spectrum to the model."
 The scaling factor is determined via y minimisation (fourth stage)., The scaling factor is determined via $\chi^2$ minimisation (fourth stage).
 After this. the model is renormalised.," After this, the model is renormalised."
 The final stage Is to iterate twice over all these four processes to Improve the model describing the stellar spectrum., The final stage is to iterate twice over all these four processes to improve the model describing the stellar spectrum.
 For the model of the planetary signal. we use a copy of the improved model of the stellar spectrum. but scaled down by the factors εί)µ(Φ.i) and shifted by velocity Ας.Φ) with respect to the stellar spectrum.," For the model of the planetary signal, we use a copy of the improved model of the stellar spectrum, but scaled down by the factors $\epsilon(\lambda)~\mu(\phi, i)$ and shifted by velocity $V_{\rm{p}}(K_{\rm{p}},\phi)$ with respect to the stellar spectrum."
 Hence. the two free parameters are the planet-to-star flux ratio for the fully-illuminated planet εί). and the orbital inclination 7. which corresponds. to the RV semi-amplitude of the planet 148.9sinikm s!.," Hence, the two free parameters are the planet-to-star flux ratio for the fully-illuminated planet $\epsilon(\lambda)$, and the orbital inclination $i$, which corresponds to the RV semi-amplitude of the planet $K_{\rm{p}}=K_{\rm{p,max}} \sin i=148.9
 \sin i~~{\rm km~s^{-1}}$ ."
 We are now ready to add this planetary signal to the improved model 7 of the stellar spectrum and consequently construct the model M describing the spectrum of the star the reflected one from the planet., We are now ready to add this planetary signal to the improved model $T$ of the stellar spectrum and consequently construct the model $M$ describing the spectrum of the star the reflected one from the planet.
 For each pixel κ. M is given by where c denotes the speed of light.," For each pixel $k$, $M$ is given by where $c$ denotes the speed of light."
 Varying Ay and εἰ). we finally search for the best-fit model M to all the object spectra by y minimisation.," Varying $K_{\rm p}$ and $\epsilon(\lambda)$ , we finally search for the best-fit model $M$ to all the object spectra by $\chi^2$ minimisation."
 The search range for the RV semi-amplitude comprised Ky=40 to 180kms! (corresponding to orbital inclinations ;=15° to 90°. plus twice the error of Kpanax: See Table 1) with a step width of 3kms—.," The search range for the RV semi-amplitude comprised $K_{\rm p} = 40$ to $180~{\rm km~s^{-1}}$ (corresponding to orbital inclinations $i=15^\circ$ to $90^\circ$, plus twice the error of $K_{\rm p,max}$; see Table 1) with a step width of $3~{\rm km~s^{-1}}$."
 This was a good compromise between computing time and sampling the average absorption line profile with the FWHM of =I5kms!.," This was a good compromise between computing time and sampling the average absorption line profile with the FWHM of $\approx
 15~{\rm km~s^{-1}}$."
 Using simulations. we found that for small inclinations of the planetary orbit. where the planets appear only slightly illuminated. the method is unable to detect Jupiter-size objects with veryy high albedos.," Using simulations, we found that for small inclinations of the planetary orbit, where the planets appear only slightly illuminated, the method is unable to detect Jupiter-size objects with very high albedos."
" Once the best model M[A,.eC0] has been evaluated. we determine the confidence level of the y minimum by applying the bootstrap randomisation method (e.g. Kürrster et al."," Once the best model $M[K_{\rm p},\epsilon(\lambda)]$ has been evaluated, we determine the confidence level of the $\chi^2$ minimum by applying the bootstrap randomisation method (e.g. Kürrster et al."
 1997)., 1997).
 Retainmg the orbital phases. we randomly redistribute the observed spectra amongst the phases. thereby creating N different data sets.," Retaining the orbital phases, we randomly redistribute the observed spectra amongst the phases, thereby creating $N$ different data sets."
 Any signal present in the original data is now scrambled i1 these artificial datasets., Any signal present in the original data is now scrambled in these artificial datasets.
 For all these randomised data sets. we again evaluate the model for the two free parameters. and locate the best fit with its specific γ΄ minimum.," For all these randomised data sets, we again evaluate the model for the two free parameters, and locate the best fit with its specific $\chi^2$ minimum."
 We set 77 to be the number of best-fit models to the N randomised data sets that have a minimum y? less or equal than the minimum y- fourd for the original data set., We set $m$ to be the number of best-fit models to the $N$ randomised data sets that have a minimum $\chi^2$ less or equal than the minimum $\chi^2$ found for the original data set.
 The confidence level can then be estimated by =|ΗΝ., The confidence level can then be estimated by $\approx 1-m/N$.
 Applying the data synthesis method to the HD 75289A data. we adopted the following approximations to the atmospheric models by Sudarsky et al. (," Applying the data synthesis method to the HD 75289A data, we adopted the following approximations to the atmospheric models by Sudarsky et al. ("
2000). (,2000). (
1) We adopted a grey-albedo model to resemble the Class Vmodel. which describes the atmospheres of hot Jupiters with temperatures >1500 K.,"i) We adopted a grey-albedo model to resemble the Class Vmodel, which describes the atmospheres of hot Jupiters with temperatures $>1500~{\rm
 K}$ ."
 As can be seen in Figure l.. this was," As can be seen in Figure \ref{fig:albedo}, , this was"
"plots above, except that our error bars are generally larger due to scatter from our estimates of L,.","plots above, except that our error bars are generally larger due to scatter from our estimates of $L_x$."
" Since X- luminosities are generally easier than virial masses to compute from observations, observations of many more radio halos may reduce the statistical uncertainties to such a level as to potentially distinguish the allowed scalings and dependencies."," Since X-ray luminosities are generally easier than virial masses to compute from observations, observations of many more radio halos may reduce the statistical uncertainties to such a level as to potentially distinguish the allowed scalings and dependencies."
" The redshift evolution of the Pi4—L4 relation in particular may provide a way of determining the dominant components of radio power and the average magnetic strength of clusters, as we have discussed above for the P,.4—M, relation.. In general, if the observational uncertainties in and are reduced by approximately a factor of two, Aymany degeneraciesby in the model parameters will be eliminated."," The redshift evolution of the $P_{1.4}-L_x$ relation in particular may provide a way of determining the dominant components of radio power and the average magnetic strength of clusters, as we have discussed above for the $P_{1.4}-M_v$ relation.. In general, if the observational uncertainties in $A_f$ and $b_f$ are reduced by approximately a factor of two, many degeneracies in the model parameters will be eliminated."
 We note that we are basing this analysis on our sample of only 131 clusters., We note that we are basing this analysis on our sample of only $131$ clusters.
" While this is significantly more than the current known number of radio halos, it is still far fewer than we expect to see with instruments such as"," While this is significantly more than the current known number of radio halos, it is still far fewer than we expect to see with instruments such as"
explaain this observational fact.,ain this observational fact.
"x10"".. comparable to the 2003 epoch. and approximately a factor of 2 better than in the 2002 epoch.","$\times$, comparable to the 2003 epoch, and approximately a factor of 2 better than in the 2002 epoch."
" A Gaussian fit to the 2004 detection vields a position of (J2000) right ascension Έτ 45™ 5:009 (20:17). declination —30° +2""). which is consistent with the 2003 and 2002 positions and is approximately 2.5x and 5x more accurate. respectively."," A Gaussian fit to the 2004 detection yields a position of (J2000) right ascension $17^{\mathrm{h}}$ $45^{\mathrm{m}}$ 09 $\pm
0\fs17$ ), declination $-30\arcdeg$ $\pm 2\arcsec$ ), which is consistent with the 2003 and 2002 positions and is approximately $\times$ and $\times$ more accurate, respectively."
 The source position and uncertainty cited above include a correction for ionospheric refraction which is prevalent in low [frequency observations ancl discussed in IHvmanetal.(2006) and Nordetal.(2004)., The source position and uncertainty cited above include a correction for ionospheric refraction which is prevalent in low frequency observations and discussed in \cite{hlrrkn06} and \cite{nlkhlbd04}.
".. separale images were mace for the upper (333 MIIZ) and lower (817 MIIz) sicdebauds ol the observations ancl vield fIux densities of 42.147.2 wiJv and 72.5z9.5 5Hr mJy. respectively,"," Separate images were made for the upper (333 MHz) and lower (317 MHz) sidebands of the observations and yield flux densities of $\pm$ 7.2 mJy and $\pm$ 9.5 mJy, respectively."
 No significant differences are found in the shapes of the separate light curves generated [or each sideband., No significant differences are found in the shapes of the separate light curves generated for each sideband.
 Figure 4. shows the spectrum of oobtained by imaging pairs of adjacent frequency channels across the two sidebands., Figure \ref{fig:spectrum04} shows the spectrum of obtained by imaging pairs of adjacent frequency channels across the two sidebands.
" A power-law fit vields a very steep spectrum of SxvP?—*"" forJ1745—3009..", A power-law fit yields a very steep spectrum of $S \propto \nu^{-13.5 \pm 3.0}$ for.
 An identical analvsis of the data for the nearby strong source G358.638— 1.160 vields a spectral index of —1.5d0.5. consistent with the determination of Nordetal.(2004). who found a spectral index of —1.2 between 330 and 1400 MITz.," An identical analysis of the data for the nearby strong source $-$ 1.160 yields a spectral index of $-1.5 \pm 0.5$, consistent with the determination of \cite{nlkhlbd04} who found a spectral index of $-1.2$ between 330 and 1400 MHz."
 A Monte-Carlo simulation was conducted to assess the confidence level of the steep spectrum obtained for the 2004. detection ofJ1745—3009., A Monte-Carlo simulation was conducted to assess the confidence level of the steep spectrum obtained for the 2004 detection of.
. First. a spectrum was eeneraled based on the fitted spectral index of —13.5 ancl normalized to the observed Πας density al a particular channel.," First, a spectrum was generated based on the fitted spectral index of $-13.5$ and normalized to the observed flux density at a particular channel."
 One thousand spectra were simulated by randomly adding Gaussian noise to the flux densities of the normalized spectrum. based on (hie observed noise level obtained for the individual channel images.," One thousand spectra were simulated by randomly adding Gaussian noise to the flux densities of the normalized spectrum, based on the observed noise level obtained for the individual channel images."
 A flat spectrum fit to the ddata is ruled out with a confidence level of99., A flat spectrum fit to the data is ruled out with a confidence level of.
7%... Unfortunately. however. due to limitations in the analvsis of the 2002 and 2003 observations. we were not able to detect reliable evidence of a steep spectrum for those bursts.," Unfortunately, however, due to limitations in the analysis of the 2002 and 2003 observations, we were not able to detect reliable evidence of a steep spectrum for those bursts."
 No emission is detected [rom wwhen imaging the 2004 observation al times when the burst is not occurring., No emission is detected from when imaging the 2004 observation at times when the burst is not occurring.
" From {hese 2004 observations. we are able to improve the (50) upper limit for quiescent 330 MITz emission between bursts to 6 mJy. as compared to earlier limits of 75 mJy and 25 mJy from the 2002 and 2003 observations. respectively,"," From these 2004 observations, we are able to improve the $\sigma$ ) upper limit for quiescent 330 MHz emission between bursts to 6 mJy, as compared to earlier limits of 75 mJy and 25 mJy from the 2002 and 2003 observations, respectively."
 The upper limit on quiescent emission during periods ol no burst activity is 15 mJv at 330 MIIz (νταetal.2005)., The upper limit on quiescent emission during periods of no burst activity is 15 mJy at 330 MHz \citep{hlkrmy-z05}.
.. In addition. we find an upper limit of circular polarization for the 2004 burst. while an upper limit of was previously determined for both the 2002 and 2003 bursts.," In addition, we find an upper limit of circular polarization for the 2004 burst, while an upper limit of was previously determined for both the 2002 and 2003 bursts."
our conclusions.,our conclusions.
 Although the remaining surveys do not lucet our criteria for selection. we do our best to estimae to what degree these additional data affect the upper limits ou he planet frequency.," Although the remaining surveys do not meet our criteria for selection, we do our best to estimate to what degree these additional data affect the upper limits on the planet frequency."
 Iu iiost of these surveys tje autlors uade no attempt to put upper μμ ou the frequency of plaucts in the fields they observed. often selected rausits by eve. and rarely estimated the nunber of cluster οας observed.," In most of these surveys the authors made no attempt to put upper limits on the frequency of planets in the fields they observed, often selected transits by eye, and rarely estimated the number of cluster members observed."
 We estimate from the couteuts of cach paper the παο of stars with suficicutly precise xiotomietry for planetary transits to be visible. aud he umber of cluster members likely to be within this subset of stars.," We estimate from the contents of each paper the number of stars with sufficiently precise photometry for planetary transits to be visible, and the number of cluster members likely to be within this subset of stars."
 A list of the additional survevs aud estimates of the umber of stars they coutribute to the otal sample of cluster stars is presented in Table 5.., A list of the additional surveys and estimates of the number of stars they contribute to the total sample of cluster stars is presented in Table \ref{tbl:other_surveys}.
 Iu total. the 10 additional surveys add ~5000 stars to our sample.," In total, the 10 additional surveys add $\sim5000$ stars to our sample."
 Assuming an average detecion efficiency of and a maxima cficicucy of this implics hat ..frog.7aun(00010.<6% qm the best case and Foun.d~7TSWURUSES—30eg1 on average.," Assuming an average detection efficiency of, and a maximum efficiency of, this implies that $f_{p_{other}} \approx \frac{3.0}{(5000)(0.01)} \le 6\%$ in the best case and $f_{p_{other}} \approx \frac{3.0}{(5000)(0.005)} \le 12\%$ on average."
"VOT)OO Thehe coustraiutsοfay]; ou the population of 1.0 Ry ILJ planets from the main 6 surveys are the weakest of amy considered here with f,€0.055.", The constraints on the population of 1.0 $R_J$ HJ planets from the main 6 surveys are the weakest of any considered here with $f_p \le 0.055$.
" Using our standard method of combining upper Πές. the addition of the 5000 stars from the other surveys vields a new Tut of f,x0.029. which isa ~DUX tighter coustraint."," Using our standard method of combining upper limits, the addition of the 5000 stars from the other surveys yields a new limit of $f_p \le 0.029$, which is a $\sim50\%$ tighter constraint."
" Iu the case iu which Το0.005. the combined wpper Tit is f,€0.037."," In the case in which $\mathcal{P}_{\epsilon} = 0.005$, the combined upper limit is $f_p \le 0.037$."
" Iu the ΥΠ range. the upper Inuits ou for 1.0 Π plaucts decreases by 18 and 1054 for detectionf£, efficiencies. of 1.054 and 0.554 vesectivelv."," In the VHJ range, the upper limits on $f_p$ for 1.0 $R_J$ planets decreases by $18\%$ and $10\%$ for detection efficiencies of $1.0\%$ and $0.5\%$ respectively."
" At larecr planetary radii tle o‘hauges in f, for | Ry plaucts due to the addition of —rese J5OOU stars 1s ¢ Forder ~ο205€.", At larger planetary radii the changes in $f_p$ for 1.5 $R_J$ planets due to the addition of these 5000 stars is of order $\sim5-20\%$.
 The conclusions do rot qualitatively change with the inclusion of metallicity information., The conclusions do not qualitatively change with the inclusion of metallicity information.
 The mean weighted metallicity of the stars oe1 the unused 10 smvevs is ΡοΠΠ)~--|0.1 (according ο 1ο WEDDA database). comparable to ([Fe/II|;~--LO.y) ound for the 6 surveys utilized in this paper.," The mean weighted metallicity of the stars in the unused 10 surveys is $\langle\textrm{[Fe/H]}\rangle\approx +0.1$ (according to the WEBDA database), comparable to $\langle\textrm{[Fe/H]}\rangle\approx +0.09$ found for the 6 surveys utilized in this paper."
 We expect that by neglecting the observations present oei these other surveys our derived upper limits may be p to a factor of two too high., We expect that by neglecting the observations present in these other surveys our derived upper limits may be up to a factor of two too high.
 However. it is highly ulikely that all of these survevs have achieved the optimistic 1.0% detection efficiency. and maprobable that all have even achieved a 0.5% efficiency.," However, it is highly unlikely that all of these surveys have achieved the optimistic $1.0\%$ detection efficiency, and improbable that all have even achieved a $0.5\%$ efficiency."
 We therefore conclude that ueelecting these other surveys does not qualitativev chauge our primarily conclusion. that the lack of detections is consistent with the hypothesis that cluster anc field stars host the same planet population.," We therefore conclude that neglecting these other surveys does not qualitatively change our primarily conclusion, that the lack of detections is consistent with the hypothesis that cluster and field stars host the same planet population."
 We do note that. had each of these surveys carefully quantified heir detection efficiencies. the coustraiuts on the umber of short-period plauets in open clusters could have been roticeably tighter.," We do note that, had each of these surveys carefully quantified their detection efficiencies, the constraints on the number of short-period planets in open clusters could have been noticeably tighter."
 Tt is useful to ask. even our results. how may more cluster stars ust be observed nh surevs with null results before the combined upper lit derived using all extant surveys becomes meonsisteut wit1 the observed frequency of plaucts around field stars.," It is useful to ask, given our results, how many more cluster stars must be observed in surveys with null results before the combined upper limit derived using all extant surveys becomes inconsistent with the observed frequency of planets around field stars."
 Because of the low detection efficiencies and relatively fevsuitable open clusters iu our ealaxy. it is wnlikely that upper linits derived from transit surveys in open custers will he inconsistent with the resuts of CUS and €06 in the rear future. even if it is the case that the frequency : plauets in open clusters is significanlv lower than hat of the field.," Because of the low detection efficiencies and relatively few suitable open clusters in our galaxy, it is unlikely that upper limits derived from transit surveys in open clusters will be inconsistent with the results of C08 and G06 in the near future, even if it is the case that the frequency of planets in open clusters is significantly lower than that of the field."
" For the €JS result. a combined upper (at coufidenuce) would be inconsistent with confidence lower ]und on the COs frequency yaction of stars wih planets was found to he f,<0.0076 for 1.2 Ry plaucts in the 3<P5 day veriod range."," For the C08 result, a combined upper limit (at confidence) would be inconsistent with the confidence lower bound on the C08 frequency of the fraction of stars with planets was found to be $f_p \le 0.0076$ for 1.2 $R_J$ planets in the $3<P<5$ day period range."
" The six-survey"" upper limit is f,<0.019. which 1uplies that ~Ls.00! inore cluster stars lust be observed (with null results) at a detection ¢LCICLCY efore he Tait is in conflict with COs (currently. 1300) stars have Όσοι observed at ~0.55 efficiency)."," The six-survey upper limit is $f_p \le 0.019$, which implies that $\sim 48,000$ more cluster stars must be observed (with null results) at a detection efficiency before the limit is in conflict with C08 (currently, $\sim13000$ stars have been observed at $\sim0.5\%$ efficiency)."
 This 111iiber drops to 9000 with a detection eLCICLCY O|Cu., This number drops to 9000 with a detection efficiency of.
 Given that there are about 1200 known open clusters iu the ealaxy (WEDDA). ouly a handful of whicji are rich enough to contain thousands ft stars. the «mlv wav to make the upper limits onu the plauct freqicacy in open clusters derived from trausit surveys competitive with field surveys is to drastically 1lcrease the detection efficiency of the surveys imuuber of clusters observed.," Given that there are about 1200 known open clusters in the galaxy (WEBDA), only a handful of which are rich enough to contain thousands of stars, the only way to make the upper limits on the planet frequency in open clusters derived from transit surveys competitive with field surveys is to drastically increase the detection efficiency of the surveys number of clusters observed."
 When we ask how many stars would, When we ask how many stars would
topological statistic. (he genus number.,"topological statistic, the genus number."
 By doing so. we can identify the central period οἱ (he reionization process.," By doing so, we can identify the central period of the reionization process."
 The topological signature of overlap will work whether reionization proceeds from high- to low-densityv regions or vice versa., The topological signature of overlap will work whether reionization proceeds from high- to low-density regions or vice versa.
 Topological tests could be applied using anv method that allows mapping ionized and neutral regions during the epoch of reionization., Topological tests could be applied using any method that allows mapping ionized and neutral regions during the epoch of reionization.
 Both 21cm emission [rom neutral gas and obscuration of eoalaxies by neutral gas could provide such maps., Both 21cm emission from neutral gas and obscuration of galaxies by neutral gas could provide such maps.
 Each tool has its own strengths: The 21cm maps can in principle map smaller bubbles. but diffieulties associated with foreground removal will not be fully resolved. before the first test data [rom new experiments becomes available.," Each tool has its own strengths: The 21cm maps can in principle map smaller bubbles, but difficulties associated with foreground removal will not be fully resolved before the first test data from new experiments becomes available."
 We have given particular attention to applications of (his test based on mapping the distribution of eenulling galaxies., We have given particular attention to applications of this test based on mapping the distribution of emitting galaxies.
 For reasonable expectations. the ionized bubbles during overlap will be large enough to permit transmission of Iflux through an otherwise neutral medium.," For reasonable expectations, the ionized bubbles during overlap will be large enough to permit transmission of flux through an otherwise neutral medium."
 Moreover. the number density of emitting galaxies provides a sample of several objects per bubble.," Moreover, the number density of emitting galaxies provides a sample of several objects per bubble."
 Complementary survevs for Lyman break selected: ealaxies can provide control samples to separate the topological signature of structure lormation from that of reionization., Complementary surveys for Lyman break selected galaxies can provide control samples to separate the topological signature of structure formation from that of reionization.
 Applications of this test are practical at redshilts up to 6.9 with CCD cameras. and at least to z~10 with the new generation of large format near-inlrared detectors now becoming available.," Applications of this test are practical at redshifts up to $6.9$ with CCD cameras, and at least to $z\sim 10$ with the new generation of large format near-infrared detectors now becoming available."
 Indeed. several survevs for eealaxies al 2Z8 are already underway.," Indeed, several surveys for galaxies at $z\ga 8$ are already underway."
 Thus. egalaxies could well provide our first direct evidence for individual ionized bubbles in the epoch of reionization.," Thus, galaxies could well provide our first direct evidence for individual ionized bubbles in the epoch of reionization."
 Topological tests lor the overlap phase would be practical once a contiguous volume corresponding to several bubbles had been mapped., Topological tests for the overlap phase would be practical once a contiguous volume corresponding to several bubbles had been mapped.
 IT thank Steven Furlanetto. Benedetta Ciardi. Michael Strauss. and Sangeeta Malhotra for helpful discussions on various aspects of this idea over the last few vears.," I thank Steven Furlanetto, Benedetta Ciardi, Michael Strauss, and Sangeeta Malhotra for helpful discussions on various aspects of this idea over the last few years."
Observations of the inner regions (X 5 AU) of circustellar disks are esseutial for obtaining a comete undersandiug of star aud planet formation.,Observations of the inner regions $\lesssim$ 5 AU) of circumstellar disks are essential for obtaining a complete understanding of star and planet formation.
 The iuner disk iucracts with the central star. thereby controlling he ac‘cretion aud ejection of material :uid. setting he timescale for star formation aud disk evolution.," The inner disk interacts with the central star, thereby controlling the accretion and ejection of material and setting the timescale for star formation and disk evolution."
 lu adition. inuer disks are the likely birthplace of orrestyjal planets.," In addition, inner disks are the likely birthplace of terrestrial planets."
 However. these regions ax» iticult to study. )ecause of their small angular size at the distance of nearw ostar-foriuing regions aud the proximity to hei xweut stars.," However, these regions are difficult to study, because of their small angular size at the distance of nearby star-forming regions and the proximity to their parent stars."
 Receitly. sieuificaut advancements iu our πο.anding of inner disks have Όσοι made with Wo Coniementarv techniques IR interferometry and high-esolutiou spectroscopy.," Recently, significant advancements in our understanding of inner disks have been made with two complementary techniques: IR interferometry and high-resolution spectroscopy."
 IR interferonetrv ds capable of observing thermal ciission from the clusty COMpPoOlrent of disks with resolutions of a few las (probing size scales down to a few huudyrect o ean AU: Alillan-Ciavot et 11999: Eisner et 22003:ls Akesou et 22005b. Monnicr et 22005).," IR interferometry is capable of observing thermal emission from the dusty component of disks with resolutions of a few mas (probing size scales down to a few hundredths of an AU; Millan-Gabet et 1999; Eisner et 2003; Akeson et 2005b, Monnier et 2005)."
 These observatious have shown that standard. optically thick accretion dis- models (such as outlined bv IHilleubraud 19923) fail to sinultaueouslv fit spectral energy. distributious (SEDs) and visibilities (Millau-Ciabetetal.2001:AXeson 2002).," These observations have shown that standard, optically thick accretion disk models (such as outlined by \citealt{Hillenbrand92}) ) fail to simultaneously fit spectral energy distributions (SEDs) and visibilities \citep{Millan-Gabet01, Akeson02}."
. Better fits to visibilities were obtained with a- optically thin iuner eas disk iuterior to a hot. putffed-u wall of dust (Dullemondetal.2001:Natta2001).. with the dust wall located where temperatures are hnieh cnough to sublimate silicate erains (Monnierctal. 2005).," Better fits to visibilities were obtained with an optically thin inner gas disk interior to a hot, puffed-up wall of dust \citep{Dullemond01, Natta01}, with the dust wall located where temperatures are high enough to sublimate silicate grains \citep{Monnier05}."
. Recent observations and modeling efforts have introduced complications to this simple picture. including a significant source of ciissiou of uuknowu origi the dust sublimation radius (foranexten-sivereview.seeDullemoud&Mounier 2010).," Recent observations and modeling efforts have introduced complications to this simple picture, including a significant source of emission of unknown origin the dust sublimation radius \citep[for an extensive review, see][]{Dullemond10}."
.. ILosvever. the major conclusion that there is a defined ier radius consistent with dust sublimation Sill holds true.," However, the major conclusion — that there is a defined inner radius consistent with dust sublimation — still holds true."
 The complementary technique of high-resolutiou spectroscopy has been— used to study rovibrational cnussion from hot gaseous moleciles. specifically IT20 and CO (e.g...Brittainetal.2003:Najita2001:Salvketal. 2008).. that originate im the iuncer disk atinosphere.," The complementary technique of high-resolution spectroscopy has been used to study rovibrational emission from hot gaseous molecules, specifically $_2$ O and CO \citep[e.g.,][]{Brittain03,Najita03, Blake04, Carr04, Rettig04, Salyk08}, that originate in the inner disk atmosphere."
 Because of the high temperatures (21000 IX) required to populate vibrationally excited states. CO vibrational cinission originates at disk radi similar to those probed by IR interferometry <a few AU).," Because of the high temperatures $\gtrsim 1000$ K) required to populate vibrationally excited states, CO vibrational emission originates at disk radii similar to those probed by IR interferometry $\lesssim$ a few AU)."
 When the spectral resolution is high cuouerh that the emission lines are spectrally resolved. the li1e profile acts asx a proxy for the spatial location of he eus.ons under the assuniptiou that the enüssion origilates In a rotating Keplerian disk.," When the spectral resolution is high enough that the emission lines are spectrally resolved, the line profile acts as a proxy for the spatial location of the gas, under the assumption that the emission originates in a rotating Keplerian disk."
 Siuce the emission ine wings represent the highest observed velocities. the fux in the line wines originates at the inner edge of the ujolecular disk.," Since the emission line wings represent the highest observed velocities, the flux in the line wings originates at the inner edge of the molecular disk."
 Thus. Cluission lines (after a correction for disk inclination) eau," Thus, emission lines (after a correction for disk inclination) can"
((r)) for different epochs «irectly using spectroscopic redshifts (LeFevreefαἱ.1996:Carlbere«al.1997.1999:Sinallefal. 1999).,"$\xi(r)$ ) for different epochs directly using spectroscopic redshifts \citep{leFevre96,carlberg97,carlberg99,small99}."
. These two techuiques. however. sulfer from. cliferent limitations that have resricted their uility.," These two techniques, however, suffer from different limitations that have restricted their utility."
 Sttdies which utilize cli[Iereut magnittide ittervals are limiecd in that au apο maguitude selection samsles galaxies of ¢illerent intrinsic |uninosities al cifferent redsifts. complicating the analysis. considerably.," Studies which utilize different magnitude intervals are limited in that an apparent magnitude selection samples galaxies of different intrinsic luminosities at different redshifts, complicating the analysis considerably."
 Furtjerigore. the clustering of galaxies Ol stuall scales is the result of a highly ou-linear. complex p'Ocess: acl. therefore. the actual validity- of he power law model for the evoluion of the spatial clustering fuuction is uot guvanteec. altlough it is at least useful ¢lagnostic.," Furthermore, the clustering of galaxies on small scales is the result of a highly non-linear, complex process; and, therefore, the actual validity of the power law model for the evolution of the spatial clustering function is not guaranteed, although it is at least a useful diagnostic."
 Finally. this approach is also lunited by the ayplicability of the asstumecl recdshi clistribtjon. which cau heaviM7 influence the theoretical conversion [rom aigular coordiuates to spatial coordinates.," Finally, this approach is also limited by the applicability of the assumed redshift distribution, which can heavily influence the theoretical conversion from angular coordinates to spatial coordinates."
 The spectroscopic approach. on the other haud. is hindered either by tte size of the available samples. especially when the data is binued into clistinet redshift intervals. or by the depth or wiclt1 of the survey. (which implies either a redshift variable. intrinsic bumiuosity selection efTect or possible contamination [rou strong clusteriug).," The spectroscopic approach, on the other hand, is hindered either by the size of the available samples, especially when the data is binned into distinct redshift intervals, or by the depth or width of the survey (which implies either a redshift variable, intrinsic luminosity selection effect or possible contamination from strong clustering)."
 For example. LeFevreetal(11996) analyze the spatial clustering for 591 galaxies iu the CFRS with J«22.5. Siuallefal.(1909) analyze the spatial clustering of 831 galaxies with rpom o lneasure the evolutiou in the correlation length for 0.2<2<cU0.5. auc Carlbergefal.(1JOT) use a sample of 218 galaxies wih A«uw21.5 while Carlergefab(1999) use 2300 high intri uniiosity galaxies distributed over a wide area. to clete‘mune tje spatial correlation fujcton Tereit epochs.," For example, \citet{leFevre96} analyze the spatial clustering for 591 galaxies in the CFRS with $I < 22.5$, \citet{small99} analyze the spatial clustering of 831 galaxies with $r \leq 21^m$ to measure the evolution in the correlation length for $0.2 \leq z \leq 0.5$, and \citet{carlberg97} use a sample of 248 galaxies with $K < 21.5$ while \citet{carlberg99} use 2300 high intrinsic luminosity galaxies distributed over a wide area, to determine the spatial correlation function for different epochs."
 In this yaper. we continue our developi falew technique which uses photometric redshifts O lease the angular correlation functiOl ln reshift shells (Bruner1997:Connollyefad.1998:Brueretal. 1999b).," In this paper, we continue our development of a new technique which uses photometric redshifts to measure the angular correlation function in redshift shells \citep{myThesis,connolly98,brunner99c}."
. This j0vel adproach nMinimizes the galaxs: projection ellect inherent in standard augular correlation measureurents. wlile utilizing a signiicantly large sample that nininizes tje. effects of shot nolse i1 OUP alalysis.," This novel approach minimizes the galaxy projection effect inherent in standard angular correlation measurements, while utilizing a significantly large sample that minimizes the effects of shot noise in our analysis."
 By adoptiug au etserible approach. we are able ο Weastlre he evolution of clustering with both redshift aud intrinsic luuiuosity.," By adopting an ensemble approach, we are able to measure the evolution of clustering with both redshift and intrinsic luminosity."
" Unless otherwise i0ted. we assume /;=1.0. Qa,=0.3. and Q4=0.7. throughout this pagel."," Unless otherwise noted, we assume $h = 1.0$, $\Omega_M =
0.3$, and $\Omega_\Lambda = 0.7$, throughout this paper."
 The observations aud reduction of the data used in this analysis have been extensively detailed elsewhere (Brunuer1997:Brunuerefaf.1997.1999a).," The observations and reduction of the data used in this analysis have been extensively detailed elsewhere \citep{myThesis,brunner97,brunner99}."
. In this section. we discuss the importaut poiuts which impact the rest of our ciscussiou.," In this section, we discuss the important points which impact the rest of our discussion."
 The photometric data analyzed in this paper are located at 1120. +E9:30 covering approximately," The photometric data analyzed in this paper are located at 14:20, +52:30 covering approximately"
Charlot Bruzual 2007 models with the Padova 1994 evolutionary tracks (7) anda? mass function.,Charlot Bruzual 2007 models with the Padova 1994 evolutionary tracks \citep{bertelli1994} and a \citet{chabrier2003} mass function.
" We use a ? extinction law to estimate the internal extinction, and fit the photometry at observed wavelengths A« Ίθμπι to exclude PAH emission."," We use a \citet{calzetti2000}
 extinction law to estimate the internal extinction, and fit the photometry at observed wavelengths $\lambda<10\mu$ m to exclude PAH emission."
 We refer the reader to ffor further details., We refer the reader to for further details.
" In deriving confidence intervals on the age and extinction, we find that the data are best fit by a 10 Myr population."," In deriving confidence intervals on the age and extinction, we find that the data are best fit by a 10 Myr population."
" The solutions for the emission-weighted age bifurcate though, permitting both very young templates and solutions with ages of a few Gyrs."," The solutions for the emission-weighted age bifurcate though, permitting both very young templates and solutions with ages of a few Gyrs."
 The confidence intervals on the age are t«90 Myrs and 1.4«t2.6 Gyrs., The confidence intervals on the age are $t<90$ Myrs and $1.4<t<2.6$ Gyrs.
 We note however that strong observed submillimeter emission provides a compelling argument for a very young stellar population., We note however that strong observed submillimeter emission provides a compelling argument for a very young stellar population.
 The extinction meanwhile is constrained to be Ay=3.8*0 confidence)., The extinction meanwhile is constrained to be $A_V=3.8^{+0.5}_{-1.0}$ confidence).
 The confidence interval reduces to Ay=3.8793 if one considers only the younger age solutions., The confidence interval reduces to $A_V=3.8^{+0.5}_{-0.2}$ if one considers only the younger age solutions.
" Next, we update our estimate of the stellar mass using the code (?),, as inI."," Next, we update our estimate of the stellar mass using the code \citep{blanton2007}, as in."
" We fit the combined flux from images A and B, using the data at observed wavelengths of -8um."," We fit the combined flux from images A and B, using the data at observed wavelengths of $-$."
".Forz=2.79andAy =3.8, we obtain a stellar mass M.=4x10°(uap/100)-! Μο. This value is roughly a factor of 3 lower than the previously published result."," For $z=2.79$ and $A_V=3.8$, we obtain a stellar mass $M_*=4\times10^{9}$ $M_\sun$ This value is roughly a factor of 3 lower than the previously published result."
" The added leverage from the ddata point is the largest factor in the decrease, with the addition of this data point accounting for roughly a factor of 2."," The added leverage from the data point is the largest factor in the decrease, with the addition of this data point accounting for roughly a factor of 2."
" The revised magnification estimates account for the remainder of the change, while the changes in redshift and extinction have only a minor impact."," The revised magnification estimates account for the remainder of the change, while the changes in redshift and extinction have only a minor impact."
 The updated stellar mass implies that the target is a low-mass dwarf galaxy., The updated stellar mass implies that the target is a low-mass dwarf galaxy.
 There exist multiple different techniques for estimating the total infrared luminosity for a galaxy where the infrared emission is dominated by star formation., There exist multiple different techniques for estimating the total infrared luminosity for a galaxy where the infrared emission is dominated by star formation.
 The preferred technique is to use data spanning the peak of the far-infrared (FIR) spectral energy distribution and directly fit a modified blackbody to the far-infrared emission., The preferred technique is to use data spanning the peak of the far-infrared (FIR) spectral energy distribution and directly fit a modified blackbody to the far-infrared emission.
" This technique, which should now become the default method in the era ofHerschel,, provides the most straightforward constraint on DyR with the added advantage of directly yielding the temperature of the dust if the redshift is known."," This technique, which should now become the default method in the era of, provides the most straightforward constraint on $L_{IR}$ with the added advantage of directly yielding the temperature of the dust if the redshift is known."
" Many past studies, in the absence of the requisite ΕΤΗ, data, have instead utilized either 24 eemission or PAH luminosities to estimate L;g."," Many past studies, in the absence of the requisite FIR data, have instead utilized either 24 emission or PAH luminosities to estimate $L_{IR}$."
" With the unique data sets available for our lensed galaxy behind the Bullet Cluster, we are able to compare estimates via all three approaches and assess the level of consistency for this particular dusty starburst."," With the unique data sets available for our lensed galaxy behind the Bullet Cluster, we are able to compare estimates via all three approaches and assess the level of consistency for this particular dusty starburst."
steeper slope.,steeper slope.
 The upper-mass slope only matches the slope of the CMP if fragmentation is independent of mass for cores above the knee in the IMF at 0.5M..., The upper-mass slope only matches the slope of the CMF if fragmentation is independent of mass for cores above the knee in the IMF at $0.5 M_\odot$.
 The problem with the upper-mass slope can be alleviated somewhat by assuming that all stars form with the field binary fraction (rising from for M-dwarfs to for G-dwarts)., The problem with the upper-mass slope can be alleviated somewhat by assuming that all stars form with the field binary fraction (rising from for M-dwarfs to for G-dwarfs).
 However. this solution conflicts with observations that the initial binary fraction for stars >1M. is consistent with unity (Goodwin Kroupa 2005: Duchénne et al.," However, this solution conflicts with observations that the initial binary fraction for stars $>1 M_\odot$ is consistent with unity (Goodwin Kroupa 2005; Duchênne et al."
 2007: Goodwin et al., 2007; Goodwin et al.
 2007)., 2007).
 These observations suggest that there must be a fairly rapid transition between 0.5 and 1M. from a low to a high primordial binary fraction which will result in too-steep an upper-mass slope of the IMF., These observations suggest that there must be a fairly rapid transition between $0.5$ and $1 M_\odot$ from a low to a high primordial binary fraction which will result in too-steep an upper-mass slope of the IMF.
 We have assumed that the mass ratio of binaries Is a flat distribution., We have assumed that the mass ratio of binaries is a flat distribution.
 Biasing the mass ratio distribution to low-g (1e., Biasing the mass ratio distribution to $q$ (ie.
 highly unequal mass systems) improves the problems at the high-mass end of the IMF slightly., highly unequal mass systems) improves the problems at the high-mass end of the IMF slightly.
 If most high-mass cores produce one large star and one or two very low-mass stars. then the IMF at the high-mass end becomes more similar to the MSMF (as this is dominated by one of the stars).," If most high-mass cores produce one large star and one or two very low-mass stars, then the IMF at the high-mass end becomes more similar to the MSMF (as this is dominated by one of the stars)."
 However. the mass ratio distribution needs to be very biased for this to have a significant effect.," However, the mass ratio distribution needs to be very biased for this to have a significant effect."
 The too-steep slope of the upper-end of the IMF can also be solved by assuming that the SFE increases with increasing core mass (in just the right way)., The too-steep slope of the upper-end of the IMF can also be solved by assuming that the SFE increases with increasing core mass (in just the right way).
 However. we feel this solution is unlikely as the SFE would have to be fine-tuned to give the correct slope and it would seem peculiar to postulate that low-mass cores produce stars at very low efficiencies (~ 10%)). whilst higher-mass cores are able to convert more of their gas (~ 30%)) into stars (the opposite of what might be expected from arguments based on feedback).," However, we feel this solution is unlikely as the SFE would have to be fine-tuned to give the correct slope and it would seem peculiar to postulate that low-mass cores produce stars at very low efficiencies $\sim 10$ ), whilst higher-mass cores are able to convert more of their gas $\sim 30$ ) into stars (the opposite of what might be expected from arguments based on feedback)."
 We have shown that the observed mass functions of cores in Orion B (Nutter Ward-Thompson 2007) can give rise to the IMF of stars., We have shown that the observed mass functions of cores in Orion B (Nutter Ward-Thompson 2007) can give rise to the IMF of stars.
 In particular we have shown that. to produce the stellarsub-stellar IMF. the majority of these cores must fragment into multiple systems.," In particular we have shown that, to produce the stellar IMF, the majority of these cores must fragment into multiple systems."
 However. there are a number of issues about cores and the CMF that are worth discussing in this context.," However, there are a number of issues about cores and the CMF that are worth discussing in this context."
" It should be noted that it may not be fragmentation into ""cores! in clusters that sets the IMF of stars.", It should be noted that it may not be fragmentation into `cores' in clusters that sets the IMF of stars.
 If competitive accretion (see Bonnell et al., If competitive accretion (see Bonnell et al.
 2007 and references therein) is the dominant process. then the CMF at best acts to set the initial masses upon which competitive accretion begins to work.," 2007 and references therein) is the dominant process, then the CMF at best acts to set the initial masses upon which competitive accretion begins to work."
 In such a scenario there would be little or no relationship between the CMF and the IMF., In such a scenario there would be little or no relationship between the CMF and the IMF.
 However. we would argue that the form of the CMF in diffuse star forming regions have a direct relevance to the origin and form of the IMF.," However, we would argue that the form of the CMF in diffuse star forming regions have a direct relevance to the origin and form of the IMF."
 Given the apparent universality of the IMF across a wide range of star forming environments (e.g. Kroupa 2002) we are presented with two options., Given the apparent universality of the IMF across a wide range of star forming environments (e.g. Kroupa 2002) we are presented with two options.
 Firstly. that the mechanism(s) that produce the IMF are fundamentally different in different environments. but they always produce the same outcome.," Firstly, that the mechanism(s) that produce the IMF are fundamentally different in different environments, but they always produce the same outcome."
 Or. secondly. that there is a single. underlying. mechanism that produces the IMF i all environments.," Or, secondly, that there is a single, underlying, mechanism that produces the IMF in all environments."
 The latter possibility appeals due to its simplicity. and would suggest that the form of the CMF is the driving factor in establishing the form of the IMF. and that the form of the CMF is roughly the same in diffuse and clustered regions (even if the cores themselves are different in. spacial size).," The latter possibility appeals due to its simplicity, and would suggest that the form of the CMF is the driving factor in establishing the form of the IMF, and that the form of the CMF is roughly the same in diffuse and clustered regions (even if the cores themselves are different in spacial size)."
 Indeed. simulations of turbulence always seem to produce roughly normal CMFs whatever the environment.," Indeed, simulations of turbulence always seem to produce roughly log-normal CMFs whatever the environment."
 We have examined the relationship between the core mass function (CMF) and the stellar initial mass function (IMF)., We have examined the relationship between the core mass function (CMF) and the stellar initial mass function (IMF).
 We use the Orion CMF from Nutter Ward-Thompson (2007) as a ‘standard’ which we fit using a log-normal distribution., We use the Orion CMF from Nutter Ward-Thompson (2007) as a `standard' which we fit using a log-normal distribution.
 We note that this CMF is not dissimilar to the stellar (Kroupa 2002) IMF shifted upwards in mass by a factor of 8 (see also Alves 2007)., We note that this CMF is not dissimilar to the stellar (Kroupa 2002) IMF shifted upwards in mass by a factor of $8$ (see also Alves 2007).
 We randomly sample cores from the CMF and assumed that each core produces a certain number of stars with à random distribution of masses between the components., We randomly sample cores from the CMF and assumed that each core produces a certain number of stars with a random distribution of masses between the components.
 The canonical IMF is reproduced very well by à scenario in which every low-mass cores fragment into binartes. and high-mass cores fragment into a multiple system with a ratio of binaries-to-triples of 3:1 (see e.g. Goodwin Kroupa 2005) and a star formation efficiency (SFE) of ~30%.," The canonical IMF is reproduced very well by a scenario in which every low-mass cores fragment into binaries, and high-mass cores fragment into a multiple system with a ratio of binaries-to-triples of $3\!:\!1$ (see e.g. Goodwin Kroupa 2005) and a star formation efficiency (SFE) of $\sim\! 30$."
. Dynamical disruption (Kroupa 1995a.b: Goodwin Whitworth 2007) of systems then evolves the initial binary fraction of unity into the field population.," Dynamical disruption (Kroupa 1995a,b; Goodwin Whitworth 2007) of systems then evolves the initial binary fraction of unity into the field population."
 We find that a scenario in which low-mass stars preferentially form single systems (e.g. Lada 2006) cannot reproduce the observed IMF from a log-normal CMF., We find that a scenario in which low-mass stars preferentially form single systems (e.g. Lada 2006) cannot reproduce the observed IMF from a log-normal CMF.
 Firstly. the slope of the high-mass IMF ts too steep.," Firstly, the slope of the high-mass IMF is too steep."
 Secondly. and most seriously. this model cannot reproduce the correct numbers of brown dwarfs to high-mass stars.," Secondly, and most seriously, this model cannot reproduce the correct numbers of brown dwarfs to high-mass stars."
 The best-fit to the canonical IMF is found when the SFE is only -15%., The best-fit to the canonical IMF is found when the SFE is only $\sim\! 15$.
. Such a low SFE is required. as the only way in which brown dwarfs may be produced in significant numbers is through the formation of a single brown dwarf from à core.," Such a low SFE is required, as the only way in which brown dwarfs may be produced in significant numbers is through the formation of a single brown dwarf from a core."
 Higher SFEs are required to produce sufficient. high-mass stars. however such SFEs significantly under-produce brown dwarfs and low-mass stars.," Higher SFEs are required to produce sufficient high-mass stars, however such SFEs significantly under-produce brown dwarfs and low-mass stars."
 A lingering question is the value of the star formation efficiency that must be applied to fit the IMF., A lingering question is the value of the star formation efficiency that must be applied to fit the IMF.
 The best-fit value of € in the fully multiple model suggest that only ~30% of the mass in a core ends-up in the stars which that core forms (a similar value for the SFE is found by Alves et al., The best-fit value of $\epsilon$ in the fully multiple model suggest that only $\sim\! 30$ of the mass in a core ends-up in the stars which that core forms (a similar value for the SFE is found by Alves et al.
 2007)., 2007).
 This seems a very low value and may suggest that the determinations of the absolute core masses are wrong., This seems a very low value and may suggest that the determinations of the absolute core masses are wrong.
 Another possibility i5 that feedback from jets is far more efficient than previously thought and manages to disperse most of the gas initially in the core., Another possibility is that feedback from jets is far more efficient than previously thought and manages to disperse most of the gas initially in the core.
" A final possibility ts that we are not observing ""typical cores which produce the IMF and that the observed CMFS will produce somewhat top-heavy IMFs (cf.", A final possibility is that we are not observing `typical' cores which produce the IMF and that the observed CMFs will produce somewhat top-heavy IMFs (cf.
 Taurus. Goodwin et al.," Taurus, Goodwin et al."
 200450., 2004c).
 We conclude that a model in which«// stars and brown dwarfs form in multiple systems from a log-normal core mass distribution provides a very good fit the observed IMF., We conclude that a model in which stars and brown dwarfs form in multiple systems from a log-normal core mass distribution provides a very good fit the observed IMF.
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" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10."," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{1"
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" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10.6 "," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{13}"
" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10.6 +"," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{13}$"
" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10.6 +)"," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{13}$$"
" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10.6 +) "," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{13}$$^"
" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10.6 +) I"," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{13}$$^{"
" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10.6 +) II"," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{13}$$^{+"
" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10.6 +) IIC"," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{13}$$^{+}"
" 0Ο— Lb.¢ ""CO ?? Vjag !). (101 sam IICO TtbntheP-—Vdiagrem.thereareatleasttieocomponentsioneisaneasterncomponentallheveloeilyrangeof ioll.5kms !(() ?2?b)andlheotherwestern-componentatthevelocilyo[ Vjag !. ?2?bshowsblue shifledemission(V9.6 +) (Viag—10.6 +) IICO"," $^{13}$$^{+}$ $b,c$ $^{12}$ \ref{12CO_ch} $V_{\rm{LSR}}$ $^{-1}$ $^{4}$ $\mu$ $^{13}$ $^{+}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ \ref{H13_PV}$ $b$ $V_{\rm{LSR}}$ $^{-1}$ $V_{\rm{LSR}}$ $^{-1}$ $^{13}$$^{+}$"
The resulting fit NOT aud ALO pressure profiles are used to solve for the radial profile of Vandre} (Equation 5).,The resulting fit N07 and A10 pressure profiles are used to solve for the radial profile of $\Ysph(r)$ (Equation \ref{eq:Ysph}) ).
 For cach acceted. link in the AICAIC. we fit the function described x Equation 19 assmuineg a coustaut fas0.12 and pa.=1.17.," For each accepted link in the MCMC, we fit the function described by Equation \ref{eq:YsphNFW}
 assuming a constant $\fgas=0.13$ and $\mu_{\rm e}=1.17$."
 The resulting mass profiles. computed using Ixuation 12.. are used to fud ra ancl Αν). which arc- respectively the radius within which the average deusity is A times greater than the critical density of the uuiverse at that redshift. aud the total lass contained witvin thatradius.," The resulting mass profiles, computed using Equation \ref{eq:Mtot}, , are used to find $r_{\Delta}$ and $\Mtot(r_{\Delta})$, which are respectively the radius within which the average density is $\Delta$ times greater than the critical density of the universe at that redshift, and the total mass contained within thatradius."
 As in M09. we report ry. Ανν). aud for A= with statistical error bars. in Your)Table 1..," As in M09, we report $r_{\Delta}$, $\Mtot(r_{\Delta})$, and $\Ysph(r_{\Delta})$ for $\Delta=[2500,500]$, with statistical error bars, in Table \ref{table:derivedQuants}."
 We discuss [2500.systematics500). along with our co1cTusious iu Section ??.., We discuss systematics along with our conclusions in Section \ref{conc}.
 We conclude that this method is remarkably consistcut eiven the simplifving assumptions required to derive total nass using the virial relation and SZE data alone with the X-ray ouly aud N-ray|SZE mass determination methods in MO (see Table 1)5, We conclude that this method is remarkably consistent — given the simplifying assumptions required to derive total mass using the virial relation and SZE data alone — with the X-ray only and X-ray+SZE mass determination methods in M09 (see Table \ref{table:derivedQuants}) ).
 The assumption of constant f=0.13 has perhaps tje largest systematic iupact on the derived values of Mr) and ra for overdeusitv A., The assumption of constant $\fgas=0.13$ has perhaps the largest systematic impact on the derived values of $\Mtot(r_{\Delta})$ and $r_{\Delta}$ for overdensity $\Delta$.
 Thο radial lass xofile ALG) is x Vas can ])j6 seen by examine he relation between the NEW 4xuanneter py aud in Equation 11..," The radial mass profile $\Mtot(r)$ is $\propto \fgas^{-1/2}$ , as can be seen by examining the relation between the NFW parameter $\rho_0$ and in Equation \ref{eq:UgravNFW}."
 Ikvever. any change in Afar(re) atfects ry and therefore Myr). so the systematic change iu the ass at fixed overdensity ds arecr than a simple rescaling by the inverse square root of the ratio of the correct to the assumed.fos...," However, any change in $\Mtot(r)$ affects $r_{\Delta}$ and therefore $\Mtot(r_{\Delta})$, so the systematic change in the mass at fixed overdensity is larger than a simple rescaling by the inverse square root of the ratio of the correct to the assumed."
 Fitting the same data with an assumed for.=11. for example. increases Mr) by an average of (rather than the change in the profile Af (r7).," Fitting the same data with an assumed $\fgas=0.11$, for example, increases $\Mtot(r_{\Delta})$ by an average of (rather than the change in the profile $\Mtot(r)$ )."
 The assmuption that 44.LAT. bv contrast. can be expected to have a much smaller impact on the mass determination method preseuted here.," The assumption that $\mu_{\rm e}=1.17$, by contrast, can be expected to have a much smaller impact on the mass determination method presented here."
For typical abundance eradients due to inetal euriclunent. pi varies ou the ~| levelwhich οjuges the (1|1/44) factor in Equatio1 15 on the ~0.5% level.,"For typical abundance gradients due to metal enrichment, $\mu_{\rm e}$ varies on the $\sim 1\%$ level, which changes the $(1 + 1/\mu_{\rm e})$ factor in Equation \ref{eq:YsphNFW} on the $\sim 0.5\%$ level."
 Large systematic deviations in metalicity therefore affect the fit Aro(ir) at the (25% level., Large systematic deviations in metallicity therefore affect the fit $\Mtot(r)$ at the $\sim 0.25\%$ level.
 The assmuptiou of a single. constant metallicity is also common in X-rav studies of hieh recshift chsters. where the limited πο of N-rav counts is iusufficieu to constrain more than a sinee spectroscoplc biu.," The assumption of a single, constant metallicity is also common in X-ray studies of high redshift clusters, where the limited number of X-ray counts is insufficient to constrain more than a single spectroscopic bin."
 Ou the other haud. helium sediucutatio iint1 abseice of magnetic fields. in a cluser unudisturbec for 5 Cars. could increase ji. du the core region by ~n. (Peng&Nagai2009).," On the other hand, helium sedimentation in the absence of magnetic fields, in a cluster undisturbed for 3 Gyrs, could increase $\mu_{\rm e}$ in the core region by $\sim 5\%$ \citep{peng2009}."
. Using the results of Peuο&Nagai(2009).. we note that the sedinentatio1i of helimm has litte effect ou the average Ho OV On fdr) at laree The expectation is that merecrs and magnetic fields wil both suppress holiuu secimenutation (Pe1ο&Nagai2009).," Using the results of \citet{peng2009}, we note that the sedimentation of helium has little effect on the average $\mu_{\rm e}$ or on $\mu_{\rm e}(r)$ at large The expectation is that mergers and magnetic fields will both suppress helium sedimentation \citep{peng2009}."
. Another poteuti:d source of bias is due to uncertainties iu the calibration of the SZE data., Another potential source of bias is due to uncertainties in the calibration of the SZE data.
 As discussed. iu Achovejetal.(207).. the absolute calibration of SZA da ais knownto better than aud the variation TOi observation ο observation in amplitude of a fiux calibrator (in this case Mars) is $5 5%. Calibration errors would result iu scaiar svsteniatic errors 1 ithe fit pressure xofile aud. have a linear inpact ou," As discussed in \citet{muchovej2007}, the absolute calibration of SZA data is knownto better than , and the variation from observation to observation in amplitude of a flux calibrator (in this case Mars) is $\lesssim 5 \%$ Calibration errors would result in scalar systematic errors in the fit pressure profile and have a linear impact on"
a stun of three components: bulge. disk. and dark matter halo.,"a sum of three components: bulge, disk, and dark matter halo."
 A convenient way to cleseribe the Galactic potential has been proposed by (MiyamotoanclNagai.1975).. while a series of more detailed models were constructed by (IxuijkenandGilmore.1989). and used in modeling the galactic halo population of neutron stars1998).," A convenient way to describe the Galactic potential has been proposed by \cite{1975PASJ...27..533M}, while a series of more detailed models were constructed by \cite{1989MNRAS.239..571K}
 and used in modeling the galactic halo population of neutron stars."
. The (AlivamotoandNagai.1975) potential for a galactic disk and bulee is where e; and 6; are the parameters. M is the mass. and /?=[usmag.," The \cite{1975PASJ...27..533M} potential for a galactic disk and bulge is where $a_i$ and $b_i$ are the parameters, $M$ is the mass, and $R=\sqrt{x^2 = y^2}$ ."
 he dark matter halo potential is spherically symmetric corresponds to a mass distribution. p—p.f71|(rr)].," The dark matter halo potential is spherically symmetric corresponds to a mass distribution $\rho = \rho_c/[1 +
(r/r_c)^2]$."
"2 The mass of such halo is infinite. so we introduce a cutoll value 724,=I00kpc above which the density of the halo falls to zero."," The mass of such halo is infinite, so we introduce a cutoff value $r_{cut} = 100\,$ kpc above which the density of the halo falls to zero."
 While the details of the model of galactic potential are not important for this study we have to adopt a particular value of the masses ancl sizes of cach of the components., While the details of the model of galactic potential are not important for this study we have to adopt a particular value of the masses and sizes of each of the components.
 We use the values of the parameters asdetermined by (BlaesancRajagopal.L991) for the Alilky Wav: e;=Okpe. bj=O.277 kpc. ae4.2kpe. by—0.198 kpe. A4;=112.1017AZ. Als—SOS101AL... ro=60kpe. and Adj—5.01077 AL.," We use the values of the parameters asdetermined by \cite{1991ApJ...381..210B} for the Milky Way: $a_1 =0\,$ kpc, $b_1 = 0.277\,$ kpc, $a_2 = 4.2\,$ kpc, $b_2 = 0.198\,$ kpc, $M_1 =
1.12\times 10 ^{10}\,M_\odot$, $M_2 = 8.78\times
10^{10}\,M_\odot$, $r_c = 6.0\,$ kpc, and $M_h = 5.0 \times
10^{10}\,M_\odot$ ."
" We assume that the distribution of binaries in. our model galaxy follows the mass distribution in the voung disk (Paczváski.1990).. that is The raclial distribution is exponential with with Row,= 4.5kpe and extends to Rie= 20kpc."," We assume that the distribution of binaries in our model galaxy follows the mass distribution in the young disk \cite{1990ApJ...348..485P}, that is The radial distribution is exponential with with $R_{exp} =
4.5\,$ kpc and extends to $R_{max}= 20\,$ kpc."
 The vertical distribution is pls)xe and no= 75pc.," The vertical distribution is $p(z) \propto e^{-z/z_{exp}}$ and $z_{exp} =
75\,$ pc."
 We note that this is not à self. consistent approach: the density inferred. [rom the disk potential is not the same as the clensity of binaries., We note that this is not a self consistent approach: the density inferred from the disk potential is not the same as the density of binaries.
 However in this work we are not interested in determining high accuracy positions around the host galaxy. and rather with an estimate of the eeneral properties of the distribution of compact object mergers.," However in this work we are not interested in determining high accuracy positions around the host galaxy, and rather with an estimate of the general properties of the distribution of compact object mergers."
 Each binary moves initially with the local rotational velocity in the galactic disk., Each binary moves initially with the local rotational velocity in the galactic disk.
 After each supernova explosion we add an appropriate velocity. provided that the svsten survives the explosion.," After each supernova explosion we add an appropriate velocity, provided that the system survives the explosion."
 We calculate the orbit of each system until it merger time provided that the merger time is smaller than the Hubble time (15 Caves here)., We calculate the orbit of each system until it merger time provided that the merger time is smaller than the Hubble time (15 Gyrs here).
 The kick velocity distribution is not very well known., The kick velocity distribution is not very well known.
" Therefore. we use the population svnthesis code. with four values of the kick. velocity. distribution width: with no kick velocities o= Okm s +. and with o,=200.400.SOO km |."," Therefore, we use the population synthesis code with four values of the kick velocity distribution width: with no kick velocities $\sigma_v =0\,$ km $^{-1}$ , and with $\sigma_v = 200,\, 400,\,
800\,$ km $^{-1}$."
 This covers the range of values this distribution is likely to have., This covers the range of values this distribution is likely to have.
 This the same approach as acloptecl in our previous work (BelezvnskiandBulik. 1999).., This the same approach as adopted in our previous work \cite{BB1998}. .
 The binaries receive kicks for two reasons., The binaries receive kicks for two reasons.
 First. the envelope of the supernovaislost. [rom the system ancl it," First, the envelope of the supernovaislost from the system and it"
The effect. of euvironmeut on galaxy evolution bas long been a subject of intense research aud debate cliscussion).,The effect of environment on galaxy evolution has long been a subject of intense research and debate .
. Kuown environmental effects include tidal eucounters aix mereers. altered Morj»holoegies. alc st‘ipping of gas from disks.," Known environmental effects include tidal encounters and mergers, altered morphologies, and stripping of gas from disks."
 A natiral question is whether the clister environment has signifiaut ellects of the chemical evolution of sealaxies., A natural question is whether the cluster environment has significant effects of the chemical evolution of galaxies.
 This topic has received increasing attention i the last few years., This topic has received increasing attention in the last few years.
 explore the effect of environment on chemical evolutiou Or spirals in the Virgo cluster., explore the effect of environment on chemical evolution for spirals in the Virgo cluster.
 Ενα]ug H II region spectra [rom 9 Vireo spirals. they find e three most H I deficient objects lolave O/H aouucdauces 0.3-0.5 dex higher thau their gas-1ια counterparts.," Examining H II region spectra from 9 Virgo spirals, they find the three most H I deficient objects to have O/H abundances 0.3-0.5 dex higher than their gas-normal counterparts."
 They suggest that |he abuudaice differential results in part. from a lack of iall of metal-poor eas into the spirals in the cluster core., They suggest that the abundance differential results in part from a lack of infall of metal-poor gas into the spirals in the cluster core.
 fit phoolonizzion models to the Virgo data. c«firmiug the alindauce excess lor O/H aud N/O. Other stucles. involviug large-scale spectrose¢yple surveys 2000).. see a qualitatively simiar galactic metalicity depeudence on local galaxy density or eas [raction.," fit photoionization models to the Virgo data, confirming the abundance excess for O/H and N/O. Other studies, involving large-scale spectroscopic surveys , see a qualitatively similar galactic metallicity dependence on local galaxy density or gas fraction."
 analvze a sample οἱ 5060 galaxies in the HyperLeda catalog. concludiug gas-poor galaxies clisplay |igher heavy-eleiuent couteut [or a given stellar πάς».," analyze a sample of 800 galaxies in the HyperLeda catalog, concluding gas-poor galaxies display higher heavy-element content for a given stellar mass."
and the Cepheids (larrisetal.1999:Rejkuba2004;Ferrarese2006).,"and the Cepheids \citep{hhp99,rejkuba04,ferr06}."
. IICIII5 and R122 have not been included in our kinematic study. as our study was completed before publication of these velocities.," HCH15 and R122 have not been included in our kinematic study, as our study was completed before publication of these velocities."
 The weighted velocities used in (his kinematic study do not include (he most recent 25 velocities of previously known GC's published in Rejkubaetal.(2007)., The weighted velocities used in this kinematic study do not include the most recent 25 velocities of previously known GCs published in \cite{rejkuba07}.
. Note that the velocities published in Table 1. do. however. include the Rejkubaetal.(2007) velocities in the quoted final weighted radial velocities Lor completeness.," Note that the velocities published in Table \ref{tab:cat_GC} do, however, include the \cite{rejkuba07} velocities in the quoted final weighted radial velocities for completeness."
 The velocity distribution of the entire sample of 340 is shown in Figure 2. leff). binned in 50 kins ! intervals.," The velocity distribution of the entire sample of 340 is shown in Figure \ref{fig:gausfit_all} ), binned in 50 km $^{-1}$ intervals."
 A fit with a single Gaussian vields a mean velocity of 54647 lan 1 ft. nicely matching the known svstemic velocity of 54147 kms | (Huietal.1995).," A fit with a single Gaussian yields a mean velocity of $546\pm7$ km $^{-1}$ , nicely matching the known systemic velocity of $541\pm7$ km $^{-1}$ \citep{hui95}."
. There is a slight asvmunetiv at the low-velocitv end that is likely due to contamination by a few metal-poor Milkv Way halo stars (also seen in (he metal-poor subpopulation in the bottom left panel. which has a mean velocity determined by (he Gaussian fit as 532413 kin LH.," There is a slight asymmetry at the low-velocity end that is likely due to contamination by a few metal-poor Milky Way halo stars (also seen in the metal-poor subpopulation in the bottom left panel, which has a mean velocity determined by the Gaussian fit as $532\pm13$ km $^{-1}$ )."
 Selecting the clusters with radial velocity uncertainties less than 50 kins ! leaves 226 clusters. plotted in Fig.," Selecting the clusters with radial velocity uncertainties less than 50 km $^{-1}$ leaves 226 clusters, plotted in Fig."
 2. right)., \ref{fig:gausfit_all} ).
 The close fit toa single Gaussian is consistent wilh an isotropic distribution of orbits: the mean velocity is 55445 km |., The close fit toa single Gaussian is consistent with an isotropic distribution of orbits; the mean velocity is $554\pm5$ km $^{-1}$.
 The metal-rich population. with a mean velocity determined by the Gaussian fit of 565411 km b. is plotted in the bottom right panel. and also shows no strong asvimnmetries.," The metal-rich population, with a mean velocity determined by the Gaussian fit of $565\pm11$ km $^{-1}$, is plotted in the bottom right panel, and also shows no strong asymmetries."
 Looking closer at the metal-poor velocity asymmetry. we note (hat the 15 metal-poor clusters between 250 and 300 km 1 (in the region where contamination by Milky Way field stars could occur) are balanced by only two GCs at the high-velocity end on reflection across the svstemic velocitv.," Looking closer at the metal-poor velocity asymmetry, we note that the 15 metal-poor clusters between 250 and 300 km $^{-1}$ (in the region where contamination by Milky Way field stars could occur) are balanced by only two GCs at the high-velocity end on reflection across the systemic velocity."
 The same velocity regions in the metal-rich. population are nearly equally balanced. with low clusters between 250 and 300 km 1 with three clusters αἱ the reflected high-velocity range., The same velocity regions in the metal-rich population are nearly equally balanced with four clusters between 250 and 300 km $^{-1}$ with three clusters at the reflected high-velocity range.
 Interestingly. the four metal-rich clusters between 250 and 300 km ! have projected radii >17 kpe even though the metal-rich population is more centrallv. concentrated (han the metal-poor (seePene.Ford&Freeman2000:Woodley.lluris.&LHlarris2005.among others).," Interestingly, the four metal-rich clusters between 250 and 300 km $^{-1}$ have projected radii $> 17$ kpc even though the metal-rich population is more centrally concentrated than the metal-poor \citep[see][among others]{pff04II,whh05}."
 The metal-poor clusters between 250 and 300 km LH. conversely. are more evenly distributed. with five clusters between projected radii of 5 and 10 kpc. five clusters between 10 and 20 κρο and five clusters bevond 20 kpe from the center of NGC 5128.," The metal-poor clusters between 250 and 300 km $^{-1}$, conversely, are more evenly distributed, with five clusters between projected radii of 5 and 10 kpc, five clusters between 10 and 20 kpc, and five clusters beyond 20 kpc from the center of NGC 5128."
 Some of these low-velocitv. metal-poor objects could be foreground stars with velocities in the realm of GCs in NGC 5128 (ο>250 kins !).," Some of these low-velocity, metal-poor objects could be foreground stars with velocities in the realm of GCs in NGC 5128 $v_r \gtrsim 250$ km $^{-1}$ )."
 However. with only 340 GCs currently confirmed within ~ 45° trom the center of NGC 5128. out of an estimated ~1500 total clusters within 25° (ILarrisetal.2006).. these metal-poor. low-velocily objects could simply be part of a very incomplete GC sample that is also spatially biased.," However, with only 340 GCs currently confirmed within $\sim45$ ' from the center of NGC 5128, out of an estimated $\simeq
1500$ total clusters within 25' \citep{harris06}, these metal-poor, low-velocity objects could simply be part of a very incomplete GC sample that is also spatially biased."
 This potential bias is clearlyshown in Figure 3.. which shows the projected radial distribution as a function of azimuthal angle for our GC sample.," This potential bias is clearlyshown in Figure \ref{fig:gc_thetar}, , which shows the projected radial distribution as a function of azimuthal angle for our GC sample."
 Devond 12 kpe. the two “voids” coincide," Beyond 12 kpc, the two ”voids” coincide"
507 independent measurements of ο in this wav. we arrive al an average value of 0.0011.,"507 independent measurements of $\beta$ in this way, we arrive at an average value of $\beta_{ave} = 0.254 \pm
0.0011$ ."
 While Chis value is only ~4% lower than the value given in Table 1. the difference is statistically significant at the 7.90 level.," While this value is only $\sim 4 \%$ lower than the value given in Table 1, the difference is statistically significant at the $7.9 \sigma$ level."
 This may indicate that “noise” in the Doppler shilts may in fact be impacting Che parameter estimates for the kinematic moclel in a svstemalic wav. as cliscussecl in Section 3.1.," This may indicate that “noise” in the Doppler shifts may in fact be impacting the parameter estimates for the kinematic model in a systematic way, as discussed in Section 3.1."
 As noted above. the upper limit on precessional period derivative of P<5x10? shows that there is no large long-term ο in (he precessional timing properties of 55433.," 	As noted above, the upper limit on precessional period derivative of $\dot P < 5 \times 10^{-5}$ shows that there is no large long-term drift in the precessional timing properties of SS433."
" The presence of jitter in (he svstem implies some ""torque noise"" in the process driving the precession. according to the phase noise model."," The presence of jitter in the system implies some “torque noise” in the process driving the precession, according to the phase noise model."
 However. il this were the case. (hiat noise must average oul over timescales of ~20 vears.," However, if this were the case, that noise must average out over timescales of $\sim 20$ years."
 We can also see from Figure 7 that there are fairly large phase deviations of «Ao~0.1 eveles over limescales as short as ~10 davs., We can also see from Figure 7 that there are fairly large phase deviations of $\Delta \phi \sim 0.1$ cycles over timescales as short as $\sim 10$ days.
 This implies that the torque noise Av has a maximum relative amplitude of al least Thus. the variation in torque can in [act exceed the time-averaged torque driving the precession.," This implies that the torque noise $\Delta \tau$ has a maximum relative amplitude of at least Thus, the variation in torque can in fact exceed the time-averaged torque driving the precession."
 This may be a problem lor certain plvsical models of the precession and timing noise in 55433., This may be a problem for certain physical models of the precession and timing noise in SS433.
 Finally. we note that the phase noise model is incapable of producing the observed Doppler shifts which exceed the maximum amplitude predicted by the kinematic model.," 	Finally, we note that the phase noise model is incapable of producing the observed Doppler shifts which exceed the maximum amplitude predicted by the kinematic model."
 We have considered (he possibility that (he phase noise itself causes (he \-squarecl fitting procedure used to determine the model parameters to svstematically underestimate the true jet velocity. and thus undershoot the maxima.," We have considered the possibility that the phase noise itself causes the $\chi$ -squared fitting procedure used to determine the model parameters to systematically underestimate the true jet velocity, and thus “undershoot” the maxima."
 Iowever. Monte Carlo simulations of data sets with higher (rue velocities and phase noise identical to that observed here fail to produce such undershooting.," However, Monte Carlo simulations of data sets with higher true velocities and phase noise identical to that observed here fail to produce such undershooting."
 Therefore. we conclude that phase noise model cannot reproduce the observed Doppler shift residuals near the maximum projected velocities.," Therefore, we conclude that phase noise model cannot reproduce the observed Doppler shift residuals near the maximum projected velocities."
improve the accuracy of the spectral measurement.,improve the accuracy of the spectral measurement.
" Given this and the brightness of the BAT data, if a spectral break is present, the XRT+BAT data are not sensitive to it."," Given this and the brightness of the BAT data, if a spectral break is present, the $+$ BAT data are not sensitive to it."
" The expected Galactic line-of-sight absorption for MAXI J1659—152 is 1.7x10?! ccm""? etal.2005), however the fitted absorption(Kalberla column is higher and variable, indicating an additional intrinsic absorption component."," The expected Galactic line-of-sight absorption for MAXI $-$ 152 is $1.7
\times 10^{21}$ $^{-2}$ \citep{Kalberla05}, however the fitted absorption column is higher and variable, indicating an additional intrinsic absorption component."
" The fitted Ny increases rapidly during the initial stages of the outburst, beginning at Ng=2.440.3x10?!cm?! on MJD 55464 and rising to a mean value of Ny=5x10?!cm? on MJD 55465."," The fitted $N_\mathrm{H}$ increases rapidly during the initial stages of the outburst, beginning at $N_\mathrm{H} = 2.4
\pm 0.3 \times 10^{21}\ \mathrm{cm^{21}}$ on MJD 55464 and rising to a mean value of $N_\mathrm{H} = 5 \times 10^{21}\ \mathrm{cm^{2}}$ on MJD 55465."
 Measured absorption remains consistent with this value until observations ceased on MJD 55491., Measured absorption remains consistent with this value until observations ceased on MJD 55491.
" Fitting more complex models for absorption such as a warm absorber or partial covering model, with a fixed Galactic absorption also provide good fits to the increasing absorption, although given the spectral resolution of the XRT data, these more complex models are not required over a simple single-parameter variable absorption model."," Fitting more complex models for absorption such as a warm absorber or partial covering model, with a fixed Galactic absorption also provide good fits to the increasing absorption, although given the spectral resolution of the XRT data, these more complex models are not required over a simple single-parameter variable absorption model."
" A later follow-up observation taken on MJD 55598 after MAXI J1659—152 had faded significantly to a flux of 2.4+0.1x107ergs~!cm""? (0.5-10 keV) and entered the Hard State (Τ=1.81+0.1, no significantly detected disk component), gives a fitted absorption of Ny=4.2+0.6x10?!cm-?, consistent with the post-outburst value, suggesting that the additional absorption component is still present despite the lowered X-ray flux."," A later follow-up observation taken on MJD 55598 after MAXI $-$ 152 had faded significantly to a flux of $2.4 \pm 0.1 \times 10^{-11}\ \mathrm{erg\
 s^{-1}\ cm^{-2}}$ (0.5-10 keV) and entered the Hard State $\Gamma =
1.81\pm0.1$, no significantly detected disk component), gives a fitted absorption of $N_\mathrm{H} = 4.2 \pm 0.6 \times 10^{21}\
\mathrm{cm^{-2}}$, consistent with the post-outburst value, suggesting that the additional absorption component is still present despite the lowered X-ray flux."
" With moderate resolution spectral fitting, variable absorption may be due to a statistical correlation between spectral parameters."," With moderate resolution spectral fitting, variable absorption may be due to a statistical correlation between spectral parameters."
" To investigate this we examined confidence contours in T) parameter space, and find that the low Ny spectra (Ng,(MJD 55464) are distinct from the higher Ny spectra (MJD 55465) with 5c confidence."," To investigate this we examined confidence contours in $N_\mathrm{H}$, $\Gamma$ ) parameter space, and find that the low $N_\mathrm{H}$ spectra (MJD 55464) are distinct from the higher $N_\mathrm{H}$ spectra (MJD 55465) with $5\sigma$ confidence."
 Joint BAT and XRT spectral fits allow to constrain I and Ny more independently than by fitting XRT alone., Joint BAT and XRT spectral fits allow to constrain $\Gamma$ and $N_\mathrm{H}$ more independently than by fitting XRT alone.
" Care was taken to remove the effects of pile-up from the spectra, as pile-up can considerably affect continuum spectra fitting (Milleretal."," Care was taken to remove the effects of pile-up from the spectra, as pile-up can considerably affect continuum spectra fitting \citep{Miller10}."
" The fitted values of Ny and T do not vary in lock-step 2010)..either, given the fast initial rise in Ng between MJD 55464 and MJD 55465, compared with an linear rise in I ending around MJD 55470."," The fitted values of $N_\mathrm{H}$ and $\Gamma$ do not vary in lock-step either, given the fast initial rise in $N_\mathrm{H}$ between MJD 55464 and MJD 55465, compared with an linear rise in $\Gamma$ ending around MJD 55470."
 The consistency of the measured absorption in the later follow-up observation of MAXI J1659—152 provides further evidence that the measured Ny is not related to the fitted model or source brightness., The consistency of the measured absorption in the later follow-up observation of MAXI $-$ 152 provides further evidence that the measured $N_\mathrm{H}$ is not related to the fitted model or source brightness.
 We therefore conclude that the variable absorption is physical and not an artifact of the fit., We therefore conclude that the variable absorption is physical and not an artifact of the fit.
" We searched for QPOs using a fast Fourier transform method, adopting the power-spectral normalization of Leahyetal. and the search technique described by vanderKlis(1983)(1989)."," We searched for QPOs using a fast Fourier transform method, adopting the power-spectral normalization of \cite{Leahy83} and the search technique described by \cite{vanderKlis89}."
". For each orbit of XRT data, power density spectra (PDS) were generated for M continuous sections of data of 4096 bins duration, with a bin size of 0.01 s, and averaged."," For each orbit of XRT data, power density spectra (PDS) were generated for $M$ continuous sections of data of 4096 bins duration, with a bin size of 0.01 s, and averaged."
" The averaged PDS from each orbit was then rebinned in frequency so that W continuous frequencies were averaged, using a geometrical series binning scheme."," The averaged PDS from each orbit was then rebinned in frequency so that $W$ continuous frequencies were averaged, using a geometrical series binning scheme."
" Each rebinned/averaged PDS was fit with a model consisting of a power-law for the low frequency noise, a Lorentzian for the QPO (whose width was fixed to preserve a quality factor Q= of 5) and a constant for the Poisson noise level."," Each rebinned/averaged PDS was fit with a model consisting of a power-law for the low frequency noise, a Lorentzian for the QPO (whose width was fixed to preserve a quality factor $Q = \nu / \Delta\nu$ of 5) and a constant for the Poisson noise level."
" The ν/ΔνQPO was considered detected if the Lorentzian amplitude exceeded the local detection level, Puctect(MW) (given by the integral probability of a chi-squared distribution for 2MW d.o.f,."," The QPO was considered detected if the Lorentzian amplitude exceeded the local detection level, $P_\mathrm{detect}(MW)$ (given by the integral probability of a chi-squared distribution for $2MW$ d.o.f,."
" scaled by a factor of minus the mean noise level, which is 2 for the Leahy1/MW)etal.(1983) normalization."," scaled by a factor of 1/MW) minus the mean noise level, which is 2 for the \cite{Leahy83}
 normalization."
 Example PDS for 4 epochs are shown in Figure 4.., Example PDS for 4 epochs are shown in Figure \ref{fig:4_pspe}.
" Figure 5 shows in two energy bands (0.3— 2kkeV and 2—10 kkeV), the QPO frequency, the fractional rms variability of the fitted Lorentzian for PDS in which QPO were detected at greater than 50, and the broadband continuum rms for 0.02—10 HHz, including the QPO and low-frequency noise components."," Figure \ref{fig:qpo_freq} shows in two energy bands $0.3-2$ keV and $2-10$ keV), the QPO frequency, the fractional rms variability of the fitted Lorentzian for PDS in which QPO were detected at greater than $5\sigma$, and the broadband continuum rms for $0.02-10$ Hz, including the QPO and low-frequency noise components."
 The QPO frequency and detection energy evolves with the QPO peak frequency increasing approximately linearly with time., The QPO frequency and detection energy evolves with the QPO peak frequency increasing approximately linearly with time.
" After MJD 55466 QPOs are not detected in the 0.3— 2kkeV band, but are still detected in the 2— 10kkeV band until MJD 55472."," After MJD 55466 QPOs are not detected in the $0.3-2$ keV band, but are still detected in the $2-10$ keV band until MJD 55472."
 The QPO, The QPO
residuals are minimized in the least square sense by y7E which. can be expressed in. terms of the data (V)EI and the model data (V ) as Often. this results in complex and non-linear algorithms but these seem to work well most of the time.,"residuals are minimized in the least square sense by $\chi^2$ which can be expressed in terms of the data $\vec{V}$ ) and the model data $\vec{V^M}$ ) as Often, this results in complex and non-linear algorithms but these seem to work well most of the time."
 To make a practical algorithm. it is ecessary to find efficient ways of calculating the gradients of y with respect to the unknowns.," To make a practical algorithm, it is necessary to find efficient ways of calculating the gradients of $\chi^2$ with respect to the unknowns."
 In this paper. we consider the case of estimating the sky brightness in the presence of directionally dependent gain terms.," In this paper, we consider the case of estimating the sky brightness in the presence of directionally dependent gain terms."
 In a subsequent paper. we will consider the estimation of parameters describing gain terms.," In a subsequent paper, we will consider the estimation of parameters describing gain terms."
 There are cases in which the deconvolution and correction for the Mueller matrix can be decoupled., There are cases in which the deconvolution and correction for the Mueller matrix can be decoupled.
 For example. direction dependent effects which are identical for all the measurements can be removed by dividing the deconvolved image byΜ," For example, direction dependent effects which are identical for all the measurements can be removed by dividing the deconvolved image by."
"Υ, The correction for an azimuthally symmetric and time-constant antenna power pattern provides one such example.", The correction for an azimuthally symmetric and time-constant antenna power pattern provides one such example.
 The deconvolution is then performed on the entire data set. ignoring the antenna power pattern. whose inverse function is applied to the image only after the deconvolution and self-calibration have been completed.," The deconvolution is then performed on the entire data set, ignoring the antenna power pattern, whose inverse function is applied to the image only after the deconvolution and self-calibration have been completed."
 However. this assumption often breaks down.," However, this assumption often breaks down."
 In such case. processing time slices of the data independently might lower the range of the gain variations in each subset.," In such case, processing time slices of the data independently might lower the range of the gain variations in each subset."
 The final deconvolved images for each subset are averaged post-deconvolution., The final deconvolved images for each subset are averaged post-deconvolution.
 This is straightforward and often used. but can be expected to be sub-optimal because the deconvolution step is inherently non-linear and higher PSF sidelobes for individual subsets increase the level of (non-symmetric) deconvolution errors in each sub-image.," This is straightforward and often used, but can be expected to be sub-optimal because the deconvolution step is inherently non-linear and higher PSF sidelobes for individual subsets increase the level of (non-symmetric) deconvolution errors in each sub-image."
 Hence it would seem preferable to follow a procedure that applied the corrections while imaging the full data set., Hence it would seem preferable to follow a procedure that applied the corrections while imaging the full data set.
 In this seetion. we consider in detail an example of directionally dependent gains - the antenna far-field voltage pattern.," In this section, we consider in detail an example of directionally dependent gains - the antenna far-field voltage pattern."
 The far-field voltage pattern ts the Fourier transform of the antenna illumination function (?).., The far-field voltage pattern is the Fourier transform of the antenna illumination function \citep{KRAUS}.
 Thus it is typically the case that because of the details of the antenna geometry (such as quadrupod legs) and feed design. the antenna voltage patterns are azimuthally asymmetric.," Thus it is typically the case that because of the details of the antenna geometry (such as quadrupod legs) and feed design, the antenna voltage patterns are azimuthally asymmetric."
 Furthermore. the polarization response of the antenna will vary away from the antenna optical axis due to antenna geometry and the physics of the reflection of electromagnetic waves from curved surfaces.," Furthermore, the polarization response of the antenna will vary away from the antenna optical axis due to antenna geometry and the physics of the reflection of electromagnetic waves from curved surfaces."
 In addition. as an interferometric array composed of altitude-elevation mounted antenas tracks a region of the sky. these asymmetrical antenna voltage patterns rotate on the sky.," In addition, as an interferometric array composed of altitude-elevation mounted antennas tracks a region of the sky, these asymmetrical antenna voltage patterns rotate on the sky."
 This. along with significant time varying antenna pointing errors. makes time varying and different for each antenna pur (interferometric baseline).," This, along with significant time varying antenna pointing errors, makes time varying and different for each antenna pair (interferometric baseline)."
 Even equatorially mounted antennas share in this problem to the extent that changes in elevation (temperature) might deform the antennas due to gravity (dilation)., Even equatorially mounted antennas share in this problem to the extent that changes in elevation (temperature) might deform the antennas due to gravity (dilation).
 The Mueller matrix is an outer product of the two antenna based Jones matrices. (22)...," The Mueller matrix is an outer product of the two antenna based Jones matrices \citep{Jones,HBS1}."
 A’ full direction-dependent polarimetric description requires a Jones matrix per pixel in the image., A full direction-dependent polarimetric description requires a Jones matrix per pixel in the image.
 For the two orthogonal polarizations. labeled p and q. the Sky Jones matrix as a function of direction is given by: The super-scripts pg and gp represent leakage of the g- polarization signal to p-polarization signal and vice-versa.," For the two orthogonal polarizations, labeled $p$ and $q$, the Sky Jones matrix as a function of direction is given by: The super-scripts $pq$ and $qp$ represent leakage of the $q$ -polarization signal to $p$ -polarization signal and vice-versa."
 The diagonal elements correspond to the antenna voltage patterns on the sky while the off-diagonal elements correspond to the polarization leakage terms (p—g and g-p) due to instrumental leakage (antenna geometry. electronics) and/or atmospheric. ionospheric or other transmission effects such as Faraday rotation.," The diagonal elements correspond to the antenna voltage patterns on the sky while the off-diagonal elements correspond to the polarization leakage terms $p\rightarrow q$ and $q\rightarrow p$ ) due to instrumental leakage (antenna geometry, electronics) and/or atmospheric, ionospheric or other transmission effects such as Faraday rotation."
 The full direction-dependent Sky Mueller matrix Mj for baseline i-/ is a 4x matrix: The diagonalJ elementsJ of thisJ matrix areJ the antenna power patterns for the four polarization products. whereas the off-diagonal products incorporate the cross-polarization leakage terms.," The full direction-dependent Sky Mueller matrix $\MS{ij}{Sky}{}$ for baseline $i$ $j$ is a $4\times 4$ matrix: The diagonal elements of this matrix are the antenna power patterns for the four polarization products, whereas the off-diagonal products incorporate the cross-polarization leakage terms."
 For the VLA antennas. where the two circular polarization power patterns are squinted with respect to each other. the power pattern for the parallel hand (J ο. and the difference between a parallel hanc and a cross hand product (PAP- JE are shown in Fig.," For the VLA antennas, where the two circular polarization power patterns are squinted with respect to each other, the power pattern for the parallel hand $\JS{i}{R}{}\JS{j}{R^{\textstyle *}}{}$ ) and the difference between a parallel hand and a cross hand product $\JS{i}{R}{}\JS{j}{R^{\textstyle *}}{} - \JS{i}{R}{}\JS{j}{L^{\textstyle *}}{}$ ) are shown in Fig."
 1. (super-seript R and L denotes the right- and left-circular polarizations respectively)., \ref{JONES_DIAG} (super-script $\tens{R}$ and $\tens{L}$ denotes the right- and left-circular polarizations respectively).
 The main lobe of the power patterr is azimuthally asymmetric and. clearly. highly asymmetric in the first sidelobe.," The main lobe of the power pattern is azimuthally asymmetric and, clearly, highly asymmetric in the first sidelobe."
 This asymmetry is due to aperture blockage by the feed and the feed-legs., This asymmetry is due to aperture blockage by the feed and the feed-legs.
 The two parallel-hand power patterns ων. and JJ diagonal terms) are also not identical because of differences between the power patterns for the two orthogonal, The two parallel-hand power patterns $\JS{i}{R}{}\JS{j}{R^{\textstyle *}}{}$ and $\JS{i}{L}{}\JS{j}{L^{\textstyle *}}{}$ diagonal terms) are also not identical because of differences between the power patterns for the two orthogonal
To calculate the influence of the gravitational microlensing magnification upon the BLR. each image of the source (as a unction of velocity) was convolved with the magnification maps.,"To calculate the influence of the gravitational microlensing magnification upon the BLR, each image of the source (as a function of velocity) was convolved with the magnification maps."
 For the larger BLR models. the source size becomes comparable to he scale of the magnification maps.," For the larger BLR models, the source size becomes comparable to the scale of the magnification maps."
 Hence. appropriate regions are rimmed from the convolved maps to negate edge effects.," Hence, appropriate regions are trimmed from the convolved maps to negate edge effects."
 For the smaller sources. this means that the central 187 ER were employed or analysis. whereas the larger sources yielded a region 12? ER.," For the smaller sources, this means that the central $^2$ ER were employed for analysis, whereas the larger sources yielded a region $^2$ ER."
 ote that for the purposes of this study. all models are oriented yerpendicular to the shear field.," Note that for the purposes of this study, all models are oriented perpendicular to the shear field."
 Random orientations of the BLR models with respect to the microlensing structure is reserved to a ‘uture contribution., Random orientations of the BLR models with respect to the microlensing structure is reserved to a future contribution.
shows the error in the numerical frequency. (shown as a fractional deviation from the exact value) in each case.,shows the error in the numerical frequency (shown as a fractional deviation from the exact value) in each case.
 The unequal particle mass simulations at this resolution show CLEOLS © 2% for all modes up to jf=Ls., The unequal particle mass simulations at this resolution show errors of $\lesssim 2\%$ for all modes up to $j=18$.
 The results using equal mass particles have comparable accuracy up to the 7=6 mode but thereafter show errors of ~10., The results using equal mass particles have comparable accuracy up to the $j=6$ mode but thereafter show errors of $\sim 10\%$.
 One interesting point to note in the equal particle mass case is that the 7=10 mode seems to ἄοσαν to the j=δ mode and correspondingly the j=20 mode seems to decay to the j=16 mode., One interesting point to note in the equal particle mass case is that the $j=10$ mode seems to decay to the $j=8$ mode and correspondingly the $j=20$ mode seems to decay to the $j=16$ mode.
 The frequencies obtained with the time-reversible integrator are indistinguishable from those obtained using the predicetor-corrector. method. provided that the timestep does not change rapidly between timesteps as discussed in re[secistatic..," The frequencies obtained with the time-reversible integrator are indistinguishable from those obtained using the predictor-corrector method, provided that the timestep does not change rapidly between timesteps as discussed in \\ref{sec:static}."
 The two dimensional. Vor Star can also oscillate non-axisvmmetricallv., The two dimensional Toy Star can also oscillate non-axisymmetrically.
 Phe frequencies in the numerical solutions at a resolution of 1000 particles for the j=0 modes (j—0. s=2.4.6 etc) are shown in Figure 11..," The frequencies in the numerical solutions at a resolution of 1000 particles for the $j=0$ modes (j=0, s=2,4,6 etc) are shown in Figure \ref{fig:phifreq}."
 As in Figure 10. the absolute frequencies are shown in the top panel whilst the [ractional error is shown in the bottom panel., As in Figure \ref{fig:rfreq} the absolute frequencies are shown in the top panel whilst the fractional error is shown in the bottom panel.
 Using unequal mass particles (filled circles. dashed line) the frequencies in the numerical solutions show good agreement with the exact solutions (errors 2%) for modes up to s=16. above which the modes are damped out.," Using unequal mass particles (filled circles, dashed line) the frequencies in the numerical solutions show good agreement with the exact solutions (errors $\lesssim 2\%$ ) for modes up to $s=16$, above which the modes are damped out."
 The results using equal mass particles (open circles. dotted line) show somewhat lower errors C50.64) but only the modes up tos =S are captured in this case.," The results using equal mass particles (open circles, dotted line) show somewhat lower errors $\lesssim 0.6\%$ ) but only the modes up to $s=8$ are captured in this case."
 Finally the Tov Star can oscillate with modes which have both jz0 and sz0., Finally the Toy Star can oscillate with modes which have both $j\neq 0$ and $s\neq 0$.
 Phe density perturbation in the modes with 2—j<12 and 2<s12 is shown in Ligure 12.., The density perturbation in the modes with $2\le j \le 12$ and $2\le s \le 12$ is shown in Figure \ref{fig:mixedmodes_deltarho}.
 The numerical frequencies of the perturbations show similar accuracy to the svmmetric modes., The numerical frequencies of the perturbations show similar accuracy to the symmetric modes.
 As mentioned earlier. one of the most useful features of the ‘Tow Star is that it is possible to get exact. or very accurate solutions of the full non linear equations.," As mentioned earlier, one of the most useful features of the Toy Star is that it is possible to get exact, or very accurate solutions of the full non linear equations."
 These. provide excellent tests of the ability of a numerical code to follow a surface into à region devoid of matter., These provide excellent tests of the ability of a numerical code to follow a surface into a region devoid of matter.
 We assume that the velocity Ποια is a linear function of the cartesian coordinates and that the density is given. by the following second degree function of the coordinates Lor. this. case we choose |Zu=\cAa(f) and |ud=11-030) in which case the velocity field can be written where the first. term produces. an axisvnunetric expansion or contraction. and the second term gives a rigid rotation with angular velocity S3(/)z where @ is à unit vector in the z direction.," We assume that the velocity field is a linear function of the cartesian coordinates and that the density is given by the following second degree function of the coordinates For this case we choose $V^{11} = V^{22} = \alpha(t)$ and $V^{12} = - V^{21} = - \beta(t)$ in which case the velocity field can be written where the first term produces an axisymmetric expansion or contraction, and the second term gives a rigid rotation with angular velocity $\beta(t) \hat{\bf z}$ where $\hat{\bf z}$ is a unit vector in the z direction."
 The motion takes place so that. ab any time. each clement of ης has the same angular velocity.," The motion takes place so that, at any time, each element of fluid has the same angular velocity."
 The reader will appreciate that the solution has many features in common with the svmmetric pulsation of a polvtropic star. for example a model White Dwarf. under gravity.," The reader will appreciate that the solution has many features in common with the symmetric pulsation of a polytropic star, for example a model White Dwarf, under gravity."
 For this axisvmmetric case Co=D. D— 0. so that Substitution of the assumed. forms for v and. p into the acceleration and. continuity equations. with P—Αρ and replacing the Lagrangian derivative by the Eulerian accordingto and equating powers of wv and y we get," For this axisymmetric case $C=D$, $B=0$ , so that Substitution of the assumed forms for ${\bf v}$ and $\rho$ into the acceleration and continuity equations, with $P = K \rho^\gamma$ and replacing the Lagrangian derivative by the Eulerian accordingto and equating powers of $x$ and $y$ we get"
reproduce the observed A sstellar P-Cveni absorption feature and A sstellar emission line.,reproduce the observed $\lambda$ stellar P-Cygni absorption feature and $\lambda$ stellar emission line.
 The shape and strength of these broad ines are determined primarily by the stellar content of a ealaxv. in combination with a relatively narrow nebular component.," The shape and strength of these broad lines are determined primarily by the stellar content of a galaxy, in combination with a relatively narrow nebular component."
 Massive. main-sequence OB stars. dominate he line (with a small contribution from highly stripped WC \Woll-Ravet stars). while the line emission owimarilv arises from. evolved. hydrogen. poor. Wolf-Iavet (WR) stars (with a small. contribution from rare but uminous Of stars).," Massive main-sequence OB stars dominate the line (with a small contribution from highly stripped WC Wolf-Rayet stars), while the line emission primarily arises from evolved, hydrogen poor, Wolf-Rayet (WR) stars (with a small contribution from rare but luminous Of stars)."
 Recently Drinchmann.Petting&Char-ot(2008). revised. predictions for the line strengths expected from a stellar population by including updated Wolf-Itavet. star line equivalent widths. (EWs) in the population svnthesis code., Recently \citet{brinchmann1} revised predictions for the line strengths expected from a stellar population by including updated Wolf-Rayet star line equivalent widths (EWs) in the population synthesis code.
 From this the authors were able to predict a EW that was in agreement with that observed in the Shapleyetal.(2003). spectrum. suggesting that careful consideration of these massive stars and their evolutionary pathways is vital in the interpretation of these distant. sources.," From this the authors were able to predict a EW that was in agreement with that observed in the \citet{shapley} spectrum, suggesting that careful consideration of these massive stars and their evolutionary pathways is vital in the interpretation of these distant sources."
 While the use of composite spectra is necessary to study the majority of distant sources. there are now a small but. &rowing number of individual. Lyman-break galaxies for which high signal-to-noise rest-UV. spectra have been obtained.," While the use of composite spectra is necessary to study the majority of distant sources, there are now a small but growing number of individual Lyman-break galaxies for which high signal-to-noise rest-UV spectra have been obtained."
 The majority of these observations are made possible by high magnification due to strong lensing by intervening material along the line of sight., The majority of these observations are made possible by high magnification due to strong lensing by intervening material along the line of sight.
 They have highlighted a diversity in the population that is obscured by use of a composite. with some galaxies having extremely strong. emission and others. vanishinely weak. undetectable lines.," They have highlighted a diversity in the population that is obscured by use of a composite, with some galaxies having extremely strong emission and others vanishingly weak, undetectable lines."
 Phis variety leacs to a dilemma in its interpretation., This variety leads to a dilemma in its interpretation.
 While strong lines indicate the presence of massive O stars. a weak line would suggest a surprising absence of WR stars in the same galaxies.," While strong lines indicate the presence of massive O stars, a weak line would suggest a surprising absence of WR stars in the same galaxies."
 This dichotomy suggests that a reexamination of the spectral synthesis predictions of these and. features. is DOCOCSSÜAV., This dichotomy suggests that a reexamination of the spectral synthesis predictions of these and features is necessary.
 Aluch work has been done over the past few vears improving stellar. population ancl spectral svnthesis. and cquantifving the uncertainties of these models (c.g.LeithererConroy.White&Gunn2010:Conroy 2010)..," Much work has been done over the past few years improving stellar population and spectral synthesis and quantifying the uncertainties of these models \citep[e.g.][]{1999ApJS..123....3L,2003MNRAS.344.1000B,2004A&A...425..881L,2005MNRAS.362..799M,2007ASPC..374..303B,uncertain,uncertain1,uncertain2}."
 Our approach has been to consider the uncertainties inherent in the use of only single-star evolution models as the building blocks of svnthesis codes., Our approach has been to consider the uncertainties inherent in the use of only single-star evolution models as the building blocks of synthesis codes.
 We have expanded: our. input stellar. evolution models to take account. of binary stars and the many new evolutionary paths wavs this entails., We have expanded our input stellar evolution models to take account of binary stars and the many new evolutionary paths ways this entails.
 In Eldridge&Stanway(2009) we showed that when recent single star stellar models are used to predict the line strength. the measured line equivalent width (EW) is very small. ancl that binary evolution mocels are a better match for the observed. strength (and for other spectral Wh population indicators) in star-forming galaxies.," In \citet{ES09} we showed that when recent single star stellar models are used to predict the line strength, the measured line equivalent width (EW) is very small, and that binary evolution models are a better match for the observed strength (and for other spectral WR population indicators) in star-forming galaxies."
 Ilere we build on that work. ancl consider two uncertainties in the stellar evolution models in an elfort to interpret both the Shapleyetal.(2003). composite spectrum and those of individual lensed LBGs at 2=3.," Here we build on that work, and consider two uncertainties in the stellar evolution models in an effort to interpret both the \citet{shapley} composite spectrum and those of individual lensed LBGs at $z=2-3$."
 First. we investigate the οσοι of variation in the surface carbon abundance of OB stars on the derived stellar spectra.," First, we investigate the effect of variation in the surface carbon abundance of OB stars on the derived stellar spectra."
 Erbοἱal.(2010) show that the amount of carbon in high redshift ealaxies. as measured by nebular emission lines. decreases more rapidlv than their O/I]-derived. metallicity. at low abundances.," \citet{erb} show that the amount of carbon in high redshift galaxies, as measured by nebular emission lines, decreases more rapidly than their [O/H]-derived metallicity at low abundances."
 Pherefore we investigate the ellect ofdecreasing the relative abundance of carbon on the absorption line. in order to examine and mocel this trend.," Therefore we investigate the effect of decreasing the relative abundance of carbon on the absorption line, in order to examine and model this trend."
 Second. we further investigate the importance. of duplicity in. a synthesised.— stellar population when determining the line equivalent width. assuming both instantaneous burst and. constant. star-formation histories.," Second, we further investigate the importance of duplicity in a synthesised stellar population when determining the line equivalent width, assuming both instantaneous burst and constant star-formation histories."
 We now include a new evolutionary process that may only be possible at. low metallicities., We now include a new evolutionary process that may only be possible at low metallicities.
 Quasi-homogeneous evolution (OLI) occurs when a massive star rotates sullicientIv rapidly that the star becomes fully mixed. during its main-sequence Lifetime (AlaederLOST:Yoon&Langer2005:AMevnet&Maeder2007).," Quasi-homogeneous evolution (QHE) occurs when a massive star rotates sufficiently rapidly that the star becomes fully mixed during its main-sequence lifetime \citep{maeder87,yoon1,2007A&A...464L..11M}."
. While it is difficult for a single star to be born rapidly rotating. cllicient mass-transfer in massive binaries can spin up secondary stars to high rotation rates with case (Cantielloetal.2007)..," While it is difficult for a single star to be born rapidly rotating, efficient mass-transfer in massive binaries can spin up secondary stars to high rotation rates with ease \citep{cantiello}."
. At Solar metallicities such stars are likely to spin down quickly due to strong stellar winds., At Solar metallicities such stars are likely to spin down quickly due to strong stellar winds.
 However with the weakening of stellar winds at lower metallicities. elficient rotational mixing can occur.," However with the weakening of stellar winds at lower metallicities, efficient rotational mixing can occur."
 In. this paper we model the elect of this unusual form of evolution on stars that acerete material during a nmiass-transfer event. and investigate the dramatic elect such stars would have on the integrated: spectrum. of a stellar population.," In this paper we model the effect of this unusual form of evolution on stars that accrete material during a mass-transfer event, and investigate the dramatic effect such stars would have on the integrated spectrum of a stellar population."
 This paper is organised. as follows., This paper is organised as follows.
 In Section 2. we discuss the moclilications mace to our. Binary Population and Spectral Synthesis (BPASS) code in order to investigate the phenomena outlined above., In Section \ref{sec:synthetic_spectra} we discuss the modifications made to our Binary Population and Spectral Synthesis (BPASS) code in order to investigate the phenomena outlined above.
 In Section 3. we describe the ellects of these phenomena on the strength of the diagnostic aad spectral features., In Section \ref{sec:pred-equiv-widths} we describe the effects of these phenomena on the strength of the diagnostic and spectral features.
 In Section 4d. we go on to compare our predicted spectra to a composite spectrum constructed from ~900 Lyman-break galaxies by Shapleyetal.(2003). and to various individual examples of z~203 Lyman-break ealaxies., In Section \ref{sec:comp_spect} we go on to compare our predicted spectra to a composite spectrum constructed from $\sim$ 900 Lyman-break galaxies by \citet{shapley} and to various individual examples of $z\sim2-3$ Lyman-break galaxies.
 Finally. in Section 5 we brielly cliscuss our results and outline our conclusions.," Finally, in Section \ref{sec:conclusions} we briefly discuss our results and outline our conclusions."
 Thesvnthetic spectra used in this paper are created: using the Binary Population and Spectral Synthesis. (BASS) codel., Thesynthetic spectra used in this paper are created using the Binary Population and Spectral Synthesis (BPASS) .
. LU is described in detail in Eldridge. (2008).. ElLdridge&Stanway(2009) and. Eldridge.Langer.Tout (2011)..," It is described in detail in \citet{EIT}, \citet{ES09} and \citet{2011arXiv1103.1877E}."
" We use stellar models from the Cambridge STATS code (Eeeleton1971:Eldridege.Γκαν&""Tout.2008.ences therein).. specifically those calculated in IEldridge.Lz-zard&""Tout."," We use stellar models from the Cambridge STARS code \citep[][ and
 references therein]{egg,EIT}, specifically those calculated in \citet{EIT}."
 (2008).. Their kev feature is an extensive set of detailed binary star models (in addition to the detailed single star models) which are kev to producing a realistic svnthetie stellar population., Their key feature is an extensive set of detailed binary star models (in addition to the detailed single star models) which are key to producing a realistic synthetic stellar population.
 We consider stellar models at live dillerent metallicities: Z= 0.001. 0.004. 0.008. 0.020 and 0.040 (where a metallicity of Z=0.020 is conventionally considered Solar). with hyerogen massfraction.," We consider stellar models at five different metallicities: $Z=0.001$ , 0.004, 0.008, 0.020 and 0.040 (where a metallicity of $Z=0.020$ is conventionally considered Solar), with hydrogen massfraction,"
b; and of the Levi-Civita symbol when contracting one obtains the result. that the expression given in equation (X1)) vanishes in case of toroidal modes. (seeMaggiore 2008).,"$\ddot{h}_{ij}$ and of the Levi-Civita symbol when contracting one obtains the result, that the expression given in equation \ref{eq:integral}) ) vanishes in case of toroidal modes \citep[see][]{Mag}."
. Therefore. toroidal modes do not couple to external &ravitational waves.," Therefore, toroidal modes do not couple to external gravitational waves."
 For spheroidal modes one has to consider the expression which is obtained byinserting (17)) into equation considerCX1)), For spheroidal modes one has to consider the expression which is obtained byinserting \ref{eq:sphmodes}) ) into equation \ref{eq:integral}) ).
 ‘The solid angle is denoted by ©., The solid angle is denoted by $\Omega$.
 1n the following. we the contributions from the two terms in brackets separately: the expressions arising from the first and second. term. are denoted by Land LE. respectively.," In the following, we consider the contributions from the two terms in brackets separately; the expressions arising from the first and second term are denoted by I and II, respectively."
" ὃν making use of equation (6)). the first contribution (1) can be rewritten as In this expression the contribution arising from the first terni in. brackets since with the help of equation (1) one has 5;;$;;∕∕vanishes.=hi,im"," By making use of equation \ref{eq:rel_2}) ), the first contribution (I) can be rewritten as In this expression the contribution arising from the first term in brackets vanishes, since with the help of equation \ref{eq:tt_gauge}) ) one has $\ddot{h}_{ij}\delta_{ij}=\ddot{h}^i_{\phantom{i}i}=0$."
 The contribution arising5 from the second term is seen to be non-vanishing only for /=2 due to the orthogonality property of the spherical harmonics., The contribution arising from the second term is easily seen to be non-vanishing only for $l=2$ due to the orthogonality property of the spherical harmonics.
 Consequently. in order to obtain a simple analvtical expression for Ll. we again start with the original expression but now setting /—2 and substitute equation (5)) therein.," Consequently, in order to obtain a simple analytical expression for I, we again start with the original expression but now setting $l=2$, and substitute equation \ref{eq:rel_1}) ) therein."
 Then. again using the orthogonality property of the spherical harmonics. one is left with Finally we define a new variable. z=H. such that the integral is independent of the stellar radius Ze.," Then, again using the orthogonality property of the spherical harmonics, one is left with Finally we define a new variable, $z\equiv r/R$, such that the integral is independent of the stellar radius $R$."
" Fhis vields Proceeding as in the former case. we employ. equation (60) to gain the [following expression. for the second contribution (LL): since Lia, gives a linear combination of spherical harmonics with the same value of /. the contribution [roni the first term in brackets vanishes unless /=0 due to the orthogonality property of the spherical harmonics."," This yields Proceeding as in the former case, we employ equation \ref{eq:rel_2}) ) to gain the following expression for the second contribution (II): Since $L_q Y_{lm}$ gives a linear combination of spherical harmonics with the same value of $l$, the contribution from the first term in brackets vanishes unless $l=0$ due to the orthogonality property of the spherical harmonics."
" Lowever. for /=0 the coellicient function 6,07) is zero. b,o(r)=0 (sce Section 4)."," However, for $l=0$ the coefficient function $b_{nl}(r)$ is zero, $b_{n0}(r)=0$ (see Section 4)."
 Likewise. the contribution arising from the second term in brackets is seen to vanish unless /=2," Likewise, the contribution arising from the second term in brackets is seen to vanish unless $l=2$."
 Ixnowing that Ll is non-vanishing only for /=2. we start again with the original expression. where ωρα has already been inserted.," Knowing that II is non-vanishing only for $l=2$, we start again with the original expression, where $L_q=-\rmn{i}\epsilon_{qab}x_a\partial_b$ has already been inserted."
 Making use of the evclic property of the Levi-Civita symbol and contracting the epsilon tensors vielcds where the n term in brackets M since ↔⊔∣⋡≱∖⋯⋯↓⊔⋏∙≟_," Making use of the cyclic property of the Levi-Civita symbol and contracting the epsilon tensors yields where the second term in brackets vanishes, since $x_p\partial_p Y_{2m}^*=r\frac{\partial}{\partial r}Y_{2m}^*=0$ ."
≼∍↗⊓∕⋟∣≼∙↗⊔∪↓((A2 1: ntSTET ⋅⋅ ∩≖RETI ine quation dus (3))). (2)). (3)) (5)): (+) CX1)), Substituting $\left(\mathcal{Y}_{pq}^{2m}\right)^*\partial_i\left(\frac{x_px_q}{r^2}\right)$ for $\partial_i Y_{2m}^*$ in equation \ref{eq:int_sph_1}) \ref{eq:sph.harm}) \ref{eq:expan.sph.harm.}) \ref{eq:sph.harm}) \ref{eq:rel_1}) \ref{eq:orth.rel}) \ref{eq:integral})
al. (,al. (
2004) model with all three sources.,2004) model with all three sources.
 The low values of [F/O] in the w Cen stars were discussed by both Cunhla et al. (, The low values of [F/O] in the $\omega$ Cen stars were discussed by both Cunha et al. (
2003) and Renda οἱ al. (,2003) and Renda et al. (
2004) in the context of the unusual star formation history and chemical evolution within this sell-enriched stellar svstem that has been captured by the Galaxy.,2004) in the context of the unusual star formation history and chemical evolution within this self-enriched stellar system that has been captured by the Galaxy.
 We detect the HF molecular line at iin WAL dwarls and present the first fiaorine abundance measurements in young stars still in (he pre-anain sequence phase of evolution., We detect the HF molecular line at in K-M dwarfs and present the first fluorine abundance measurements in young stars still in the pre-main sequence phase of evolution.
 These (targets are members of the Orion association. in particular [rom the Orion Nebula cluster. will masses around 0.4-0.5 M...," These targets are members of the Orion association, in particular from the Orion Nebula cluster, with masses around 0.4-0.8 $_{\odot}$."
 Our results for JW433 and JW?22. which do not show substantial emission from a cireumstellar disk. reveal abundances of C and O that are in excellent agreement with those Chat are found in B-type stellar members of Orion Id (Cunha Lambert 1994).," Our results for JW433 and JW22, which do not show substantial emission from a circumstellar disk, reveal abundances of C and O that are in excellent agreement with those that are found in B-type stellar members of Orion Id (Cunha Lambert 1994)."
 This agreement bolsters confidence in the «quantitative spectroscopic abundance analyses techniques used in the hotter D. stars. as well as the eool IX and AL dwarfs.," This agreement bolsters confidence in the quantitative spectroscopic abundance analyses techniques used in the hotter B stars, as well as the cool K and M dwarfs."
 Moreover. JW433 and JW22 also clisplay abundance patterns in agreement. wilh the general behavior of fhiorine versus oxvgen for the Milkv Way disk that has been established [rom stars in a distinctly different evolutionary state.," Moreover, JW433 and JW22 also display abundance patterns in agreement with the general behavior of fluorine versus oxygen for the Milky Way disk that has been established from stars in a distinctly different evolutionary state."
 All previous F abundances had been derived from studies of red giants., All previous F abundances had been derived from studies of red giants.
 The overlap in these abundances provides an important confirmation for the relation of the fluorine abundance with oxveen in the Disk., The overlap in these abundances provides an important confirmation for the relation of the fluorine abundance with oxygen in the Disk.
 In the future. larger samples of Ix aud AI cias. as well as L aud T clwarls. can be used {ο measure f[Inorine and oxvgen abundances both in the field and in (he nearer star-forming regions.," In the future, larger samples of K and M dwarfs, as well as L and T dwarfs, can be used to measure fluorine and oxygen abundances both in the field and in the nearer star-forming regions."
 Based on observations obtained at the Gemini Observatory. which is operated by the Association of Universities for Research in Astronomy. Inc.. under a cooperative agreement with (he NSF on behalf of the Gemini partnership: the National Science Foundation (United States). the Particle Physics and Astronomy Research Couneil (United Ixingdom). the National Research Council (Canada). CONICYT (Chile). the Australian Research Couneil (Australia). CNPq (Brazil). and CONICRT (Argentina). as program GS-2002D-Q-2.," Based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Particle Physics and Astronomy Research Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), CNPq (Brazil), and CONICRT (Argentina), as program GS-2002B-Q-2."
 This work is also supported in part bv the National Science Foundation through ASTO3-07534 (VVS) and NASA through NAG5-9213 (VV$)., This work is also supported in part by the National Science Foundation through AST03-07534 (VVS) and NASA through NAG5-9213 (VVS).
Ol course. (he terminology “texture matter” does not seem to be perfectly apposite because (he real e-nodel textures are ονποσα] defects ancl the equation of state above is not. valid in general case.,"Of course, the terminology ""texture matter"" does not seem to be perfectly apposite because the real $\sigma$ -model textures are dynamical defects and the equation of state above is not valid in general case."
 However. in numerous papers such a terminology was fixedly settled (see [1] and references therein) thus we will follow it in present paper as Some known properties of textures sav that it is probably another kind of vacuum similar to the de Sitter vacuum =+p0 (the latter is known also as the bubble matter).," However, in numerous papers such a terminology was fixedly settled (see \cite{dn} and references therein) thus we will follow it in present paper as Some known properties of textures say that it is probably another kind of vacuum similar to the de Sitter vacuum $\varepsilon + p = 0$ (the latter is known also as the bubble matter)."
 Let us consider. for instance. the O(4)—O(3) textures arising in the scalar fourplet theory described by the action in a closed FRW universe (0<€< x) Then the texture solution of winding number one. has the following stvess-enerey tensor. which evidently satisfies with the above-mentioned equation of state.," Let us consider, for instance, the $\to$ O(3) textures arising in the scalar fourplet theory described by the action in a closed FRW universe $0\leq\xi\leq\pi$ ) Then the texture solution of winding number one, has the following stress-energy tensor, which evidently satisfies with the above-mentioned equation of state."
 The zero-zero component of (his tensor will be compared in Sec., The zero-zero component of this tensor will be compared in Sec.
 3 wilh a surface case., 3 with a surface case.
 The gravitational effects caused by 3D texture matter were intensively studied in many works 1.2]..," The gravitational effects caused by 3D texture matter were intensively studied in many works \cite{dn,texture}."
 The main aim of present paper is to study the 2D fluid of global textures which forms spherically svinmetrie singular bypersurlaces (surfaces of discontinuities of second kind)., The main aim of present paper is to study the 2D fluid of global textures which forms spherically symmetric singular hypersurfaces (surfaces of discontinuities of second kind).
 These hypersurfaces can be interpreted both as the (hin-wall approximation of the laver of bulk matter and as the brane-like objects embedded in spacetime of higher dimensionality., These hypersurfaces can be interpreted both as the thin-wall approximation of the layer of bulk matter and as the brane-like objects embedded in spacetime of higher dimensionality.
 As such. the singular model (turns to be simple enough to obtain important and instructive exact results not only when studsyiug classical dynamics but also when considering quantum aspects.," As such, the singular model turns to be simple enough to obtain important and instructive exact results not only when studying classical dynamics but also when considering quantum aspects."
 With respect to the 3D case this model appears to be the thin-wall approximation. which can elicit main features common for 2D ancl 3D cases.," With respect to the 3D case this model appears to be the thin-wall approximation, which can elicit main features common for 2D and 3D cases."
 The paper is organized as follows., The paper is organized as follows.
 In section 2 we give a comparative description of thermodynamics of 2D and 3D texture matter al [finite temperature wilh respect to each other ancl with respect to bubble matter ancl ordinary matter represented by radiation fluid., In section 2 we give a comparative description of thermodynamics of 2D and 3D texture matter at finite temperature with respect to each other and with respect to bubble matter and ordinary matter represented by radiation fluid.
" Section 3 is devoted to Classical οναός of (he isentropic singular shells ""made"" from 2D texture fluid.", Section 3 is devoted to classical dynamics of the isentropic singular shells “made” from 2D texture fluid.
 In section 4 we perform minisuperspace quantization of the singular model with provision lor both the through (wormhole-like) ancl ordinary topology., In section 4 we perform minisuperspace quantization of the singular model with provision for both the through (wormhole-like) and ordinary topology.
 Conclusions are made in section 5., Conclusions are made in section 5.
simulations of convection (e.g..Si-—eh.Boxburgh&Chan1998).,"simulations of convection \citep[e.g.,][]{singh}."
. The extent to which overshooting actually occurs in stars. however. is unclear.," The extent to which overshooting actually occurs in stars, however, is unclear."
 Since the stars in our simulation do not have convective cores. we are coucerned ouly with overshooting at the base of the surface convection zone.," Since the stars in our simulation do not have convective cores, we are concerned only with overshooting at the base of the surface convection zone."
 The stellar evolution calculations moclel convective overshooting by assuming that the region in which the chemical composition is homogenized by convective mixing extends some cdistauce below the Schwartzschild boundary into the stable radiative region., The stellar evolution calculations model convective overshooting by assuming that the region in which the chemical composition is homogenized by convective mixing extends some distance below the Schwartzschild boundary into the stable radiative region.
 Temperature gradients. however. are taken to be unaffected by overshooting.," Temperature gradients, however, are taken to be unaffected by overshooting."
 The single parameter iu this treatment is the depth by which convective mining reaches into the radiative region. and this distauce is expressed as a fraction of the pressure scale height at the Scliwartzschild boundary.," The single parameter in this treatment is the depth by which convective mixing reaches into the radiative region, and this distance is expressed as a fraction of the pressure scale height at the Schwartzschild boundary."
 Au upper limit on convective overshooting in metal-poor stars is set by observed. lithium abundauces., An upper limit on convective overshooting in metal-poor stars is set by observed lithium abundances.
 Lithium breaks down iu the high temperatures of stellar interiors. beginuiug near the bottom of the surface convection zone.," Lithium breaks down in the high temperatures of stellar interiors, beginning near the bottom of the surface convection zone."
 A large amount of convective overshooting would carry lithium more quickly from the surface to the ---interior. aud lithium depletion would occur at a faster rate.," A large amount of convective overshooting would carry lithium more quickly from the surface to the interior, and lithium depletion would occur at a faster rate."
" Overshooting depths greater than about 0.2 4, would be inconsistent with the relatively high lithium abuucauces observed in metal-poor stars.", Overshooting depths greater than about 0.2 $H_p$ would be inconsistent with the relatively high lithium abundances observed in metal-poor stars.
 Iu our simulation. therefore. we draw. values [or the overshooting depth frou the uniform distribution 0.0 — 0.2 Ap.coefficients.," In our simulation, therefore, we draw values for the overshooting depth from the uniform distribution 0.0 – 0.2 $H_p.$."
. Models of stable astrophysical plasinas predict that heliuui aud heavy elements in a stars radiative regions should settle toward the center of the star over time. while hydrogen rises toward the sur(ace.," Models of stable astrophysical plasmas predict that helium and heavy elements in a star's radiative regions should settle toward the center of the star over time, while hydrogen rises toward the surface."
 The extent to which this actually occurs. however. is subject to considerable uncertainty.," The extent to which this actually occurs, however, is subject to considerable uncertainty."
 There is clear evidence from belioseismology that element cliffusiou occurs inthe sun (Christenseu-Dalsgaard.Proffitt&Thompson1993:Basu.Pinsouneault 2000).," There is clear evidence from helioseismology that element diffusion occurs in the sun \citep{dals,basu}."
. Studies of surface abuudauces in metal-poor stars. though. iudicate that in these stars (illusion for some reason does uot occur in the outer layers (Chaboveretal.2001).," Studies of surface abundances in metal-poor stars, though, indicate that in these stars diffusion for some reason does not occur in the outer layers \citep{chab01}."
. Our stellar evolution calculations incorporate element diffusion using the treatment of &Loeb (1991)., Our stellar evolution calculations incorporate element diffusion using the treatment of \citet{thoul}.
. Because cdiffusiou is uot seen in the outer layers of metal-poor stars. we include a modification introduced by Chaboyveretal.(2001) which suppresses diffusion near he surface.," Because diffusion is not seen in the outer layers of metal-poor stars, we include a modification introduced by \citet{chab01} which suppresses diffusion near the surface."
 By comparing observed iron abuudances in globular clusters to the iron abundance oedieted by their stellar evolution models. Chaboyerοἱal.(2001) estimate that whatever process inhibits cdiffusiou in metal-poor stars must act over an outer regiou of at least 0.005 AL..," By comparing observed iron abundances in globular clusters to the iron abundance predicted by their stellar evolution models, \citet{chab01} estimate that whatever process inhibits diffusion in metal-poor stars must act over an outer region of at least 0.005 $M_\odot$."
 Ou the her hand. the fact that diffusion is not found to be inhibited in the sun suggests that the process inhibiting diffusion extends no lower than the bottom of the solar surface couvection zone. whicl las a Luass of O.O2AL..," On the other hand, the fact that diffusion is not found to be inhibited in the sun suggests that the process inhibiting diffusion extends no lower than the bottom of the solar surface convection zone, which has a mass of $0.02
M_\odot$."
 Therefore Chaboveretal. couclude that the process inhibiting clilfusion ikely acts over a surlace region with mass somewhere between 0.005 aud 0.02 AL.., Therefore \citeauthor{chab01} conclude that the process inhibiting diffusion likely acts over a surface region with mass somewhere between 0.005 and 0.02 $M_\odot$.
 To reflect this in our calculatious we follow Chaboveretal.(2001) in setting the ciffusioi coellicients to zero in the outer 0.005 AL. layer of the star.," To reflect this in our calculations we follow \citet{chab01}
 in setting the diffusion coefficients to zero in the outer 0.005 $M_\odot$ layer of the star."
" In the interior region delined by where M, is the star's total mass. the clilfusion coellicients are set to the standar values of Thoul.Bahcall&Loeb(199 1)."," In the interior region defined by$M_* - M(r) > 0.02\,M_\odot$ where $M_*$ is the star's total mass, the diffusion coefficients are set to the standard values of \citet{thoul}. ."
". In the middle region 0.005AL.<AL,—M(r)0.02 M..."," In the middle region $0.005\,M_\odot < M_* - M(r) < 0.02\,M_\odot$ ,"
factor of ~3 with respect to that of The possibility that space weatlering is responsible for the spectral müsmiateh is also reinforced ly the few experiments published to date of iou bombarcdianeut of Bercha eucrite and Johustown diogeuite (Troi&Pieters1998:Veruazzaotal. 2006).,"factor of $\sim$ 3 with respect to that of The possibility that space weathering is responsible for the spectral mismatch is also reinforced by the few experiments published to date of ion bombardment of Bereba eucrite and Johnstown diogenite \citep{hir98,ver06}."
. They both exhibit reddening (aud darkening)., They both exhibit reddening (and darkening).
 Note tha these experiments also confiui a slower timescale with respect to The true nature of the spectral mismatch still relains elusive iu several aspects: uevertheless sole noteworthy characteristics have been identified., Note that these experiments also confirm a slower timescale with respect to The true nature of the spectral mismatch still remains elusive in several aspects; nevertheless some noteworthy characteristics have been identified.
 Iu particular. we explore m detail the possibility that the spectral mismatch is due to space weathering Fist of all. the spectral slope auti-correlates with exposure to solar wind.," In particular, we explore in detail the possibility that the spectral mismatch is due to space weathering First of all, the spectral slope anti-correlates with exposure to solar wind."
 This is the opposite of what was found. for S-tvpes aud other spectral vpes (Lazzarinetal.2006)., This is the opposite of what was found for S-types and other spectral types \citep{laz06}.
. Therefore. if some sud of Suuaclated space weathering is operating ou V-tvpes. either it behaves in a different niuimner with respect to S-tvpes or other factors wipe out je reddenimg-exposure relation.," Therefore, if some kind of Sun-related space weathering is operating on V-types, either it behaves in a different manner with respect to S-types or other factors wipe out the reddening-exposure relation."
" Concerning the atter. a possibility is represcuted by a composition eradieut across προς, frou eucrite-like for the smallest imuenmibers (1 kin) to diogenite-like for he largest members (—10 kin)."," Concerning the latter, a possibility is represented by a composition gradient across V-types, from eucrite-like for the smallest members $\sim$ 1 km) to diogenite-like for the largest members $\sim$ 10 km)."
 This putative conrposition eradieut would help to explain the observed slope-exposure trend for two reasons: 1) diogenites are bluer. on average. than eucrites: Hxd ii) according to the few experiuents available. the reddening of dioseuites seen less pronounced than for eucrites. although the space parameters of TED compositions aud alteration processes are far frou being exhaustively investigated.," This putative composition gradient would help to explain the observed slope-exposure trend for two reasons: i) diogenites are bluer, on average, than eucrites; and ii) according to the few experiments available, the reddening of diogenites seem less pronounced than for eucrites, although the space parameters of HED compositions and alteration processes are far from being exhaustively investigated."
 Note that the above explanation is preferred with respect to other possibilities. e$. grain size variation. since the latter would require a erain size fuer than ~25 ((i.c. higher slope) for smaller objects.," Note that the above explanation is preferred with respect to other possibilities, e.g. grain size variation, since the latter would require a grain size finer than $\sim25$ (i.e. higher slope) for smaller objects."
 This is the opposite of what is expected. since smaller objects tend to have a larger grain size due to the low eravitv.," This is the opposite of what is expected, since smaller objects tend to have a larger grain size due to the low gravity."
 Also. the substantial presence of S-type interlopors amoung the red W-types would not ereatlv affect the observed slope-exposure trend since they are nearly equally distributed iu terms of E (see Fig. 3))," Also, the substantial presence of S-type interlopers among the red V-types would not greatly affect the observed slope-exposure trend since they are nearly equally distributed in terms of $E$ (see Fig. \ref{f1})"
. If coufirmed. the above conrpositional trend amone family V-tvpes could be the result of cratering ejecta frou various depths in Vesta's crust (eucrite is expected in the upper crust. while ciogenite is expected in the lower crust): or nav be due to different episodes of cratering occurrnue im regions with different compositions.," If confirmed, the above compositional trend among family V-types could be the result of cratering ejecta from various depths in Vesta's crust (eucrite is expected in the upper crust, while diogenite is expected in the lower crust); or may be due to different episodes of cratering occurring in regions with different compositions."
 However. since huge fragnmieuts are expected to originate iu the near-surface spall region. the second lypothesis seems more xobaljle.," However, since large fragments are expected to originate in the near-surface spall region, the second hypothesis seems more probable."
 This inv also be confirmed by the variety 7041-19 Ar shock ages of WEDs (Bogard&Carrison2003)., This may also be confirmed by the variety $^{39}$ $^{40}$ Ar shock ages of HEDs \citep{bog03}.
 Furthermore. the spectral data of V-tvpes seca to imdicate that both nuünceralogies are preseut (αναotal.2001).. but the Ini5 salple prevents a firma The proposed scenario could be tesdoas SOOM as lnore venir spectra of small V-types would become available.," Furthermore, the spectral data of V-types seem to indicate that both mineralogies are present \citep{duf04}, but the limited sample prevents a firm The proposed scenario could be tested as soon as more v-nir spectra of small V-types would become available."
 Note that the above discussion holds for both famuly aud non-fuuiv V-types., Note that the above discussion holds for both family and non-family V-types.
 For the latter. however. the auti-correlation is less xononunced. aud it becomes nearly flat if the outlicrs (red aud blue) are excluded.," For the latter, however, the anti-correlation is less pronounced, and it becomes nearly flat if the outliers (red and blue) are excluded."
" This could be an indication that most nou-funilv V-tvpes have a differcut orieiu with respect to family The NASA Dawn mission will aid iu uudoerstaulue the weatheriug process on Vesta, thanks to spectral dmaging and global mapping."," This could be an indication that most non-family V-types have a different origin with respect to family The NASA Dawn mission will aid in understanding the weathering process on Vesta, thanks to spectral imaging and global mapping."
 Therefore. the possibility to have detailed spectral informatio of specific areas of differcut conrposition ας texture will shed light ou the differcut effects of space weathering on basaltic asteroids.," Therefore, the possibility to have detailed spectral information of specific areas of different composition and texture will shed light on the different effects of space weathering on basaltic asteroids."
 We thank the anonymous referee for the holptu conumnents on the manuscript., We thank the anonymous referee for the helpful comments on the manuscript.
a resolution of 173x035 at 1.3 maim.,a resolution of $1''\!.3\times0''\!.85$ at 1.3 mm.
 For both sources. the peak positions al 1.3 mm and 3.4 mim coincide well with each other.," For both sources, the peak positions at 1.3 mm and 3.4 mm coincide well with each other."
 In 123151. a fan-shaped structure opening to the east can be roughly identified in the 3.4 mm continuum emission.," In I23151, a fan-shaped structure opening to the east can be roughly identified in the 3.4 mm continuum emission."
 In the 1.3 mm continuum enission. (here is a clisconlinuous arch structure at the lowest contour level which goes from a little bit northeast to the southeast of the mm contünuum peak.," In the 1.3 mm continuum emission, there is a discontinuous arch structure at the lowest contour level which goes from a little bit northeast to the southeast of the mm continuum peak."
 We will further discuss these features in Sect. 3.2.., We will further discuss these features in Sect. \ref{sio}.
 Because the weather conditions were only adequate for 1ο 2. mm. wave band during the observing seasons. we use the 3.4 mm continuum data lor quantitative analvsis.," Because the weather conditions were only adequate for the 3 mm wave band during the observing seasons, we use the 3.4 mm continuum data for quantitative analysis."
" Asstunine that the 3.4 mam continuum is mainly produced by optically (hin dust emission. we can calculate (he masses of the dense cores following the relation Algasdust=ΕΙ] (Hildebrand1983).. where £5 is the flux density of the dust enussion. D is the clistance to (he source. ancl D, is the Plank function at a dust temperature of Ty."," Assuming that the 3.4 mm continuum is mainly produced by optically thin dust emission, we can calculate the masses of the dense cores following the relation $M_{gas+dust}=F_{\nu}D^2/B_{\nu}(T_d)\kappa{_\nu}$ \citep{Hildebrand83}, where $F_\nu$ is the flux density of the dust emission, D is the distance to the source, and $B_\nu$ is the Plank function at a dust temperature of $T_d$."
 Sridharanetal.(2002) derive dust temperatures of 35 Ix for 118264 and 6&8 Ix. [or 123151 by eravbody fits to the IRAS and mim data., \citet{Sridharan02} derive dust temperatures of 35 K for I18264 and 68 K for I23151 by graybody fits to the IRAS and mm data.
" Here the dust opacity per eram is taken to her,= 0.1(r/I.2TIIz) 'engg! (Hildebrand.1983).. where the opacity index 3 is set to be 1.5."," Here the dust opacity per gram is taken to be $\kappa_\nu=0.1(\nu/1.2$ $)^{\beta}$ $^2$ $^{-1}$ \citep{Hildebrand83}, where the opacity index $\beta$ is set to be 1.5."
 The results of the ealeulations (M) ave listed in Table. 1.., The results of the calculations $M_{core}$ ) are listed in Table. \ref{table1}.
 The uncertainty of this estimation mainly comes from the determinations of ? and Z7., The uncertainty of this estimation mainly comes from the determinations of $\beta$ and $T_d$.
 The masses will decrease by a [actor of 4 il 7=1. and increase by a [actor of 2 if T; decreases to 17/2.," The masses will decrease by a factor of 4 if $\beta=1$, and increase by a factor of 2 if $T_d$ decreases to $T_d/2$."
 The integrated fIux al 3.4 nun ds 0.13 Jv for 118264 and 0.029 Jv lor 123151., The integrated flux at 3.4 mm is 0.13 Jy for I18264 and 0.029 Jy for I23151.
 When compared with the 1.2 nun sinele-clish flux (Beutheretal. 2002a).. the total flux [rom PdBI amounts to for 118264 and for 23151 of the single-dish flux extrapolated from 1.2 mm using S(v)xi|i with >=]1.5.," When compared with the 1.2 mm single-dish flux \citep{Beuther02a}, , the total flux from PdBI amounts to for I18264 and for I23151 of the single-dish flux extrapolated from 1.2 mm using $S({\nu})\,{\propto}\,{\nu}^{2+{\beta}}$ with $\beta=1.5$."
 Some extended emission is not recovered by (he interferometer., Some extended emission is not recovered by the interferometer.
 Fig., Fig.
 2 presents the channel maps in SiO (2-1) in 118264. where the velocity resolution is smoothed to 5 !|.," \ref{siochan1} presents the channel maps in SiO (2-1) in I18264, where the velocity resolution is smoothed to 5 $^{-1}$."
 The SiO emission mostly appears in the redshifted channels in Fig. 2..," The SiO emission mostly appears in the redshifted channels in Fig. \ref{siochan1},"
 and only the 38.6 ! channel shows prominent blueshifted emission., and only the 38.6 $^{-1}$ channel shows prominent blueshifted emission.
 The most remarkable feature in the channel maps is an elongated structure in the southeast., The most remarkable feature in the channel maps is an elongated structure in the southeast.
 This redshifted emission has verv high velocities up to Ac ~60 kms+ with respect to the svstemic velocity (ος) 43.6 |., This redshifted emission has very high velocities up to $\Delta{v}\sim$ 60 $^{-1}$ with respect to the systemic velocity $v_{LSR}$ ) 43.6 $^{-1}$.
" We have examined the data from the 320 MlIz band and [found that there is no detectable SiO emission bevond eps, of 110 !.", We have examined the data from the 320 MHz band and found that there is no detectable SiO emission beyond $v_{LSR}$ of 110 $^{-1}$.
 The integrated blue- and redshilted SiO emission is shown in Fig., The integrated blue- and redshifted SiO emission is shown in Fig.
 3aa. where (he sinele-dish bipolar CO outflow is resolved into (wo quasi-perpendicular outflows: The southeast to northwest (SE-NW) outflow and (he northeast (NE) outflow.," \ref{sioint1}a a, where the single-dish bipolar CO outflow is resolved into two quasi-perpendicular outflows: The southeast to northwest (SE-NW) outflow and the northeast (NE) outflow."
 Both outflows seem to originate from the western peak of the mm continu., Both outflows seem to originate from the western peak of the mm continuum.
 Along the SE-NW outflow. both red- ancl blueshifted emission can be found. which is a tvpical feature for expanding bow shocks near the plane ofthe sky.," Along the SE-NW outflow, both red- and blueshifted emission can be found, which is a typical feature for expanding bow shocks near the plane ofthe sky."
 From its alienment wilh the SE jet-like outflow. (he bipolar emission in the northwest seems {ο," From its alignment with the SE jet-like outflow, the bipolar emission in the northwest seems to"
wavelength range to fit (heFUSE spectirun.,wavelength range to fit the spectrum.
" The model with M5x10""M. {νι glves a distance of 666pc. too large to be acceptable. and with M=1xLOSAL. /vr the distance becomes twice the value found in the low state."," The model with $\dot{M}=5 \times 10^{-9}M_{\odot}$ /yr gives a distance of 666pc, too large to be acceptable, and with $\dot{M}=1 \times 10^{-8}M_{\odot}$ /yr the distance becomes twice the value found in the low state."
 As an example. a model with /vr is shown in Figure I. giving a distance of 557pe.," As an example, a model with $\dot{M} = 3.5 \times 10^{-9}M_{\odot}$ /yr is shown in Figure 1, giving a distance of 557pc."
 The flux deficiency in the shorter wavelengths is clearly seen., The flux deficiency in the shorter wavelengths is clearly seen.
 The inclusion of a hotter WD does not provide a significant improvement of the mocdel fit., The inclusion of a hotter WD does not provide a significant improvement of the model fit.
 In order to increase the flux in (he shorter wavelengths. the (temperatures of (he two inner rines of the standard disk model are modified to represent the DL.," In order to increase the flux in the shorter wavelengths, the temperatures of the two inner rings of the standard disk model are modified to represent the BL."
" The first ring is located at ry=1.0522, aud the second is al ro=1.2042,. The temperatures of the rings (Lj T5 respectively) are listed in Table 2.", The first ring is located at $r_1=1.05 R_*$ and the second is at $r_2=1.20R_*$ The temperatures of the rings $T_1$ $T_2$ respectively) are listed in Table 2.
 In the standard disk model these temperatures are below 50.000Ix [or the aceretion rate considered here.," In the standard disk model these temperatures are below 50,000K for the accretion rate considered here."
 For the modeling of the DL. rings are computed with temperatures between. 100.0001. and175.000Ix. in agreement with the BL models of Godonetal.(1995). (~125. 000Ix) and Popham&Naravan(1995) (ου180.000) for the mass aceretion rates considered here.," For the modeling of the BL, rings are computed with temperatures between 100,000K and175,000K, in agreement with the BL models of \citet{god95} $\sim 125,000$ K) and \citet{pop95} $\sim 180,000$ K) for the mass accretion rates considered here."
 In doing so. one is able to construct two models ol BL: thin (first ring only) and extended (first two rings).," In doing so, one is able to construct two models of BL: thin (first ring only) and extended (first two rings)."
 The standard disk model with a mass accretion rate of 3xLOM. /vr fits the long wavelength: end of the.FUSE spectrum using the assumed distance to MV. Lyr., The standard disk model with a mass accretion rate of $3 \times 10^{-9}M_{\odot}$ /yr fits the long wavelength end of the spectrum using the assumed distance to MV Lyr.
 For this reason models with M>3x10?M. /vr are nol considered when including the DL. since ihe DL increases the this of the model and therefore its distance becomes too large.," For this reason models with $\dot{M} \ge 3 \times 10^{-9}M_{\odot}$ /yr are not considered when including the BL, since the BL increases the flux of the model and therefore its distance becomes too large."
 Also. since MV Lyris in a high state. mass accretion rates below 1x10.M. /vr are not considered (these points are discussed in (lie section 5).," Also, since MV Lyr is in a high state, mass accretion rates below $1 \times 10^{-9}M_{\odot}$ /yr are not considered (these points are discussed in the section 5)."
" First. an accretion disk with a mass accretion rate of 1x10.9A, /vr is considered. and the DL temperature and size are then varied."," First, an accretion disk with a mass accretion rate of $1 \times 10^{-9}M_{\odot}$ /yr is considered, and the BL temperature and size are then varied."
 It is found that the best model fits lead to a distance of only 350pc-400pc., It is found that the best model fits lead to a distance of only 350pc-400pc.
 Since the mass accretion rate is fixed to κLOM. /vr. the only wav to increase the distance is to increase the contribution of the BL. bv increasing its temperature and/or size.," Since the mass accretion rate is fixed to $1 \times 10^{-9}M_{\odot}$ /yr, the only way to increase the distance is to increase the contribution of the BL, by increasing its temperature and/or size."
 In cloing so. the models that give an acceptable distance (of sav αἱ least » 430pc) have actually too much flux in the shorter wavelengths. a sign that the BL contributes too much flix.," In doing so, the models that give an acceptable distance (of say at least $\sim 430$ pc) have actually too much flux in the shorter wavelengths, a sign that the BL contributes too much flux."
 Only a few of these models are listed in Table 2., Only a few of these models are listed in Table 2.
 These models are not better than the standard disk models: their AZ is as large and/or their distance is too short., These models are not better than the standard disk models: their $\chi^2_{\nu}$ is as large and/or their distance is too short.
 The best fit models are obtained for a thin (one ring) BL with a temperature of ~150.000K-175.000K. The distance for these models is. however. far too short.," The best fit models are obtained for a thin (one ring) BL with a temperature of $\sim$ 150,000K-175,000K. The distance for these models is, however, far too short."
 The inclusion of a heated WD does not improve the models aud produces only a small increase in the distance., The inclusion of a heated WD does not improve the models and produces only a small increase in the distance.
 Next. to obtain models with a larger distance. (he mass aceretion rate is increased to 2xLOΑΙ. νο.," Next, to obtain models with a larger distance, the mass accretion rate is increased to $2 \times 10^{-9}M_{\odot}$ /yr."
 This has the elfect of decreasing the relative flux contributed bv the BL.These models agree with the assumed distance and have a lower V7. especially the two-ring," This has the effect of decreasing the relative flux contributed by the BL.These models agree with the assumed distance and have a lower $\chi^2_{\nu}$ , especially the two-ring"
inclination. and that the bulks of the H and of the K-banc emissions are unlikely to originate in the same physical region.,"inclination, and that the bulks of the $H$ and of the $K$ -band emissions are unlikely to originate in the same physical region."
 The model of a rim of dust grains directly. irradiated by the star cannot fit our data., The model of a rim of dust grains directly irradiated by the star cannot fit our data.
 However. we find that. for various dust grain properties. the silicate sublimation occurs around ~0.65 AU. a distance similar to the sharp transitior in surface brightness seen in the K-band image.," However, we find that, for various dust grain properties, the silicate sublimation occurs around $\sim$ 0.65 AU, a distance similar to the sharp transition in surface brightness seen in the $K$ -band image."
 We therefore interpret the ring-like feature in the K-band image as tracing the emission from dust at ~ 1500 K. Le.. at the transition radius where silicate The previous simple models suggest that the H-band emission is more compact than the K-band emission. and indicate that there is material located inside the silicate sublimation radius. as already found in other Herbig Ae stars.," We therefore interpret the ring-like feature in the $K$ -band image as tracing the emission from dust at $\sim$ 1500 K, i.e., at the transition radius where silicate The previous simple models suggest that the $H$ -band emission is more compact than the $K$ -band emission, and indicate that there is material located inside the silicate sublimation radius, as already found in other Herbig Ae stars."
 Assuming that the ring-like feature in the K- image is related to silicate sublimation. we compose a model made of three elements: a star. a ring at the silicate sublimation radius. and an inner disk.," Assuming that the ring-like feature in the $K$ -band image is related to silicate sublimation, we compose a model made of three elements: a star, a ring at the silicate sublimation radius, and an inner disk."
 This inner and compact emission Is expected to modify the shape of the visibility curves and to smooth the closure phases predicted by à very asymmetric component such as the puffed-up rim., This inner and compact emission is expected to modify the shape of the visibility curves and to smooth the closure phases predicted by a very asymmetric component such as the puffed-up rim.
 In this section. we attempt to derive the main characteristics of these three components. Le.. their extents and contributions to the NIR emission.," In this section, we attempt to derive the main characteristics of these three components, i.e., their extents and contributions to the NIR emission."
 Since it is unclear whether a rim would puff up in the way computed in ? 1f inside matter is blocking part of the stellar emission. we refer to the inner edge of the dusty disk as instead ofrim.," Since it is unclear whether a rim would puff up in the way computed in \citet{isella05} if inside matter is blocking part of the stellar emission, we refer to the inner edge of the dusty disk as instead of."
. Determining its exact structure is beyond the scope of this paper., Determining its exact structure is beyond the scope of this paper.
 This ring traces dust condensation and provides some asymmetric emission. as indicated by the non-zero closure phases.," This ring traces dust condensation and provides some asymmetric emission, as indicated by the non-zero closure phases."
" We compute its emission using the rim model at R;,,,20.65 AU. but where its luminosity is treated as a free parameter to enable SED fitting with an additional inner component."," We compute its emission using the rim model at $_{\rm{sub}}$ =0.65 AU, but where its luminosity is treated as a free parameter to enable SED fitting with an additional inner component."
 We describe the inner disk using a radial temperature profile T«r as expected in a circumstellar disk. and a vertical optical depth τ.," We describe the inner disk using a radial temperature profile $\propto$ $^{-\alpha}$ as expected in a circumstellar disk, and a vertical optical depth $\tau$."
" We find an acceptable fit to the SED. the visibilities. and the closure phases in the H and K bands using a model where the inner disk extends from R;,20.1 AU to Ry. with T;,=2400 K. «0.4. and a vertical optical depth +~0.4."," We find an acceptable fit to the SED, the visibilities, and the closure phases in the $H$ and $K$ bands using a model where the inner disk extends from $_{\rm{in}}$ =0.1 AU to $_{\rm{sub}}$, with $_{\rm{in}}$ =2400 K, $\alpha$ =0.4, and a vertical optical depth $\tau\sim0.4$."
 In this model. the ring contributes of the K-band flux. while the inner disk provides of it.," In this model, the ring contributes of the $K$ -band flux, while the inner disk provides of it."
 In the H-band. the ring is responsible for of the emission. the inner disk for 34%.. leaving the star as the major contributor at 1.6 jm. The parameters of the model are summarized m Tab. 1..," In the $H$ -band, the ring is responsible for of the emission, the inner disk for , leaving the star as the major contributor at 1.6 $\mu$ m. The parameters of the model are summarized in Tab. \ref{tab:bestmodels}."
 We show in Figs., We show in Figs.
 3 and 4 the model predictions for the SED. the broad-band visibilities and closure phases (full black lines).," \ref{fig:sedv2} and \ref{fig:2} the model predictions for the SED, the broad-band visibilities and closure phases (full black lines)."
 By spreading the NIR emission across a broader range of radii (compared to the puffed-up rim). re.. from Εως to R;j. the shape of the visibility-versus-baseline curve is well reproduced and the high closure phases predicted by the model of the puffed-up rim are smoothed out. resulting in values close to the observations (from 0 to 207)).," By spreading the NIR emission across a broader range of radii (compared to the puffed-up rim), i.e., from $_{\rm{sub}}$ to $_{\rm{in}}$, the shape of the visibility-versus-baseline curve is well reproduced and the high closure phases predicted by the model of the puffed-up rim are smoothed out, resulting in values close to the observations (from 0 to )."
 A temperature gradient within the inner disk is needed to reproduce the H and K band visibilities together. as a single temperature disk at a specific τ cannot.," A temperature gradient within the inner disk is needed to reproduce the $H$ and $K$ band visibilities together, as a single temperature disk at a specific $\tau$ cannot."
 The model is shown in Fig. 5..," The model is shown in Fig. \ref{fig:imagemodel},"
 right., right.
 Considering the large scatter in the observations. we do not claim the uniqueness of the parameters of our model (7. Τμ. α). although they provide a qualitatively good fit to the observations. and the extents and flux ratio of each component are well constrained and in agreement with the images.," Considering the large scatter in the observations, we do not claim the uniqueness of the parameters of our model $\tau$, $_{\rm{in}}$, $\alpha$ ), although they provide a qualitatively good fit to the observations, and the extents and flux ratio of each component are well constrained and in agreement with the images."
 Our model produces a strong variation in surface brightness in the first AU. from the star to the ring.," Our model produces a strong variation in surface brightness in the first AU, from the star to the ring."
 To better interpret the reconstructed image presented in Fig. 2..," To better interpret the reconstructed image presented in Fig. \ref{fig:image},"
 we performed an image reconstruction from the visibilities and closure phases of our model., we performed an image reconstruction from the visibilities and closure phases of our model.
 To do so. we computed synthetic data sets from the model image. with an identical coverage as the observations. the same errors. and a similar scatter in the visibility measurements.," To do so, we computed synthetic data sets from the model image, with an identical coverage as the observations, the same errors, and a similar scatter in the visibility measurements."
 We present an example of a reconstructed image from the model in Fig. 5.. ," We present an example of a reconstructed image from the model in Fig. \ref{fig:imagemodel}, ,"
middle. compared to the real image (left).," middle, compared to the real image (left)."
 The image reconstructed from the model shares the same characteristics as the real image. Le.. an incomplete ring-like feature in the K-band oriented along PA~135° and inclined by ~45°.. with an inner diameter of ~5.5 mas. and an extended central spot.," The image reconstructed from the model shares the same characteristics as the real image, i.e., an incomplete ring-like feature in the $K$ -band oriented along $\sim$ and inclined by $\sim$, with an inner diameter of $\sim$ 5.5 mas, and an extended central spot."
 This confirms that our model provides a qualitatively good description of our data., This confirms that our model provides a qualitatively good description of our data.
 In particular. the missing part of the ring-like feature can be explained by the low-brightness edge of an inclined rim (while the other edge ts much brighter).," In particular, the missing part of the ring-like feature can be explained by the low-brightness edge of an inclined rim (while the other edge is much brighter)."
 It also shows that although the star is unresolved in the model with a diameter of ~0.2 mas (r.e.. inside the central pixel). the central spot in the reconstructed Image is much more extended (~2.] màs; similar to the real image).," It also shows that although the star is unresolved in the model with a diameter of $\sim$ 0.2 mas (i.e., inside the central pixel), the central spot in the reconstructed image is much more extended $\sim$ 2.1 mas; similar to the real image)."
 Its size is about the interferometric beam size. but in the model image. it has much more flux than the star's. due to the inner disk emission on unresolved scales as small as 0.1 AU.," Its size is about the interferometric beam size, but in the model image, it has much more flux than the star's, due to the inner disk emission on unresolved scales as small as 0.1 AU."
 This could indicate that the central spot in the real image also includes an additional emission to the star's., This could indicate that the central spot in the real image also includes an additional emission to the star's.
 Several tests have led us to conclude that the scatter in the visibility measurements lowers the achievable dynamics which canresult in an image that has low or no emission insidethe, Several tests have led us to conclude that the scatter in the visibility measurements lowers the achievable dynamics which canresult in an image that has low or no emission insidethe
iu the same sense as one introduces anomalous resistivity and anomalous diffusion iu plasma plivsics: The origin of this viscosity is in fully developed turbulence which is established in the saturation regime described above.,in the same sense as one introduces anomalous resistivity and anomalous diffusion in plasma physics: The origin of this viscosity is in fully developed turbulence which is established in the saturation regime described above.
 Eq. (, Eq. (
3.15) or (3.16) could be derived frou dimensional arguments (of course. without the nuuerical coefficieut) as an estimation of viscosity in a rotating disk with turbulent motions.,"3.15) or (3.16) could be derived from dimensional arguments (of course, without the numerical coefficient) as an estimation of viscosity in a rotating disk with turbulent motions."
 Towever. we should emphasize that without au analysis such as one given above it would be impossible to reveal an underline plivsical mechauisin for the origin of such turbulence.," However, we should emphasize that without an analysis such as one given above it would be impossible to reveal an underlying physical mechanism for the origin of such turbulence."
 It is iuportaut to test whether the necessary condition for developing of zinall-scale turbulence is met., It is important to test whether the necessary condition for developing of small-scale turbulence is met.
 To this end. let us find the ratio vVenue as a function of 7=Of; of the basic parameter that characterizes the umuber of interactions per one revolution: mn both hmnüts. 7 laud rX1. the viscosity coefficient is mich less than the critical value giveu by Eqs. (," To this end, let us find the ratio $\nu/\nu_{\rm turb}$ as a function of $\tau=\Omega t_i$, of the basic parameter that characterizes the number of interactions per one revolution: Asymptotically, in both limits, $\tau\ll 1$ and $\tau \gg 1$, the viscosity coefficient is much less than the critical value given by Eqs. ("
3.15) or (3.16).,3.15) or (3.16).
" The fuuction (3.18) reaches its masta at 7=B,*. and this maxima is eiven by Even in this. the least favorable case [when 72:0.5 as one cau see from Eq. ("," The function (3.18) reaches its maximum at $\tau
=B_i^{-1}$, and this maximum is given by Even in this, the least favorable case [when $\tau \simeq 0.5$ as one can see from Eq. ("
2.1)] iis less than 144 by a factor of2 or so. Which is enough for small-scale turbulence to appear.,"2.4)] $\nu$ is less than $\nu_{\rm cr}$ by a factor of 2 or so, which is enough for small-scale turbulence to appear."
 Therefore the range of physical conditious under which the viscosity due to fully developed turbulence should donunate is indeed very broad., Therefore the range of physical conditions under which the viscosity due to fully developed turbulence should dominate is indeed very broad.
 Uulike the classical example of gravitational iustabilitv. our mechanism for the erowtl of shortwave perturbations bas a much higher level of VISCOUS stabilization. as it follows from the value of critical viscosity calculated above in comparison with that for a sclberavitatingo disk.," Unlike the classical example of gravitational instability, our mechanism for the growth of shortwave perturbations has a much higher level of viscous stabilization, as it follows from the value of critical viscosity calculated above in comparison with that for a self-gravitating disk."
 DIudeed. the erowth of shortwave perturbations leads to the increase of the amplitude by a factor of This strong imequality follows from the fact that [eQD)I|~FT. where f is the characteristic time of the erowth of perturbations and T is the period of the disk revolution.," Indeed, the growth of shortwave perturbations leads to the increase of the amplitude by a factor of This strong inequality follows from the fact that $|k_r(0)/ k_\varphi| \sim t_*/T,$ where $t_*$ is the characteristic time of the growth of perturbations and $T$ is the period of the disk revolution."
 According to the perturbation theory implemented to cxamune instability. the condition LT>>1 holds (otherwise the zero-approxinatiou of perturbation theorv is uot fulfilled: the equilibria condition is broken for the time less then that of one revolution of the disk).," According to the perturbation theory implemented to examine instability, the condition $t_*/T >> 1$ holds (otherwise the zero-approximation of perturbation theory is not fulfilled: the equilibrium condition is broken for the time less then that of one revolution of the disk)."
 As a result of the above inequality. a strong growth of perturbation takes place. which leads to the development of short-scale turbulence ar the appearance of turbulent viscosity.," As a result of the above inequality, a strong growth of perturbation takes place, which leads to the development of short-scale turbulence and the appearance of turbulent viscosity."
" A very laree factor of the erowth given above explains why the value of the critical turbulent viscosity. which stops the growth of perturbations. turus out to be much larger than that for the instability of a sclteravitating disk (οιο,, Fridian Polvacheuko 1981. p. 1)."," A very large factor of the growth given above explains why the value of the critical turbulent viscosity, which stops the growth of perturbations, turns out to be much larger than that for the instability of a self-gravitating disk (e.g., Fridman Polyachenko 1984, p. 41)."
 Before making nunercal estimates. we dist the basic parameters of the chuupy eas in the circumuuclear rine (CNR). such as the inferred clump size e. the volume filling factor F. aud velocity dispersion of the chumps σι. taken from Jacksou et al. (," Before making numerical estimates, we list the basic parameters of the clumpy gas in the circumnuclear ring (CNR), such as the inferred clump size $a$, the volume filling factor $F$, and velocity dispersion of the clumps $\sigma_v$, taken from Jackson et al. ("
1993) and Caissten at al. (,1993) and Güssten at al. (
1987): Adoptingc» the average[m] C»gas deusitv iu the clumps η=cu? one fiuds the average clin mass mn=5M.,1987): Adopting the average gas density in the clumps $n=10^5~{\rm cm^{-3}}$ one finds the average clump mass $m=5$.
 This gives the ratio ία2107. which iuplies that clastic (eravitational) imteractions between the chumps are ueelieible conrpared to melastie ones. chuup-chuup collisions.," This gives the ratio $a_G/a\simeq 10^{-3}$, which implies that elastic (gravitational) interactions between the clumps are negligible compared to inelastic ones, clump-clump collisions."
 Iu other words. ogravitation plavs no role in the interactions between the CNR clamps.," In other words, gravitation plays no role in the interactions between the CNR clumps."
 The mean free path ofthe chuups given by is rather laree (even in a nuuginal conflict with the siuplifvine asstuuption (3.1) that / hj., The mean free path of the clumps given by is rather large (even in a marginal conflict with the simplifying assumption (3.1) that $l\ll h$ ).
 The chup collision rate in the CNR is giveu by: welQs2.10324? nuplving less than one collision per revolution., The clump-clump collision rate in the CNR is given by: $\omega_c\lax\Omega\simeq 2\cdot 10^{-12}~{\rm s}^{-1}$ implying less than one collision per revolution.
 The auticipated optical depth is T=ει0.5. which. according to Eq. (," The anticipated optical depth is $\tau\simeq 0.1~-~0.5$, which, according to Eq. ("
3.17). results in<My.,"3.17), results in $\nu < \nu_{\rm cr}$."
 Therefore. the conditions for fully developed turbuleuce to appear. which are described at the cud of Sec.," Therefore, the conditions for fully developed turbulence to appear, which are described at the end of Sec."
 3. are met to vield the viscosity coefficieut It is iustructive to compare this result with the upper lait to viscosity derived by von Linden et al. (," 3, are met to yield the viscosity coefficient It is instructive to compare this result with the upper limit to viscosity derived by von Linden et al. ("
1993a.)).,"1993a,b)."
 Their results were obtained by fitting an accretion disk model with arbitrary viscosity to the velocity fields of various molecular clouds. auc then inferring the required kinematic viscosity from the fit.," Their results were obtained by fitting an accretion disk model with arbitrary viscosity to the velocity fields of various molecular clouds, and then inferring the required kinematic viscosity from the fit."
 Successful fits were made in the radial rauge from 10 to 100 pe. with an implied," Successful fits were made in the radial range from 10 to 100 pc, with an implied"
Another potentially interesting population is that defined by objects in region II of figure 3..,Another potentially interesting population is that defined by objects in region II of figure \ref{fig:coltheory}.
 These objects are clearly visible in figure | at magnitudes V.719.5., These objects are clearly visible in figure \ref{fig:color-mag} at magnitudes $V \gsim 19.5$.
 These blue objects could be either relatively hot (young) disk white dwarfs or blue horizontal branch (HB). low-metallicity halo stars.," These blue objects could be either relatively hot (young) disk white dwarfs or blue horizontal branch (HB), low-metallicity halo stars."
 However. for V220 HB stars would be located at 7100 kpc. where the density should be extremely small for standard galactic structure models.," However, for $V \gsim 20$ HB stars would be located at $\gsim100$ kpc, where the density should be extremely small for standard galactic structure models."
 There are 32 objects in region IL which are listed in table 5.., There are 32 objects in region II which are listed in table \ref{tab:wd}.
 The adopted cut-off in (VY7) (see table 1)) was chosen based on cooling sequence of disk white dwarfs (Bergeron. Wesemael. Beauchamp 1995) shown in figure 3..," The adopted cut-off in $(V-I)$ (see table \ref{tab:scheme}) ) was chosen based on cooling sequence of disk white dwarfs (Bergeron, Wesemael, Beauchamp 1995) shown in figure \ref{fig:coltheory}."
 We emphasize that the criterion adopted is somewhat arbitrary and it is used simply to illustrate the possible identification of these objects., We emphasize that the criterion adopted is somewhat arbitrary and it is used simply to illustrate the possible identification of these objects.
 As can be seen from figure 3.. this sample can be contaminated by low redshift quasars.," As can be seen from figure \ref{fig:coltheory}, this sample can be contaminated by low redshift quasars."
 In fact table 5 contains 2 already known quasar which are identified (name and redshift from the Simbad database)., In fact table \ref{tab:wd} contains 2 already known quasar which are identified (name and redshift from the Simbad database).
 The U-band data will be useful to sort out these cases., The $U$ -band data will be useful to sort out these cases.
 Finally. figure + shows the spatial distribution of these various candidates.," Finally, figure \ref{fig:starsdist} shows the spatial distribution of these various candidates."
 Note that the northeast edge of the patch has been removed because of the incompleteness of the B-band catalogs., Note that the northeast edge of the patch has been removed because of the incompleteness of the B-band catalogs.
 Similarly. a region along the southern edge was removed because of the incompleteness in the I-band catalog.," Similarly, a region along the southern edge was removed because of the incompleteness in the I-band catalog."
 A small trimming of the whole region has also been done yielding a total area of 1.27 square degrees., A small trimming of the whole region has also been done yielding a total area of 1.27 square degrees.
 From simulations of QSO tracks (figure 3)) high redshift QSOs (3«z 5) can be found in region III of the color-color diagram. while the available sample of known low redshift QSOs populate region IV (see figure 3.. Osmer 1998).," From simulations of QSO tracks (figure \ref{fig:coltheory}) ) high redshift QSOs $3<z<5$ ) can be found in region III of the color-color diagram, while the available sample of known low redshift QSOs populate region IV (see figure \ref{fig:coltheory}, Osmer 1998)."
 The rough criteria used to define region III (table 1)) were chosen based on the simulated QSO track., The rough criteria used to define region III (table \ref{tab:scheme}) ) were chosen based on the simulated QSO track.
 The blue part was chosen to be parallel to the stellar locus but shifted to minimize the contamination by stars., The blue part was chosen to be parallel to the stellar locus but shifted to minimize the contamination by stars.
 Several improvements in the selection can be made to take into account the errors in colors. as a function of the magnitude. and to optimize the yield based on the expected density of objects of different types.," Several improvements in the selection can be made to take into account the errors in colors, as a function of the magnitude, and to optimize the yield based on the expected density of objects of different types."
 Since the parent sample is public. interested groups are likely to make significant refinements to the selection eriteria adopted here.," Since the parent sample is public, interested groups are likely to make significant refinements to the selection criteria adopted here."
 In region III there are 70 objects detected in all three passbands., In region III there are 70 objects detected in all three passbands.
 These are listed in table 6.., These are listed in table \ref{tab:qsocand}.
 In addition. there are 126 objects that are detected in V and / but not detected in B (hence have lower limits in (B.— VJ) that could also lie in region IV.," In addition, there are 126 objects that are detected in $V$ and $I$ but not detected in B (hence have lower limits in $(B-V)$ ) that could also lie in region IV."
 These objects are listed in table 7.., These objects are listed in table \ref{tab:qsobdrop}.
 Note that. since the depth of the B images varies across the patch. the limits on (BV) are more meaningful in some areas than others.," Note that, since the depth of the B images varies across the patch, the limits on $(B-V)$ are more meaningful in some areas than others."
 The depth of the B frames corresponding to each object can be calculated from the V magnitude and the (BV) limits given in table 6.., The depth of the $B$ frames corresponding to each object can be calculated from the $V$ magnitude and the $(B-V)$ limits given in table \ref{tab:qsocand}.
 In the tables the following naming convention has been adopted: QSO and QSOB stand for objects in region III detected in all three bands 73.0) and B-dropouts candidates. respectively.," In the tables the following naming convention has been adopted: QSO and QSOB stand for objects in region III detected in all three bands $\gsim3.0$ ) and B-dropouts candidates, respectively."
 Adopting the criteria given in table | for region IV. where QSOs with z<3 are likely to be found. one finds 48 stellar objects which are listed in table 8..," Adopting the criteria given in table \ref{tab:scheme} for region IV, where QSOs with $z\lsim3$ are likely to be found, one finds 48 stellar objects which are listed in table \ref{tab:qsolowz}."
 This table includes 6 known QSOs. as indicated (name and redshift are from the Simbad database).," This table includes 6 known QSOs, as indicated (name and redshift are from the Simbad database)."
 In the table QLZ stands for low redshift (z <3.0) quasars., In the table QLZ stands for low redshift $z\lsim3.0$ ) quasars.
 Note. however. that with the follow-up observations in U band to be carried out later this year. 1t will be possible to select low-z QSOs more efficiently.," Note, however, that with the follow-up observations in $U-$ band to be carried out later this year, it will be possible to select low-z QSOs more efficiently."
 Figure 5. show the projected sky distribution of the QSO candidates., Figure \ref{fig:qsodist} show the projected sky distribution of the QSO candidates.
 This figure should be compared with those for the seeing and the limiting magnitudes presented in paper III to investigate possible correlations between the QSO candidates and the quality of the data. especially the B-dropouts or those detected only in the /-band.," This figure should be compared with those for the seeing and the limiting magnitudes presented in paper III to investigate possible correlations between the QSO candidates and the quality of the data, especially the B-dropouts or those detected only in the $I$ -band."
 At first glance there is no obvious correlation as the QSO candidates seem to be uniformly distributed over the surveyed area., At first glance there is no obvious correlation as the QSO candidates seem to be uniformly distributed over the surveyed area.
noted in WOO. IH» has a cross-section that is approximately larger (per IE nucleus) than atomic IH. We adopt the enhanced Is cross-section and assume the gas is fully molecular (i.e. ΠΟ)ΓΗ= 0.5).,"noted in W00, $_2$ has a cross-section that is approximately larger (per H nucleus) than atomic H. We adopt the enhanced $_2$ cross-section and assume the gas is fully molecular (i.e. $n(\textrm{H}_2 )/n_{\textrm{H}} = 0.5$ )."
 Relative to earlier work focusing on the largely atomic ISM. the inclusion of the molecular enhancement increases the cross-section most signicantlv ad extreme ultraviolet wavelengths where hydrogen opacity dominates.," Relative to earlier work focusing on the largely atomic ISM, the inclusion of the molecular enhancement increases the cross-section most signiÞcantly at extreme ultraviolet wavelengths where hydrogen opacity dominates."
 The well-tested IDL (line routines POLY_FFIT and SVD were used to evaluate aud test the uniqueness of the ts., The well-tested IDL Þtting routines FIT and SVD were used to evaluate and test the uniqueness of the Þts.
 The fitting coellicients are given in Table 1.., The fitting coefficients are given in Table \ref{table_fits}.
 The resulting opacily curves are shown in Figure 2.., The resulting opacity curves are shown in Figure \ref{fig:cross}.
 By comparison wilh a gas of pure IE ancl Ile. Figure 2 clearly shows that C. O and Noble gases Ne and Ar. contribute signicantlv to the gas opacity at energies > Q.3keV. Away from photoelectric edges the fitting errors are (vpically al the level. which is small compared to the compositional uncertainties of gas and dust.," By comparison with a gas of pure H and He, Figure \ref{fig:cross} clearly shows that C, O and Noble gases Ne and Ar, contribute signiÞcantly to the gas opacity at energies $E > 0.3$ keV. Away from photoelectric edges the fitting errors are typically at the level, which is small compared to the compositional uncertainties of gas and dust."
 Noticeable in the dust component are significant (~1054) error spikes near to metal Ix-edge thresholds., Noticeable in the dust component are significant $(\sim10\%)$ error spikes near to metal K-edge thresholds.
 These errors (consistent with those in WOO) arise from the numerical discretization of the elemental cross-sections. and trom the fundamental limitations of a low-order fit.," These errors (consistent with those in W00) arise from the numerical discretization of the elemental cross-sections, and from the fundamental limitations of a low-order fit."
 It is important to note that striving lor a more accurate polvnomial Lit ad Ix-shell edges is not entirely meaningful unless we include actual solid-state effects. which in general are too complex for a low order polvnomial fit (Draine2003)..," It is important to note that striving for a more accurate polynomial fit at K-shell edges is not entirely meaningful unless we include actual solid-state effects, which in general are too complex for a low order polynomial fit \citep{Draine:2003fk}."
" The derivation of the sell-blanketing factor. {η} for spherical. homogeneous grains is described in Appendix A. Plots of /5,CE) versus X-ray energy for a range of grain sizes are shown in Figure 3..."," The derivation of the self-blanketing factor $\fb$ for spherical, homogeneous grains is described in Appendix A. Plots of $\fb$ versus X-ray energy for a range of grain sizes are shown in Figure \ref{fig:self_blanket}. ."
" As a function of energy it bears the imprintof 64,44 since f;(E) depends", As a function of energy it bears the imprintof $\sxdust$ since $\fb$ depends
Normal form theory is one of the most effective tools for the local study of nonlinear dynamical systems.,Normal form theory is one of the most effective tools for the local study of nonlinear dynamical systems.
 The basic idea is to use permissible transformations and obtain a simplified vector field., The basic idea is to use permissible transformations and obtain a simplified vector field.
 Transformations are permissible that preserve certain dynamical features of the original system., Transformations are permissible that preserve certain dynamical features of the original system.
 The space of all permissible transformations form a group and acts on vector fields like an action of a group on a vector space., The space of all permissible transformations form a group and acts on vector fields like an action of a group on a vector space.
 Consider a set of vector fields generated by the group acting on a given vector field., Consider a set of vector fields generated by the group acting on a given vector field.
" Then, the infinite level normal form of the vector field is to find a unique representative from this set."," Then, the infinite level normal form of the vector field is to find a unique representative from this set."
" Thereby, the computation of infinite level normal forms is an important tool for classification of vector fields."," Thereby, the computation of infinite level normal forms is an important tool for classification of vector fields."
 The uniqueness of a normal form computation is determined by the (infinite) level of normal form through an specifically chosen normal form style and costyle., The uniqueness of a normal form computation is determined by the (infinite) level of normal form through an specifically chosen normal form style and costyle.
" The level of a normal form assesses the remaining spectral data at our disposal in the permissible transformation space for further simplification of the system while a normal form style and costyle makes a unique choice for the normal form vector field in each level of normal form computation, see (0,(21∙∙"," The level of a normal form assesses the remaining spectral data at our disposal in the permissible transformation space for further simplification of the system while a normal form style and costyle makes a unique choice for the normal form vector field in each level of normal form computation, see \cite{baiderchurch,Gazor,GazorYuSpec,MurdBook,Sanders03}."
" Therefore, the infinite level normal form is sometimes called the simplest normal form or unique normal form when a normal form style have already been fixed."," Therefore, the infinite level normal form is sometimes called the simplest normal form or unique normal form when a normal form style have already been fixed."
" When a system has some symmetries, it is important that its normal form would preserve the symmetries."," When a system has some symmetries, it is important that its normal form would preserve the symmetries."
 Although there are research results on the simplest normal forms of symmetric systems but they are considerably less than the existing results on normal forms without symmetry., Although there are research results on the simplest normal forms of symmetric systems but they are considerably less than the existing results on normal forms without symmetry.
 There are several reasons for this., There are several reasons for this.
" The first difficulty is to recognize the symmetries and then, to find the group of transformations preserving the symmetries."," The first difficulty is to recognize the symmetries and then, to find the group of transformations preserving the symmetries."
" Therefore, one is also concerned with the space of the symmetric vector fields invariant under the group action."," Therefore, one is also concerned with the space of the symmetric vector fields invariant under the group action."
 This needs a good understanding on the algebraic interactions of the symmetric and nonsymmetric vector fields with the transformation groups., This needs a good understanding on the algebraic interactions of the symmetric and nonsymmetric vector fields with the transformation groups.
" Once all these are successfully accomplished, in most cases the normal form computation is more difficult in systems with symmetry than in systems without symmetry."," Once all these are successfully accomplished, in most cases the normal form computation is more difficult in systems with symmetry than in systems without symmetry."
 Normal form decomposition of a nonsymmetric vector field into two symmetric vector fields can have many important potential applications., Normal form decomposition of a nonsymmetric vector field into two symmetric vector fields can have many important potential applications.
 For example Eulerian and Hamiltonian vector fields are two important families of vector fields., For example Eulerian and Hamiltonian vector fields are two important families of vector fields.
" Therefore, the study of their dynamics is important."," Therefore, the study of their dynamics is important."
 Normal form decomposition of arbitrary vector fields into Eulerian (nonconservative or dissipative) and Hamiltonian (conservative) vector fields are also important in both theory and applications., Normal form decomposition of arbitrary vector fields into Eulerian (nonconservative or dissipative) and Hamiltonian (conservative) vector fields are also important in both theory and applications.
" Wiggins (0,Chapter33] remarks that transforming a system into an integrable Hamiltonian system plus a nonconservative perturbation facilitates “a wealth of techniques for the global analysis of nonlinear dynamical systems such as Melnikov theory, perturbation theory for normally hyperbolic invariant manifolds, and Kolmogorov, Arnold, and Moser (KAM) theory”."," Wiggins \cite[Chapter 33]{Wiggins} remarks that transforming a system into an integrable Hamiltonian system plus a nonconservative perturbation facilitates “a wealth of techniques for the global analysis of nonlinear dynamical systems such as Melnikov theory, perturbation theory for normally hyperbolic invariant manifolds, and Kolmogorov, Arnold, and Moser (KAM) theory”."
" Furthermore, )nn1001 [OJindicatedthatsuchkindo| decompositioncanbeusedindevelopinganO D Esolver."," Furthermore, n \cite{PalacChaos05} indicated that such kind of decomposition can be used in developing an ODE solver."
F orexampleusin fusionte," For example using the obtained scalar function as the integral of a piece of the vector field in an ODE solver, can enhance its efficiency."
rmsandit, These signify the importance of developing methods for such kind of decomposition.
sdynamiccsiswellunder stoodasacom Section5.5].," Recently, some researchers have paid attention to this theory and have made important contributions to the subject, see cs is well understood as a combination/competition of the dynamics associated with the advection and diffusion terms, see \cite[Section 5.5]{Logan}."
".Therefore, thestudyof eachcomponentsof adecomposedvector fieldmayhelptobettert oris"," Therefore, the study of each components of a decomposed vector field may help to better understand the dynamics of the full system as a combined dynamics or as a competing behavior between its components."
"aconservativevector see1001]12, [[4]."," Thus, it is important to individually deal with the cases that the vector field is a quasi-Eulerian, or is a conservative vector field, see \cite{GazorMoazeni,GazorMokhtari1st}."
.Inthispaperavector f ieldiscalledconservativewh , In this paper a vector field is called when it has a first integral and is called when it does not have any first integral.
"This paper deals with the nonconservativefield, family of our upcoming results on such decomposition for Hopf-Zero singular vector fields.", This paper deals with the nonconservative family of our upcoming results on such decomposition for Hopf-Zero singular vector fields.
 Systems with Hopf-Zero singularity are important in applications., Systems with Hopf-Zero singularity are important in applications.
" There are several important research results on the simplest normal forms of Hopf-Zero singularity, see .."," There are several important research results on the simplest normal forms of Hopf-Zero singularity, see \cite{AlgabaHopfZ,ChenHopfZ03,ChenHopfZ,YuHopfZero}."
" However, there does not seem to exist any result on such kind of normal form decomposition(ums for Hopf-Zero singularity."," However, there does not seem to exist any result on such kind of normal form decomposition for Hopf-Zero singularity."
" Although the Hamiltonian vector fields (symplectic structures) require an even dimensionality, the decomposition idea still can work."," Although the Hamiltonian vector fields (symplectic structures) require an even dimensionality, the decomposition idea still can work."
" Indeed we instead work with conservative and nonconservative family of vector fields, see |13].."," Indeed we instead work with conservative and nonconservative family of vector fields, see \cite{GazorMokhtari}."
 In this paper we are concerned with the study of nonconservative family., In this paper we are concerned with the study of nonconservative family.
" Indeed, we consider the family of Hopf-Zero singularities given by"," Indeed, we consider the family of Hopf-Zero singularities given by"
bv the effects of the orbit of the Sun around the Galactic Center. while the motion out of the plane should contain only small terms from (he Z-component of the Solar Motion aud a possible peculiar motion ofÀ*.,"by the effects of the orbit of the Sun around the Galactic Center, while the motion out of the plane should contain only small terms from the Z-component of the Solar Motion and a possible peculiar motion of."
. In the following subsections. we investigate the various components of the apparent velocity and acceleration ofA*.," In the following subsections, we investigate the various components of the apparent velocity and acceleration of."
. lt is clear [rom Fie., It is clear from Fig.
 1 that the apparent motion of is almost entirely in the Galactic plane., 1 that the apparent motion of is almost entirely in the Galactic plane.
 Thus. we convert the positions [rom equatorial to Galactic coordinates and determine motions in Galactic coordinates. (," Thus, we convert the positions from equatorial to Galactic coordinates and determine motions in Galactic coordinates. ("
Because of the high accuracy of our observations. some pitfalls in the implementation of the equatorial to Galactic coordinate conversion (Lane 1979). and the need to transfer the LAUdefined plane [rom D1950 to J2000 coordinates. we document the procedures involved in the Appendix.),"Because of the high accuracy of our observations, some pitfalls in the implementation of the equatorial to Galactic coordinate conversion (Lane 1979), and the need to transfer the IAU–defined plane from B1950 to J2000 coordinates, we document the procedures involved in the Appendix.)"
 Fig., Fig.
 4 is a plot the position of relative to J1745.283 in Galactic coordinates., 4 is a plot the position of relative to J1745–283 in Galactic coordinates.
 Variance-weighted least-squares fits of straight lines to these data are indicated bv dashed lines., Variance-weighted least-squares fits of straight lines to these data are indicated by dashed lines.
 The apparent motion of is —6.379£0.026 and —0.2024:0.019 mas in Galactic longitude and latitude. respectively.," The apparent motion of is $-6.379\pm0.026$ and $-0.202\pm0.019$ mas in Galactic longitude and latitude, respectively."
 Assuming a distance to the Galactie center (£24) of 8.040.5 kpe (Reid 1993). the apparent angular motion of in the plane of the Galaxy translates to —2412:15..," Assuming a distance to the Galactic center$\rnot$ ) of $8.0\pm0.5$ kpc (Reid 1993), the apparent angular motion of in the plane of the Galaxy translates to $-241\pm15$."
 The uncertainty [rom measurement error alone is only 1.. and the quoted value is dominated by the 0.5 kpe uncertainty in.," The uncertainty from measurement error alone is only $1$, and the quoted value is dominated by the 0.5 kpc uncertainty in."
. Provided that the peculiar motion of is small (see 83.2). this corresponds to the reflex of (rue orbital motion of the Sun around the Galactic Center.," Provided that the peculiar motion of is small (see 3.2), this corresponds to the reflex of true orbital motion of the Sun around the Galactic Center."
 This reflex motion can be parameterized as a combination of a circular orbit of the LSR) and the deviation of the Sun from that cireular orbit. (the Solar Motion)., This reflex motion can be parameterized as a combination of a circular orbit of the LSR) and the deviation of the Sun from that circular orbit (the Solar Motion).
 The Solar Motion. determined from Iipparcos data by Dehnen Binney (1993). is 5.25+0.62 iin (he direction of Galactic rotation.," The Solar Motion, determined from Hipparcos data by Dehnen Binney (1998), is $5.25\pm0.62$ in the direction of Galactic rotation."
 Removing this component of the Solar Motion from thereffer of the apparent motion of vields an estimate for oof 236415 Note that other definitions and measurements of this component of the Solar Motion have resulted in somewhat greater values. 12 (Cox2000).. which if adopted would reduce our value of to 229.," Removing this component of the Solar Motion from the of the apparent motion of yields an estimate for of $236\pm15$ Note that other definitions and measurements of this component of the Solar Motion have resulted in somewhat greater values, 12 \citep{Allen00}, which if adopted would reduce our value of to 229."
. Should be determined independently to high accuracy. then our measurement of the apparent motion of would eive with corresponding accuracy.," Should be determined independently to high accuracy, then our measurement of the apparent motion of would give with corresponding accuracy."
 Orbital solutions for stars near that combine proper motions and radial velocities have great potential to accomplish this 2003:Ghezetal. 2003).," Orbital solutions for stars near that combine proper motions and radial velocities have great potential to accomplish this \citep{E03,Ghez03}."
. A direct comparison of our measurement of the angular rotation rate of the LSR at the, A direct comparison of our measurement of the rotation rate of the LSR at the
the Galactic field. ancl are being found in ever-increasing numbers with the Chandra X-ray observatory (Grindlay et al.,"the Galactic field, and are being found in ever-increasing numbers with the Chandra X-ray observatory (Grindlay et al."
 2001)., 2001).
 Milliseconcl pulsars. including some in binaries or wilh planets (D'Amico οἱ al.," Millisecond pulsars, including some in binaries or with planets (D'Amico et al."
 2001) are prevalent in cluster cores., 2001) are prevalent in cluster cores.
 Cataclysmic binaries in clusters have been predicted ancl are also being found. (Shara et al., Cataclysmic binaries in clusters have been predicted and are also being found (Shara et al.
 1996: Crinclay et al., 1996; Grindlay et al.
 2001)., 2001).
 A few sdD stars have been located and characterized (Aloehler et al., A few sdB stars have been located and characterized (Moehler et al.
 1997)., 1997).
 Even though the stellar neighbourhood within an open cluster is less dense (han that of a elobular cluster it is still capable of producing exotic objects., Even though the stellar neighbourhood within an open cluster is less dense than that of a globular cluster it is still capable of producing exotic objects.
 The number of BSs found in the open cluster M61 is much greater (han we would expect if they are simply produced via mass transfer in binaries exhibiting the same distribution of orbital characteristics as binary stars founcl in the field., The number of BSs found in the open cluster M67 is much greater than we would expect if they are simply produced via mass transfer in binaries exhibiting the same distribution of orbital characteristics as binary stars found in the field.
 Furthermore. these BSs have a variety of living arrangements (Leonard 1996. and references within).," Furthermore, these BSs have a variety of living arrangements (Leonard 1996, and references within)."
 Some are single while others are [ound with a companion., Some are single while others are found with a companion.
 In some cases the DS and the companion star interact in an intimate and regular manner (short-period circular orbit). in other cases the relationship is distant (long-period orbit) aud Nav even appear eccentric.," In some cases the BS and the companion star interact in an intimate and regular manner (short-period circular orbit), in other cases the relationship is distant (long-period orbit) and may even appear eccentric."
 One of the BSs is so massive. a super-D5. that it must represent the merger of three stars. ancl another is observed in an active triple-svsteni. a (van den Bere et al.," One of the BSs is so massive, a super-BS, that it must represent the merger of three stars, and another is observed in an active triple-system, a menage-a-trois (van den Berg et al."
 2001)., 2001).
 All of (his suggests that the BSs have varied formation histories ancl (hat no one mechanism is responsible for their production (Leonard 1996)., All of this suggests that the BSs have varied formation histories and that no one mechanism is responsible for their production (Leonard 1996).
 In parücular. (he presence of a super-D5 and of Bss in eccentric binaries is not. predicted by standard binary evolution and points to dynamical interactions (ampering will (he destinies ol stars.," In particular, the presence of a super-BS and of BSs in eccentric binaries is not predicted by standard binary evolution and points to dynamical interactions tampering with the destinies of stars."
 On a basic dvnamical level a star cluster is composed of No bodies interacting wilh each other due to the gravitational lorce of everv other body in the svstem., On a basic dynamical level a star cluster is composed of $N$ bodies interacting with each other due to the gravitational force of every other body in the system.
 The ideal method [or following the evolution of such a svstenm is to integrate directly the NV individual equations of motion. the N-body approach.," The ideal method for following the evolution of such a system is to integrate directly the $N$ individual equations of motion, the $N$ -body approach."
 However. the cost of integrating the cluster for a scales as ο ΑΔ per force caleulation. V7 to integrate No bodies for one crossing (dynamical) üme. and there are of order No crossing (mes per relaxation (ime — so the method is computationally expensive.," However, the cost of integrating the cluster for a relaxation-time scales as $N^3$ – $N$ per force calculation, $N^2$ to integrate $N$ bodies for one crossing (dynamical) time, and there are of order $N$ crossing times per relaxation time – so the method is computationally expensive."
 As a result most N-bocly simulations performed until recently. alühough state-ol-the-art at the (time. have involved a varying nunber of simplified and unrealistic conditions. such as including only single stus. using only equal-mass stars. neglecting stellar evolution or assuming no external tidal field (MeMillan. Hut Makino 1991: llegeie Aarseth 1992).," As a result most $N$ -body simulations performed until recently, although state-of-the-art at the time, have involved a varying number of simplified and unrealistic conditions, such as including only single stars, using only equal-mass stars, neglecting stellar evolution or assuming no external tidal field (McMillan, Hut Makino 1991; Heggie Aarseth 1992)."
 Performance has been enhanced by the development οἱ improved computational algorithms., Performance has been enhanced by the development of improved computational algorithms.
 For example. the use of individual time-steps (Aarseth 1963) enables each star to evolve on iis own natural dvnamical timescale rather rather," For example, the use of individual time-steps (Aarseth 1963) enables each star to evolve on its own natural dynamical timescale rather rather"
component is very uncertain. as discussed below.,"component is very uncertain, as discussed below."
 The peak redshifts for the different spectral Classes reflect (heir vvalues., The peak redshifts for the different spectral classes reflect their values.
 This illustrates clearly that the Euclidean lis a cosmological distance indicator., This illustrates clearly that the Euclidean is a cosmological distance indicator.
 In Figure 11 we show the huninositv. function for ease A. as well as the luminosity distribution for the 1319 GUSBAD sources with P>0.5 ph ? !.," In Figure 11 we show the luminosity function for case A, as well as the luminosity distribution for the 1319 GUSBAD sources with $P > 0.5$ ph $^{-2}$ $^{-1}$."
 Also shown are the individual luminosity functions for the five spectral classes., Also shown are the individual luminosity functions for the five spectral classes.
 The first peak of the Iuminosity funelion is contributed by spectral class 1., The first peak of the luminosity function is contributed by spectral class 1.
 The lower half of ils gaussiuir clearly plays no role. as il produces no objects in the Iuminosity distribution.," The lower half of its gaussian clearly plays no role, as it produces no objects in the luminosity distribution."
 The Iuminosity assigned to this class is uncertain. since the slope of the curve in Figure 9 is relatively shallow.," The luminosity assigned to this class is uncertain, since the slope of the curve in Figure 9 is relatively shallow."
 Actually. if the [for sp=1 were only 1.20 larger. it could not be reproduced by any value of £L...," Actually, if the for $sp=1$ were only $1.2\sigma$ larger, it could not be reproduced by any value of $L_c$."
" Altogether. (his suggests that the (large) z=0 density rates fy for sp=1 given in Table 4 are very uncertain,"," Altogether, this suggests that the (large) $z=0$ density rates $R_0$ for $sp = 1$ given in Table 4 are very uncertain."
 The second peak in the huninosity [unction is contributed by the large number of GRBs in spectral classes 2-5., The second peak in the luminosity function is contributed by the large number of GRBs in spectral classes 2-5.
 Their combined :=0 rate is 0.09—0.22 ? |. for models A and D. respectively.," Their combined $z=0$ rate is $0.09 - 0.22$ $^{-3}$ $^{-1}$, for models A and B, respectively."
 ecorrelations with radiated energy or Iuminosity are of interest in exploring (he mechanism for the prompt emission of GRBs., correlations with radiated energy or luminosity are of interest in exploring the mechanism for the prompt emission of GRBs.
" They are also of practical interest in allowing an estimation of the redshift of GRBs with measured,,.", They are also of practical interest in allowing an estimation of the redshift of GRBs with measured.
. In this section. we discuss the derivation of the relevant isotropic-equivalent Iuminositv.Lj... present the aand ccorrelations and briefly mention the problem of extracting individual redshilts from ccorrelations.," In this section, we discuss the derivation of the relevant isotropic-equivalent luminosity, present the and correlations and briefly mention the problem of extracting individual redshifts from correlations."
 As discussed in Section 3.the derivation of the huninosity function involves an iteration of the central luminosity L(sp). where each spectral component is a gaussian wilh dispersionAix.," As discussed in Section 3,the derivation of the luminosity function involves an iteration of the central luminosity $L_c(sp)$, where each spectral component is a gaussian with dispersion."
 We chose a dispersion p=0.5 that produces a reasonably smooth overall Iuminosity function., We chose a dispersion $= 0.5$ that produces a reasonably smooth overall luminosity function.
 We want to use the £.(sp) Iuminosities in deriving the isotropic-equivalent. peak huminosities uused in the correlations., We want to use the $L_c(sp)$ luminosities in deriving the isotropic-equivalent peak luminosities used in the correlations.
 It turns out. however. that £.(sp) varies considerably with oie...," It turns out, however, that $L_c(sp)$ varies considerably with ."
 We explored using, We explored using
(Hammel&Lockwood1997).,\citep{ham97}.
. ΗΕ wind speed is a function of latitude as on all the giant planets of our solar svstem. (hen spots al different. latitudes will circle the object with different periods.," If wind speed is a function of latitude as on all the giant planets of our solar system, then spots at different latitudes will circle the object with different periods."
 Observations taken several months apart will show periodic variations wilh different periods as is reported for the L-dwarf 2\TASS 1145423., Observations taken several months apart will show periodic variations with different periods as is reported for the L-dwarf 2MASS 1145+23.
 Finally. L dwarls whose clouds change on time scales of a few days or less or whose cloudy spots are distributed at several latitudes with different wind speeds could still produce a photometric signal. but the signal might not be periodic.," Finally, L dwarfs whose clouds change on time scales of a few days or less or whose cloudy spots are distributed at several latitudes with different wind speeds could still produce a photometric signal, but the signal might not be periodic."
 Clearly. more observations aud modeling are required to better characterize atmospheric circulation and weather in L-dwarl alinospheres.," Clearly, more observations and modeling are required to better characterize atmospheric circulation and weather in L-dwarf atmospheres."
 There is little doubt that some L dwarls are photometrically variable., There is little doubt that some L dwarfs are photometrically variable.
 Although most authors suggest that the variations are caused by clouds. the possibility of magnetic spots is often mentioned (e.g.Dailer-Jones&Mundi.1999.2001:Martínetal.2001).," Although most authors suggest that the variations are caused by clouds, the possibility of magnetic spots is often mentioned \citep[e.g.][]{bai99,bai01,mart01}."
. We have shown that the low ionization fraction predicted by L-cdwarf models and the accompanvinely low magnetic Revnolds numbers stronglv argue against spots as a possible cause lor the photometric variations., We have shown that the low ionization fraction predicted by L-dwarf models and the accompanyingly low magnetic Reynolds numbers strongly argue against spots as a possible cause for the photometric variations.
 On (he other hand silicate and iron grains condense im L-cwarl ablmospheres within (he photosphere., On the other hand silicate and iron grains condense in L-dwarf atmospheres within the photosphere.
 These clouds are likely responsible for the photometric variations discovered in (he various studies. particularly for the later L cdwarls (about L2 and later).," These clouds are likely responsible for the photometric variations discovered in the various studies, particularly for the later L dwarfs (about L2 and later)."
 Since the thermal emission of T cdwarfs is also influenced by clouds (Marley. et al., Since the thermal emission of T dwarfs is also influenced by clouds (Marley et al.
 2001) we predict that. variability will also be found in the opacity window regions of these objects., 2001) we predict that variability will also be found in the opacity window regions of these objects.
 Further work with models ancl more observations are clearly needed to better understand cloud composition ancl dvnanmics., Further work with models and more observations are clearly needed to better understand cloud composition and dynamics.
High luminosity aud massive high redshift clusters of galaxies are crucially inuportant tools in cosinology.,High luminosity and massive high redshift clusters of galaxies are crucially important tools in cosmology.
 Their distribution aud evolution is fully determined by the spectrum of primordial perturbations aud cosmological parameters Q0 aud A (e.g. Press Schechter 1971)., Their distribution and evolution is fully determined by the spectrum of primordial perturbations and cosmological parameters $\Omega_0$ and $\Lambda$ (e.g. Press Schechter 1974).
 In particular. the moclels of low £2 universe (witli or without cosmological coustant) (e.g. Henry 2000. Borgani Guzzo 2001) predict a higher deusity of massive clusters at high redshifts than the bieh © A sample of high redshift clusters is essential in determining the evolution of the clusters X-ray luminosity functiou (e.g. Rosati et al..," In particular, the models of low $\Omega$ universe (with or without cosmological constant) (e.g. Henry 2000, Borgani Guzzo 2001) predict a higher density of massive clusters at high redshifts than the high $\Omega$ A sample of high redshift clusters is essential in determining the evolution of the clusters X-ray luminosity function (e.g. Rosati et al.,"
 1998). aud also would allow us to determine if there is evolution in the |=uinuositv-teruperature (Ly— T) relation.," 1998), and also would allow us to determine if there is evolution in the luminosity-temperature $L_X-T$ ) relation."
 The evolution of the Ly—TF is very iniportant since it is related to plivsical mmechauisins of cooling auc heating in the central cluster region (e.g. Tozzi Norman. 2001).," The evolution of the $L_X-T$ is very important since it is related to physical mechanisms of cooling and heating in the central cluster region (e.g. Tozzi Norman, 2001)."
 Ouly a few bright high redshift clusters have been found so far (e.g. in the EMSS. Gioia Luppino 1991: in the RDCS Rosati et al.," Only a few bright high redshift clusters have been found so far (e.g. in the EMSS, Gioia Luppino 1994; in the RDCS Rosati et al."
 1999. Della Ceca et al.," 1999, Della Ceca et al."
 2000: in the WARPS Ebeling et al., 2000; in the WARPS Ebeling et al.
 1005: 2000) and only 9 of them at 2>0.5 have a measure of their temperature (e.g. Della Ceca et al., 1998; 2000) and only 9 of them at $z>0.5$ have a measure of their temperature (e.g. Della Ceca et al.
 2001. Cagnoni et al.," 2001, Cagnoni et al."
 2001. Stauford et al.," 2001, Stanford et al."
 2001)., 2001).
 Siuce the statistics is very scanty. the search for high redshift aud bieh luminosity clusters is the ouly meaus to improve such studies.," Since the statistics is very scanty, the search for high redshift and high luminosity clusters is the only means to improve such studies."
 Two high redshift (2> 0.15) clusters of galaxies have been already found zunoug the 16ROSAT blank field sources and other cau be present in the remaining 11 unidentified sources., Two high redshift $z \geq 0.45$ ) clusters of galaxies have been already found among the 16 blank field sources and other can be present in the remaining 11 unidentified sources.
 We will describe the selection iuethod in Section 2. aud cliscuss the possibilities regarding the uature of the blauks aud the presence of high redshift clusters of ealaxies among them in Section 3.," We will describe the selection method in Section 2, and discuss the possibilities regarding the nature of the blanks and the presence of high redshift clusters of galaxies among them in Section 3."
" We call blank field sources"" (blanks) all the bright X-ray sources (Fx>10.P! erg 7s 4) with no optical counterpart on the Palomar Sky survey (ο O=21.5) within their 39"" ))", We call `blank field sources' (blanks) all the bright X-ray sources $F_X > 10^{-13}$ erg $^{-2}$ $^{-1}$ ) with no optical counterpart on the Palomar Sky survey (to O=21.5) within their $39^{\prime \prime}$ )
Pin,2in
and AT); (the interval between the minimal points of the Av eveles) ancl the eliteh number.,and $\Delta{T_{min}}$ (the interval between the minimal points of the $\Delta\nu$ cycles) and the glitch number.
" This plot shows that the indicated intervals are approximately equal to 580 and GOO davs. respectively,"," This plot shows that the indicated intervals are approximately equal to 580 and 600 days, respectively."
 The bottom panel shows the relation between the glitch parameters .A4 (the relaxation time interval) and «ως (the rise time interval) and the eliteh number and defines the average values of these parameters equal to 400 and 180 days. respectively.," The bottom panel shows the relation between the glitch parameters $\Delta{T_{rel}}$ (the relaxation time interval) and $\Delta{T_{ris}}$ (the rise time interval) and the glitch number and defines the average values of these parameters equal to 400 and 180 days, respectively."
 These three relations indicate that all the slow elitches observed have similar properties which can be described by the following average parameters., These three relations indicate that all the slow glitches observed have similar properties which can be described by the following average parameters.
 The elitches have a small absolute amplitude equal to 3.5x10? Iz., The glitches have a small absolute amplitude equal to $3.5\times 10^{-9}$ Hz.
" Thev are characterized by the identical intervals AT), and approximately the same width of the intervals «Αρ. equal to ~ 600 davs."," They are characterized by the identical inter-glitch intervals $\Delta{T_{max}}$ and approximately the same width of the intervals $\Delta{T_{min}}$, equal to $\sim$ 600 days."
 The glitehes have similar signature related to a slow increase in the rotation frequency during ~ 200 davs and the subsequent relaxation back to (he pre-elitch value during ο” 400 days., The glitches have similar signature related to a slow increase in the rotation frequency during $\sim$ 200 days and the subsequent relaxation back to the pre-glitch value during $\sim$ 400 days.
 The relaxation after all the glitches can be described by a linear curve as is seen [rom Figure 4((a)., The relaxation after all the glitches can be described by a linear curve as is seen from Figure \ref{form}( (a).
 These properties suggest that the sequence of (he slow elitches observed can be approximated by a sawtooth-like function., These properties suggest that the sequence of the slow glitches observed can be approximated by a sawtooth-like function.
 We created the model sawtooth-like curve using the indicated average parameters., We created the model sawtooth-like curve using the indicated average parameters.
 This model curve has the starting point NJD 48350 and includes 10 eveles consisting of two stages the stage of a linear gliteh arising with a timescale of 200 davs and the stage of a linear post-elitch relaxation with a timescale of 400 days., This model curve has the starting point MJD 48350 and includes 10 cycles consisting of two stages – the stage of a linear glitch arising with a timescale of 200 days and the stage of a linear post-glitch relaxation with a timescale of 400 days.
 Only two eglitches observed. 2 and 3. (take off from this sequence.," Only two glitches observed, 2 and 3, take off from this sequence."
 An analvsis of the Av eveles showed that event 2 represents (he sum of two partially overlapping glitches 2 and 3., An analysis of the $\Delta\nu$ cycles showed that event 2 represents the sum of two partially overlapping glitches 2 and 3.
 Glitch 3 defines the starting point of a new phase in (he sequence of the slow glitches., Glitch 3 defines the starting point of a new phase in the sequence of the slow glitches.
" Therefore. event 2 should be described by three stages the stage of a linear gliteh arising with a timescale of 200 days is followed by the stage in which the eliteh amplitude keeps constant within 400 davs (the duration of this interval corresponds to the duration of the relaxation time interval AZ,,;) and only then is Iollowed by a Inear post-eliteh relaxation wilh a timescale of 400 days."," Therefore, event 2 should be described by three stages – the stage of a linear glitch arising with a timescale of 200 days is followed by the stage in which the glitch amplitude keeps constant within 400 days (the duration of this interval corresponds to the duration of the relaxation time interval $\Delta{T_{rel}}$ ) and only then is followed by a linear post-glitch relaxation with a timescale of 400 days."
 The derived values for this model sawtooth-like curve are given in Table 4.., The derived values for this model sawtooth-like curve are given in Table \ref{sawt}.
 Figure 4((b) shows a model sawtooth-like curve with a period of GOO days which is superimposed on the eliteh sequence observed., Figure \ref{form}( (b) shows a model sawtooth-like curve with a period of 600 days which is superimposed on the glitch sequence observed.
 It is seen that (he maxima of the model curve well coincide with the maxima of nearly all the slow glitches., It is seen that the maxima of the model curve well coincide with the maxima of nearly all the slow glitches.
 Only the maxima of glitehes 8 and 9 slightly do not correspond to the model curve., Only the maxima of glitches 8 and 9 slightly do not correspond to the model curve.
 However. as is seen [rom the plot. the slight deviations of the amplitude and phase of these evcles [rom a model curve do not change a phase of the next eveles of the sequence.," However, as is seen from the plot, the slight deviations of the amplitude and phase of these cycles from a model curve do not change a phase of the next cycles of the sequence."
" Probably. the shape of these elitches was nol restored. precisely,"," Probably, the shape of these glitches was not restored precisely."
 The model curve very. well describes partially overlapping glitches 2 and 3., The model curve very well describes partially overlapping glitches 2 and 3.
 It is seen that in this range there was a phase shift lor 400 days. exactly equal to relAT.," It is seen that in this range there was a phase shift for 400 days, exactly equal to $\Delta{T_{rel}}$."
 After that. point 3 started marking5 the starting5 point of a new phase in the sequence ol the slow elitches.," After that, point 3 started marking the starting point of a new phase in the sequence of the slow glitches."
 Despite the phase shift between points 2 and 3. we suppose that the," Despite the phase shift between points 2 and 3, we suppose that the"
we are simply looking at a field star Our analysis suggests that Bochum 10 is a very voung and poorly populated open cluster.,we are simply looking at a field star Our analysis suggests that Bochum 10 is a very young and poorly populated open cluster.
 As many other voung poor clusters. it is certainly an unbounded: objects and will gradually disrupt.," As many other young poor clusters, it is certainly an unbounded objects and will gradually disrupt."
 We provide estimates of interstellar reddening and distance compatible with previous studies., We provide estimates of interstellar reddening and distance compatible with previous studies.
 As for Bochum 11. we find that it is a voung open cluster. less than 4«10? ves old. and. confirm previous estimates for the cluster mean reddening and From our photometry we find. indications of possible pre AIS candidates in Bochum 9 and. 11.," As for Bochum 11, we find that it is a young open cluster, less than $4 \times 10^{6}$ yrs old, and confirm previous estimates for the cluster mean reddening and From our photometry we find indications of possible pre MS candidates in Bochum 9 and 11."
 This issue will be addressed in a forthcoming paper (Itomaniello et al 2001). where CDVI photometry for all the other star clusterings known to lie in the Carina spiral feature will be presented and. compared with theoretical moclels.," This issue will be addressed in a forthcoming paper (Romaniello et al 2001), where $UBVRI$ photometry for all the other star clusterings known to lie in the Carina spiral feature will be presented and compared with theoretical models."
 This paper was based on observations made at ESO-La Sila., This paper was based on observations made at ESO-La Silla.
 We acknowledge: useful discussions with M. Zoceali. M. Rejkuba and A. Brown.," We acknowledge useful discussions with M. Zoccali, M. Rejkuba and A. Brown."
 GC thanks ESO for the kind hospitality., GC thanks ESO for the kind hospitality.
 We are grateful to Drs., We are grateful to Drs.
 A. Feinstein and AL.J. Aloifat for giving us informations about the instrument set-up used to obtain their photoclectric photometry., A. Feinstein and A.F.J. Moffat for giving us informations about the instrument set-up used to obtain their photoelectric photometry.
 The referee. Dr. J-C. Alermilliod. is deeply acknowledged: for important suggestions. which led to improve the quality of the paper.," The referee, Dr. J-C. Mermilliod, is deeply acknowledged for important suggestions, which led to improve the quality of the paper."
 Finally. this paper mace use of Simbacl and WEDDA.," Finally, this paper made use of Simbad and WEBDA."
 ‘To allow for a precise photometric calibration we have observed five miultistar fieles. Crom the list of Lanclolt, To allow for a precise photometric calibration we have observed five multistar fields from the list of Landolt
This paper deals with the Sun-Earth system with the modified restricted three body problem model[as in IKushval (2009a.b)]] including radiation pressure. oblateness of the Earth ancl influence of the belt.,"This paper deals with the Sun-Earth system with the modified restricted three body problem model[as in \cite{Kushvah2009Ap&SS,Kushvah2009RAA}] ] including radiation pressure, oblateness of the Earth and influence of the belt."
 Further it considered (hat (he primary bodies are moving in circular orbits about their center of mass., Further it considered that the primary bodies are moving in circular orbits about their center of mass.
 H ds well-known (hat [ive equilibrium points(Lagrangian points) that. appear in (he planar restricted. Chree-body problem are very important [or aslronautical applications., It is well-known that five equilibrium points(Lagrangian points) that appear in the planar restricted three-body problem are very important for astronautical applications.
 The collinear points are unstable and the triangular points are conditionally stable in the classical restricted three body problem|please see Szebehely (1967)]]., The collinear points are unstable and the triangular points are conditionally stable in the classical restricted three body problem[please see \citet{Szebehely1967}] ].
 This can be seen in the Sun-Jupiter svstem where several thousand. asteroids(collectively relerred to as Trojan asteroids). ave in orbits of triangular equilibrium points.," This can be seen in the Sun-Jupiter system where several thousand asteroids(collectively referred to as Trojan asteroids), are in orbits of triangular equilibrium points."
 But collinear, But collinear
Although IKK98 251 is less inclined. a similar exercise of estimating the rotation velocities from the PV diagram was repeated for it.,"Although KK98 251 is less inclined, a similar exercise of estimating the rotation velocities from the PV diagram was repeated for it."
 Fig 7|[D] shows the adopted mean rotation curve projected outo the PV diagram as can be seen. the mean rotation curve provides a reasonably good fit to the data.," Fig \ref{fig:PV}[ [B] shows the adopted mean rotation curve projected onto the PV diagram – as can be seen, the mean rotation curve provides a reasonably good fit to the data."
 A model data cube for KIX98 251 was also constructed using the derived rotation curve. iu the same manner as for KIN9s 250.," A model data cube for KK98 251 was also constructed using the derived rotation curve, in the same manner as for KK98 250."
 Again. a good match between the model (not shown) aud the observed field was found.," Again, a good match between the model (not shown) and the observed field was found."
" The seusitivitv of IIT observations to the imucr slope of the rotation curve has been the subject of much recent discussion (e.g. vau deu Bosch Swaters. 20η,"," The sensitivity of HI observations to the inner slope of the rotation curve has been the subject of much recent discussion (e.g. van den Bosch Swaters, 2001)."
 One possible wav of overcoming the relatively poor resolution offered by TD observations is fo iustead lise Πα observations., One possible way of overcoming the relatively poor resolution offered by HI observations is to instead use $\alpha$ observations.
 For KIS9s 250. an Πα based rotation curve has been derived bv deBloketal.(20011. and is shown with triangles in Fig. 5||," For KK98 250, an $\alpha$ based rotation curve has been derived by \cite{deblok01}, and is shown with triangles in Fig. \ref{fig:vrot1}[ ["
D].,B].
 As can be seen. although the Πα curve is steeper than the HI curve at intermediate radii. in the imuermost regions of the galaxy. Gvhere the effects of beam siearing are expected to be most severe). the two rotation curves in fact show au excellent agreement.," As can be seen, although the $\alpha$ curve is steeper than the HI curve at intermediate radii, in the innermost regions of the galaxy, (where the effects of beam smearing are expected to be most severe), the two rotation curves in fact show an excellent agreement."
" As mucutioned earlier. if one wishes to use the rotation curves to estimate the total dvuamical mass. then one needs to account for the pressure support of the ITE disk: this correction (generally called the ""asvuunetrie dift correction) is given by: where ve ds the corrected circular velocity. νο is the observed rotation velocity. o ds the velocity dispersion. and ly is the scale height of the disk."," As mentioned earlier, if one wishes to use the rotation curves to estimate the total dynamical mass, then one needs to account for the pressure support of the HI disk; this correction (generally called the “asymmetric drift” correction) is given by: where $\rm{v_c}$ is the corrected circular velocity, $\rm{v_o}$ is the observed rotation velocity, $\sigma$ is the velocity dispersion, and $\rm{h_z}$ is the scale height of the disk."
" Strictly speaking. ""asyviuuetnze dift"" corrections are applicable to collisionless stellar svsteiis for which the magnitude of the vaudom motions is nich simaller than that of the rotation velocity."," Strictly speaking, “asymmetric drift"" corrections are applicable to collisionless stellar systems for which the magnitude of the random motions is much smaller than that of the rotation velocity."
 However. it is often used even for gaseous disks. where the assumption beiug made is that the pressure support can be approximated as the eas density times the square of the random velocity.," However, it is often used even for gaseous disks, where the assumption being made is that the pressure support can be approximated as the gas density times the square of the random velocity."
 The observed xofile width can be used as an estimator of the velocity dispersion. after correcting for istriuneutal broadening aud the finite," The observed profile width can be used as an estimator of the velocity dispersion, after correcting for instrumental broadening and the finite"
relevant 2-component spinor ο). and p is a measure of PSE anisotropy.,"relevant 2-component spinor $e_i$, and $p$ is a measure of PSF anisotropy."
" “Lhe tensor P7,She is the smear polarisability. a 2.2 matrix with components involving higher moments of surface brightness."," The tensor $P^g_{sm}$ is the smear polarisability, a $2\times 2$ matrix with components involving higher moments of surface brightness."
" Since for stars e5,,,4,,=0. p can be measured, using The lensing shear takes cllect before the circular smearing of the PSE."," Since for stars $e^*_{\rm corrected}=0$, $p$ can be measured using The lensing shear takes effect before the circular smearing of the PSF."
 Luppino and. Waiser (1997) showed that the presmear shear > averaged over a field. can be recovered using where lere. P ds the shear polarisability tensor for the ealaxy involving other higher order moments of the galaxy image.," Luppino and Kaiser (1997) showed that the -smear shear $\gamma$ averaged over a field can be recovered using where Here, $P_{sh}^g$ is the shear polarisability tensor for the galaxy involving other higher order moments of the galaxy image."
" The quantities P7, and PL, are the shear and smear polarisabilities calculated. for a star interpolated to the position of the galaxy in question.", The quantities $P_{sh}^*$ and $P_{sm}^*$ are the shear and smear polarisabilities calculated for a star interpolated to the position of the galaxy in question.
 With the smear aud shear polarisabilities calculated byimcat. we can therefore find an estimator for the mean shear in a given cell.," With the smear and shear polarisabilities calculated by, we can therefore find an estimator for the mean shear in a given cell."
 Firstly. we need to remove noisy detections.," Firstly, we need to remove noisy detections."
". We applied a size limit r,1.0 to reject. extrancous detections of very small objects claimed byimcat.", We applied a size limit $r_g > 1.0$ to reject extraneous detections of very small objects claimed by.
 We also applied a signal-to-noise 72»15.0 limit (see relanires! for justificalionofthisapparentlyveryconservalivecu, We also applied a signal-to-noise $\nu > 15.0$ limit (see \\ref{ani_test} for justification of this apparently very conservative cut).
l ) οσο! (0.5.," To reduce the noise in our measurement, we also remove highly elliptical objects with $e > 0.5$ ."
" Stars were identified using the non-saturatecl stellar locus on the 7, plane (see figure 11 in BRE typically with /?2 19-22."," Stars were identified using the non-saturated stellar locus on the $r_h$ plane (see figure 11 in BRE), typically with $R
\simeq$ 19-22."
 In the data. the stellar ellipticity. is à smooth function. of position on the field.," In the data, the stellar ellipticity is a smooth function of position on the field."
 We thus adopted. an iterative interpolation scheme to modelthis variation., We thus adopted an iterative interpolation scheme to modelthis variation.
 Specificallv. we first. fitted a 2-D cubic to the nieasured stellar ellipticities. plotted the residual ellipticities οesτς:eE and re-fitted⋅ after⋅ the removal of⋅ extreme outliers (caused by galaxy. contamination. blended: images ancl noise).," Specifically, we first fitted a 2-D cubic to the measured stellar ellipticities, plotted the residual ellipticities $e^{res} = e^* -
e^{fit}$ and re-fitted after the removal of extreme outliers (caused by galaxy contamination, blended images and noise)."
 Lhe stellar. cllipticity was kept constant in 10 simulations. but we nevertheless fit the 2-D eubic for correction. as a means of retaining potential systematic elfects induced in this step.," The stellar ellipticity was kept constant in the simulations, but we nevertheless fit the 2-D cubic for correction, as a means of retaining potential systematic effects induced in this step."
 In order to correct. galaxies for anisotropic smear. we not only need the fitted. stellar ellipticity field. but also 16 [our component stellar smear and shear polarisabilities as à function of position.," In order to correct galaxies for anisotropic smear, we not only need the fitted stellar ellipticity field, but also the four component stellar smear and shear polarisabilities as a function of position."
" Here a 2-D cubic is fit for cach component of P2,m and P7,.", Here a 2-D cubic is fit for each component of $P_{sm}^*$ and $P_{sh}^*$.
 Galaxies are then chosen from 10 uce-ry diagram by removing the stellar locus and objects with pj«15. ry«1. e20.5. as described above.," Galaxies are then chosen from the $r_h$ diagram by removing the stellar locus and objects with $\nu<15$, $r_{g}<1$, $e>0.5$, as described above."
" From our fitted stellar models. we then caleulate e*. P2, and P5, at each galaxy. position. ancl correct the galaxies for the anisotropic PSE using equation (2))."," From our fitted stellar models, we then calculate $e^*$, $P_{sm}^*$ and $P_{sh}^*$ at each galaxy position, and correct the galaxies for the anisotropic PSF using equation \ref{eq:ecorrect}) )."
 As a result. we obtainEM OoBuusj for all selected galaxies in cach cell.," As a result, we obtain $e^{g}_{{\rm corrected}}$ for all selected galaxies in each cell."
 We then caleulate £2. for the galaxies., We then calculate $P_{\gamma}$ for the galaxies.
" We opt to treat D, and PL, as scalurs equal to half the trace of the respective matrices.", We opt to treat $P_{sh}^*$ and $P_{sm}^*$ as scalars equal to half the trace of the respective matrices.
 This is allowable. since the non-diagonal elements. are small ancl the diagonal elements. are equal within the measurement noise (tvpical {νου = 0.10. Pisana<5WO Pogo m d. Poyea< 0.0L).," This is allowable, since the non-diagonal elements are small and the diagonal elements are equal within the measurement noise (typical $P_{sm,11,22}^*$ = 0.10, $P_{sm,12,21}^* < 5\times 10^{-4}$, $P_{sh,00,11}^*$ = 1.1, $P_{sh,12,21}^* < 0.01$ )."
 With this simplification. we calculate £2. according to equation (5)).," With this simplification, we calculate $P_{\gamma}$ according to equation \ref{eq:p_gamma}) )."
 £2. is typically a noisy quantity. so we fit it as a function of ry.," $P_{\gamma}$ is typically a noisy quantity, so we fit it as a function of $r_g$."
 We choose to treat 2. as a scalar. since the information it carries is primarily a correction for the size of a given galaxy. regardless of its ellipticitv or orientation.," We choose to treat $P_{\gamma}$ as a scalar, since the information it carries is primarily a correction for the size of a given galaxy, regardless of its ellipticity or orientation."
 We thus plot 22? and P7 together against ry. and fit a cubic to the combined points.," We thus plot $P_{\gamma}^{11}$ and $P_{\gamma}^{22}$ together against $r_g$, and fit a cubic to the combined points."
 Moreover. since /7. is unreliable for objects with ry measured to be less that ry. we remove all such objects from our prospective galaxy catalogue.," Moreover, since $P_{\gamma}$ is unreliable for objects with $r_g$ measured to be less that $r_g^*$, we remove all such objects from our prospective galaxy catalogue."
 Finally. we calculate a shear measure for cach galaxy as in Equation (4)). where the £7. is the fitted value for the galaxy in question.," Finally, we calculate a shear measure for each galaxy as in Equation \ref{eq:gamma_est}) ), where the $P_{\gamma}$ is the fitted value for the galaxy in question."
 Because of pixel noise.a lew galaxies vield. extremo. unphysical. shears ον," Because of pixel noise,a few galaxies yield extreme, unphysical, shears $\gamma$."
 To prevent these from. unnecessarily dominating the analysis. we have removed galaxies with + ," To prevent these from unnecessarily dominating the analysis, we have removed galaxies with $\gamma>2$ ."
This entire. procedure. provides us with an estimator of the shear 5 for each galaxy., This entire procedure provides us with an estimator of the shear $\gamma$ for each galaxy.
 We can also calculate the mean shear 5=(5? in a cell and its associated error ms]-ms] VIN. where N is the number of galaxies in a cell., We can also calculate the mean shear $\bar{\gamma}=\langle \gamma \rangle$ in a cell and its associated error $\sigma[\bar{\gamma}]=\sigma[\gamma]/\sqrt{N}$ where $N$ is the number of galaxies in a cell.
The munber of mechanisms capable of producing mass loss from asteroids rivals (he number of asteroids showing evidence for mass loss.,The number of mechanisms capable of producing mass loss from asteroids rivals the number of asteroids showing evidence for mass loss.
 No single mechanism can account [or the varied examples of activity. observed. but. preferred explanations can be suggested for particular objects.," No single mechanism can account for the varied examples of activity observed, but preferred explanations can be suggested for particular objects."
 lthank Yan Fernandez. Henry. Hsieh. Toshi Kasuga. Pedro Lacerda and Bin Yang: lor comments on (he manuscript. and I appreciate support from NASA's Planetary Astronomy progran.," I thank Yan Fernandez, Henry Hsieh, Toshi Kasuga, Pedro Lacerda and Bin Yang for comments on the manuscript, and I appreciate support from NASA's Planetary Astronomy program."
or. clefining (for later convenience) as We can take the quantities ofSNLUUNquM| as the independent “Fourier components” of the field. aud therefore write the V functions. in momentum space as llowever. the measure and the action are C invariant.,"or, defining (for later convenience) as We can take the quantities $\phi^{\alpha_1\ldots\alpha_4}_{\SC
N_1\ldots N_4,\Lambda}$ as the independent “Fourier components” of the field, and therefore write the $W$ functions, in momentum space as However, the measure and the action are $G$ invariant."
 Therelore the only non(rivial independent W Dunctions are given by G invariant combinations of fields. where G acts on each index a? by the representation .N7 .," Therefore the only nontrivial independent $W$ functions are given by $G$ invariant combinations of fields, where $G$ acts on each index $\alpha_{i}^n$ by the representation $N_{i}^n$ ."
 There is only one wav of obtaining G singlets: to have the indices a? all paired with the (wo indices of the pair sitting in (he same representation ancl to sum over the paired indices., There is only one way of obtaining $G$ singlets: to have the indices $\alpha_{i}^n$ all paired –with the two indices of the pair sitting in the same representation– and to sum over the paired indices.
 Each independent WW function is determined by a choice of indices and their pairing., Each independent $W$ function is determined by a choice of indices and their pairing.
" In order to describe these index choices ancl pairings. let us associate to each field opM in the integrand a four valent node: we associate to this node the inter(winer A"". and (o each of its four links a representation ANT."," In order to describe these index choices and pairings, let us associate to each field $\phi^{\alpha_1\alpha_2\alpha_3\alpha_4}_{\SC
N_1N_2N_3N_4,\Lambda}$ in the integrand a four valent node; we associate to this node the intertwiner $\Lambda^{n}$, and to each of its four links a representation $N^{n}_{i}$."
 We then connect the links between two fields with paired indices., We then connect the links between two fields with paired indices.
 We obtain a graph. with nodes labelled by intertwiners and links labelled by representations (satis[ving Clebsch-Gordan like relations). namely a spin network s (in the group G).," We obtain a graph, with nodes labelled by intertwiners and links labelled by representations (satisfying Clebsch-Gordan like relations), namely a spin network $s$ (in the group $G$ )."
 Thus. independent Wo functions are labelled bv spin networks!," Thus, independent $W$ functions are labelled by spin networks!"
" In other words. to each spin network s. with nodes η labelledbv inter(winers A, and links / labelled by representations .Vj. we can associate a gauge invariant product of field operators ©. where a? is the index associatedto the link / which is the ;-th link of the node n»."," In other words, to each spin network $s$, with nodes $n$ labelledby intertwiners $\Lambda_{n}$ and links $l$ labelled by representations $N_{l}$ , we can associate a gauge invariant product of field operators $\phi_{s}$ where $\alpha^{n}_i$ is the index associatedto the link $l$ which is the $i$ -th link of the node $n$ ."
 And wedefine, And wedefine
The thermal tide in an orbitally circularized mt asvuchronously rotating plauet is sketched iu Figure 2.,The thermal tide in an orbitally circularized but asynchronously rotating planet is sketched in Figure \ref{fig:fig1}.
 The figure enrphasizes the diurnal conrponeut. that is. the atmospheric variations undergo; oneτον full ujperiod perv longitudinal01 longitudinalins. circuit of the equator.," The figure emphasizes the diurnal component, that is, the atmospheric variations that undergo one full period per longitudinal circuit of the equator."
 The gravitational tide couples to the uext Fourier hixinonic. the scmidiurual ide.," The gravitational tide couples to the next Fourier harmonic, the semidiurnal tide."
". Thisa. also reaches a temperature maxi. in the ""afternoon.", This also reaches a temperature maximum in the “afternoon.”
" To the exteut that the atmosphere rearranges dtsolf into approximate ⋅⋅⋅ . ⋜↧↑↸∖⋯↕∐⋅↸∖↴∖↴↴∖↴↿∐⋅↸∖↸∖≺∏∐∐↴⋝↥⋅⋯⋯∙≼∐∖↕↴∖↴↕⋅↖↽↖↽⋜∐⋅↕⋜↕⊓∪∐↴∖↴⋜∐⋅↸∖⋅⋅ 150"" out of ]phase with teniperature| variations."," To the extent that the atmosphere rearranges itself into approximate lateral pressure equilibrium, density variations are $180^\circ$ out of phase with temperature variations."
 For he ποιοπια] component. this puts the density uaxina. in. the late morning. and evening.⋅ be.. at 490° of longitude with respect to the temperature uaxina.," For the semidiurnal component, this puts the density maxima in the late morning and evening, i.e. at $\pm 90^\circ$ of longitude with respect to the temperature maxima."
" The torque exerted on the thermal tidal eusitv bv the eravitational tidal potential tends o accelerate the asvuchrouous rotation of the atmosphere. as argued by ?ὃν,"," The torque exerted on the thermal tidal density by the gravitational tidal potential tends to accelerate the asynchronous rotation of the atmosphere, as argued by \cite{Arras_Socrates09}."
 ? proposed that the thermal tide in ⋅⋅⇁Veuus⋅ atmosphere explains why the plauet iuaiutains a retrograde rotation despite the fact that the Beravitational tide acting. ou its solid aasparts would expected to lead. to svuchronisia in| ~ LOdisplacingyr., \cite{Gold_Soter69} proposed that the thermal tide in Venus' atmosphere explains why the planet maintains a retrograde rotation despite the fact that the gravitational tide acting on its solid parts would be expected to lead to synchronism in $\sim 10^8{\rm yr}$.
⋅ Their theory was later refined bv Ingersoll aud Dobrovolskis (??7)..," Their theory was later refined by Ingersoll and Dobrovolskis \citep{Ingersoll_Dobrovolskis78,Dobrovolskis_Ingersoll80}."
 Às these papers make clear. the torque acting ou the thermal tide is directly proportional to the longitudinal pressure variation at the planetary surface. which reflects the variation in atmospheric colunuceusity by Pascal's Principle. siuce the atmosphere cau be assumed tfo bo in vertical livdrostatic equilibrium fo a good iyproximation.," As these papers make clear, the torque acting on the thermal tide is directly proportional to the longitudinal pressure variation at the planetary surface, which reflects the variation in atmospheric column density by Pascal's Principle, since the atmosphere can be assumed to be in vertical hydrostatic equilibrium to a good approximation."
 Venus surface can withstand this pressure. variation because. it hashat clastic strength., Venus' surface can withstand this longitudinal pressure variation because it has elastic strength.
 A jovian planct. being gaseous. lacks clastic strength.," A jovian planet, being gaseous, lacks elastic strength."
 The excess σοι density of the colder vats of the atmosphere is counterbalancedτο ↕↸∖≼∐∖∶↴∙⊾↥⋅↸∖↸∖↑∐⋜↕↑∐⋅↖⇁≼⊔⋅∪↴∖↴↑⋜↧↕↸⊳↸∖≺∣∏∐∏⋝∏⋯⊔∐∪∐∖↴↴⋝∙↖⇁ au mdenutation⋅ of. the couvective. bouudaryv aud a redistribution⋅⋅⋅ of. the core.s mass toward the hotter ougitudes., The excess column density of the colder parts of the atmosphere is counterbalanced—to the degree that hydrostatic equilibrium holds—by an indentation of the convective boundary and a redistribution of the core's mass toward the hotter longitudes.
. Insofar. as the radial⋅ range over which. nass redistribution occurs is αμα. compared to he planetary radius. the thermal tide therefore years no net mass quadrupole.," Insofar as the radial range over which mass redistribution occurs is small compared to the planetary radius, the thermal tide therefore bears no net mass quadrupole."
 The torque ou the atmosphere is opposed by a torque on the upper yarts of the convection zone., The torque on the atmosphere is opposed by a torque on the upper parts of the convection zone.
 This compensation is analogous to geological . ↕↴∖↴∪↴∖↴↑⋜↧↴∖↴∙↖↽∶↴⋝∪↑∐⋜⋯∖⋜∏∏≻∐↸⊳⋜↧↑↕∪∐↴∖↴∪↕⊀≚↥⋅↸⊳↕∐⋯↸∖≺∐∖↴∖↴ ↕⋟∏∐↸⊳↕≻↕↸∖≺∎∙↗⋝, This compensation is analogous to geological isostasy; both are applications of Archimedes' Principle \citep{Watts01}.
∙∙↽∕∏∐∖↸∖⋜∐⋅↑∐⋅↴∖↴↸⊳↥⋅∏↴∖↴↑∙∪↥⋅∐↑∐∪↴∖↴≻∐↸∖↥⋅↸∖∙ ] floats upon the more plastic aestheuosphere. approxinatelv⋅ its⋅ own⋅ weight.," The earth's crust, or lithosphere, floats upon the more plastic aesthenosphere, displacing approximately its own weight."
 Continental⋅ be⋅ crust is⋅ less dense than oceanic crust and floats . ↕∐∶↴∙∐↸∖↥⋅∙↴∖↴∪↑∐⋜↧↑⋯↕⋯⊔∐≼∐∖↕↴∖↴↕↑⋅↖⇁↕↴∖↴⋜∏∏∐⋅∪⊼∐⊔⋜↧↑↸∖," Continental crust is less dense than oceanic crust and floats higher, so that column density is approximately constant."
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖↴, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖↴↑, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖↴↑⋜, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖↴↑⋜↧, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖↴↑⋜↧↑, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖↴↑⋜↧↑↕, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖↴↑⋜↧↑↕↸, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖↴↑⋜↧↑↕↸⊳, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖↴↑⋜↧↑↕↸⊳↸, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖↴↑⋜↧↑↕↸⊳↸∖, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖↴↑⋜↧↑↕↸⊳↸∖≺, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖↴↑⋜↧↑↕↸⊳↸∖≺∣, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖↴↑⋜↧↑↕↸⊳↸∖≺∣∏, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖↴↑⋜↧↑↕↸⊳↸∖≺∣∏∐, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖↴↑⋜↧↑↕↸⊳↸∖≺∣∏∐∏, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖↴↑⋜↧↑↕↸⊳↸∖≺∣∏∐∏⋝, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖↴↑⋜↧↑↕↸⊳↸∖≺∣∏∐∏⋝∏, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖↴↑⋜↧↑↕↸⊳↸∖≺∣∏∐∏⋝∏⋯, To the extent that isostatic equilibrium
↕⋅↖↽ ⋅⋅ ⋅ ↸⊳∪∐↴∖↴↑⋜⋯↑∙⊺↴∪↑↕∐∖↸∖⊼↑↸∖∐↑↑∐⋜↧↑↕↴∖↴∪↴∖↴↑⋜↧↑↕↸⊳↸∖≺∣∏∐∏⋝∏⋯⊔, To the extent that isostatic equilibrium
'The results are summarized in Appendix B..,The results are summarized in Appendix \ref{app:sequence}.
 Figures 9--12 show contours of baryon rest-mass density for 4 EOSs in the equatorial plane., Figures \ref{fig9}- \ref{fig12} show contours of baryon rest-mass density for 4 EOSs in the equatorial plane.
" Masses of the stars on the left- and right-hand sides are MNS},=1.15Mc and MXBà,=1.55Mo, respectively."," Masses of the stars on the left- and right-hand sides are $M_{\rm ADM}^{\rm NS1}=1.15 M_{\odot}$ and $M_{\rm ADM}^{\rm NS2}=1.55 M_{\odot}$, respectively."
 All the figures are drawn for the closest separation that we can choose., All the figures are drawn for the closest separation that we can choose.
 The X- and Y-axes are measured by the coordinate length in km units., The $X$ - and $Y$ -axes are measured by the coordinate length in km units.
 Figure 9 is for the tabulated EOS of APR and Figure 10 is for that of GNH3., Figure \ref{fig9} is for the tabulated EOS of APR and Figure \ref{fig10} is for that of GNH3.
" The former EOS gives relatively compact stars, while the latter one produces rather less compact stars."," The former EOS gives relatively compact stars, while the latter one produces rather less compact stars."
" Figures 11 and 12 are selected among the EOSs of piecewise polytrope, PwPoly30-1345 and PwPoly24-1345."," Figures \ref{fig11} and \ref{fig12} are selected among the EOSs of piecewise polytrope, PwPoly30-1345 and PwPoly24-1345."
" Both of the piecewise polytropes produce stars of a similar size for a given mass, MiB.~1.3Mo, but the former model, PwPoly30-1345, has a stiff EOS for the core (T4= 3.0) while the latter one, PwPoly24-1345, has a soft EOS (Γι= 2.4)."," Both of the piecewise polytropes produce stars of a similar size for a given mass, $M_{\rm ADM}^{\rm NS} \simeq 1.3 M_{\odot}$, but the former model, PwPoly30-1345, has a stiff EOS for the core $\Gamma_1=3.0$ ) while the latter one, PwPoly24-1345, has a soft EOS $\Gamma_1=2.4$ )."
 This difference in T is reflected strongly in the structure of more massive star for which the central density is high and the effect of Γ1 is appreciated., This difference in $\Gamma_1$ is reflected strongly in the structure of more massive star for which the central density is high and the effect of $\Gamma_1$ is appreciated.
" By contrast, a striking difference is not seen for the less massive star."," By contrast, a striking difference is not seen for the less massive star."
 Figure 13 shows the binding energy of quasi-equilibrium sequences for five piecewise polytropic EOSs., Figure \ref{fig13} shows the binding energy of quasi-equilibrium sequences for five piecewise polytropic EOSs.
" Those sequences are calculated for binary neutron stars composed of equal-mass stars of MNSi,=MNS2, 1.35Mo.", Those sequences are calculated for binary neutron stars composed of equal-mass stars of $M_{\rm ADM}^{\rm NS1}=M_{\rm ADM}^{\rm NS2}=1.35 M_{\odot}$ .
" All of the piecewise polytropes we select here have Γι=3.0, but the value of ΊοδιρP; varies from 13.95 to 13.15."," All of the piecewise polytropes we select here have $\Gamma_1=3.0$, but the value of $\log_{10} P_1$ varies from 13.95 to 13.15."
" The thick (red) short-dashed, thick (green) long-dashed, thick (blue) dot-dashed, thick (violet) dot-dot-dashed, and thick (magenta) dot-dash-dashed curves denote, respectively, the results for logygδι=13.95 (PwPoly30-1395), 13.55 (PwPoly30-1355), 13.45 (PwPoly30-1345), 13.35 (PwPoly30-1335), and 13.15 (PwPoly30-1315)."," The thick (red) short-dashed, thick (green) long-dashed, thick (blue) dot-dashed, thick (violet) dot-dot-dashed, and thick (magenta) dot-dash-dashed curves denote, respectively, the results for $\log_{10} P_1=13.95$ (PwPoly30-1395), 13.55 (PwPoly30-1355), 13.45 (PwPoly30-1345), 13.35 (PwPoly30-1335), and 13.15 (PwPoly30-1315)."
 The thin (black) solid curve denotes the results in the 3PN approximation., The thin (black) solid curve denotes the results in the 3PN approximation.
 The total angular momentum for the same EOSs is also plotted in Figure 14.., The total angular momentum for the same EOSs is also plotted in Figure \ref{fig14}.
" The sequences are terminated just before the stars reach the mass-shedding limit, because the spectral method we use has a problem in handling a cusp-like figure."," The sequences are terminated just before the stars reach the mass-shedding limit, because the spectral method we use has a problem in handling a cusp-like figure."
 We will discuss the endpoint in detail inSection 4.3.., We will discuss the endpoint in detail inSection \ref{sec:endpoint}. .
Fie. 1)).,"Fig. \ref{maps}) ),"
 ie. a region of x40' in Lupus 1. in Lupus 32 and 30x .in Lupus 4.," i.e. a region of $\times$ in Lupus 1, $\times$ in Lupus 3 and $\times$ in Lupus 4."
" On the other hand. at 3 mm the telescope beam is significantly smaller (35"")) and we mapped only the regions were NIL; (1.1) emission was detected."," On the other hand, at 3 mm the telescope beam is significantly smaller ) and we mapped only the regions were $_3$ (1,1) emission was detected."
 Note Chat the Lupus 4 cloud was not mapped at 3 nin because we did not have enough time., Note that the Lupus 4 cloud was not mapped at 3 mm because we did not have enough time.
 The scanned regions were covered by mini maps of 5x5' and Ls’x18” for the observations at 3 and 12 mm. respectively.," The scanned regions were covered by mini maps of $\arcmin \times 5 \arcmin$ and $\arcmin \times 18 \arcmin$ for the observations at 3 and 12 mm, respectively."
 Each mini map was scanned twice in orthogonal directions in order to minimize artificial stripes and reduce noise level., Each mini map was scanned twice in orthogonal directions in order to minimize artificial stripes and reduce noise level.
 Data reduction was performed using (he ATNF dedicated packages Livedata andGridzilla!., Data reduction was performed using the ATNF dedicated packages Livedata and.
. Livedata performs a bandpass calibration and baseline fitting while Gridzilla regrids aud combines the data from multiple scanning directions ancl mini maps onto a single data cube., Livedata performs a bandpass calibration and baseline fitting while Gridzilla regrids and combines the data from multiple scanning directions and mini maps onto a single data cube.
 The data was Gaussian smoothed so that the effective spatial resolution of the final maps is, The data was Gaussian smoothed so that the effective spatial resolution of the final maps is
most of the electrons energy is concentrated in the range near the electron break Lorentz [actor 5.,most of the electrons energy is concentrated in the range near the electron break Lorentz factor $\gamma_{br}$.
" It is interesting lo compare 7,5; characteristic Lor the kpe-scale FR [jets with critical (cr) synchrotron frequency Γιος resulüng [rom the interplay between electron svnchrotron cooling and dynamical evolution of the emitting region."," It is interesting to compare $\nu_{syn, \, br}$ characteristic for the kpc-scale FR I jets with critical $cr$ ) synchrotron frequency $\nu_{syn, \, cr}$ resulting from the interplay between electron synchrotron cooling and dynamical evolution of the emitting region."
" The time scale for the former process can beestimated as ον75//Adag Where“her me?3a3|.{CoplL.Ugη«Ὁ57 isa, a mean⋅ rate“ad o[ electron energy losses due to svnchrotron emission. and U7,=D/8x denotes comoving jet magnetic field energy density,"," The time scale for the former process can beestimated as $t'_{loss} \sim \gamma / | \dot{\gamma} |_{syn}$, where $m c^2 \,
 | \dot{\gamma} |_{syn} = {4 \over 3} \, c \, \sigma_T \, U'_B \, \gamma^2$ is a mean rate of electron energy losses due to synchrotron emission, and $U'_B =
 B^2 / 8 \pi$ denotes comoving jet magnetic field energy density."
" The second (me scale is simply (5,/=ωμήor/cT. where D-—(1—5)4? is the jet bulk Lorentz factor. Je is a jet bulk velocity and r is the distance of the kpe-seale structure Irom the jet base at ry<r [rom the active galactic nucleus."," The second time scale is simply $t'_{dyn} = t_{dyn} / \Gamma \sim r / c \, \Gamma$ , where $\Gamma = (1 - \beta^2)^{-1/2}$ is the jet bulk Lorentz factor, $\beta c$ is a jet bulk velocity and $r$ is the distance of the kpc-scale structure from the jet base at $r_0 \ll r$ from the active galactic nucleus."
 A critical electron Lorentz factor is defined by an equality /dynmοσοfoss\(5—54).," A critical electron Lorentz factor is defined by an equality $t'_{dyn} \approx t'_{loss}(\gamma =
 \gamma_{cr})$."
" Thus. assuming initial injection of the power-law electron energy distribution at rj. one expects that at the distance r (he electron specirun steepens for 5>5, because of the efficient radiative cooling of these electrons."," Thus, assuming initial injection of the power-law electron energy distribution at $r_0$, one expects that at the distance $r$ the electron spectrum steepens for $\gamma > \gamma_{cr}$ because of the efficient radiative cooling of these electrons."
 The observed critical synchrotron frequency is (hen pius=Luep0X55BO. where is the jet Doppler factor and 8 is the jet inclination angle to the line of sight.," The observed critical synchrotron frequency is then $\nu_{syn, \, cr} = \nu'_{syn, \, cr} \, \delta \propto \gamma_{cr}^2 \, B \,
 \delta$, where is the jet Doppler factor and $\theta$ is the jet inclination angle to the line of sight."
" Assuming that the jet magnetic fiekl scales with the distance as B=(ηή]. what conserves the Povntüng. flux Li,xR>Ur,τ in. the expanding. jet. with. an opening. angle ~~cons! and a radius A4yr. one obtains where we pul ry=I pe. By—0.1 G and r4=r/Ikpe."," Assuming that the jet magnetic field scales with the distance as $B =
 B_0 \, (r_0 / r)$, what conserves the Poynting flux $L'_B \propto R^2 \, U'_B$ in the expanding jet with an opening angle $\varphi \sim const$ and a radius $R
 \sim \varphi \, r$, one obtains where we put $r_0 = 1$ pc, $B_0 = 0.1$ G and $r_1 \equiv r / 1 \, {\rm kpc}$."
 Note. that with the above values of Bo and ry characteristic for (he blazar sources. the kpc-scale jet magnetic field is expected to be Be10! G. consistently with the equipartition value.," Note, that with the above values of $B_0$ and $r_0$ characteristic for the blazar sources, the kpc-scale jet magnetic field is expected to be $B \sim
 10^{-4}$ G, consistently with the equipartition value."
 Hence. in a case of a non-relativistic kpe-scale jet velocity. uuce0νο1011 Lz.," Hence, in a case of a non-relativistic kpc-scale jet velocity, $\nu_{syn, \, cr} \sim \nu_{syn,
 \, br} \sim 10^{14}$ Hz."
" However. the spectral break resulting [rom the considered process is Aq,,.=0.5 (Ixardashev.1962)... i.e. slightly less than the one required for the FR I1 jets."," However, the spectral break resulting from the considered process is $\Delta \alpha_{cr} = 0.5$ \citep{kar62}, i.e. slightly less than the one required for the FR I jets."
 Possibly. the observed steep spectral break is a signature of the electron svnchrotron cooling in the spatially magnetic field (Cavalloetal.1980:ColemanandBicknell1988).," Possibly, the observed steep spectral break is a signature of the electron synchrotron cooling in the spatially magnetic field \citep{cav80,col88}."
. Note also. that in the cases of relativistic jetbulk velocities. the observed value of Moyne can be significantly higher than 1011 Hz (cf.," Note also, that in the cases of relativistic jetbulk velocities, the observed value of $\nu_{syn, \, cr}$ can be significantly higher than $10^{14}$ Hz (cf."
 the case of M 8T. section 3.2).," the case of M 87, section 3.2)."
 Raclio observations of FR I jets indicate moderate or even weak beaming 1999)..," Radio observations of FR I jets indicate moderate or even weak beaming \citep[e.g.,][]{lai99}. ."
 Llowever. one cannot excludepossibility that the bulk Lorentz factors of kpc-scale jets in weak radio galaxies ave of order of a few.," However, one cannot excludepossibility that the bulk Lorentz factors of kpc-scale jets in weak radio galaxies are of order of a few."
 This idea is supported by observations, This idea is supported by observations
The contrast of granulation and of magnetic features is an important diagnostic of their thermal structure and provides insight into the energy transport mechanisms acting in them.,The contrast of granulation and of magnetic features is an important diagnostic of their thermal structure and provides insight into the energy transport mechanisms acting in them.
 The contrast of granulation. bright points and other small scale features is influenced by the point spread function (PSF). the width of whose core is a measure of the spatial resolution. while the strength of the wings is determined by the amount of light scattered within the instrument (or in the atmosphere. if present).," The contrast of granulation, bright points and other small scale features is influenced by the point spread function (PSF), the width of whose core is a measure of the spatial resolution, while the strength of the wings is determined by the amount of light scattered within the instrument (or in the atmosphere, if present)."
 In particular. the scattered light strongly reduces the contrast.," In particular, the scattered light strongly reduces the contrast."
 Bright points. which are smaller in size than the granules. are more strongly affected.," Bright points, which are smaller in size than the granules, are more strongly affected."
 If the PSF is known. then it can be used to deconvolve the observed image and thus to approximately retrieve the original intensities.," If the PSF is known, then it can be used to deconvolve the observed image and thus to approximately retrieve the original intensities."
 Contrasts measured with the Hinode Solar Optical Telescope (SOT. Tsuneta et al. 2008..," Contrasts measured with the Hinode Solar Optical Telescope (SOT, Tsuneta et al. \cite{tsuneta},"
 Suematsu et al. 2008..," Suematsu et al. \cite{suematsu},"
 Kosugi et al. 2007)), Kosugi et al. \cite{kosugi}) )
 are of particular interest. due to the combination of high spatial resolution and the absence of seeing. leading to almost constant observing conditions.," are of particular interest due to the combination of high spatial resolution and the absence of seeing, leading to almost constant observing conditions."
 The value of the Hinode SOT observations. would be further enhanced if the PSF could be determined and compensated for (e.g. as done by Aathew. et al.," The value of the Hinode SOT observations would be further enhanced if the PSF could be determined and compensated for (e.g. as done by Mathew, et al."
 2007. for MDI continuum images)., \cite{mathew} for MDI continuum images).
 The PSF of the Hinode Spectro Polarimeter (SP) was determined by Danilovie. et al. (2008)), The PSF of the Hinode Spectro Polarimeter (SP) was determined by Danilovic et al. \cite{danilovic}) )
 by modeling the SOT/SP optical system using the ZEMAX optical design software., by modeling the SOT/SP optical system using the ZEMAX optical design software.
 After convolving solar granulation data from MHD simulations with the computed PSF. they found that the contrast of the simulated granulation matches closely the observations from SOT/SP.," After convolving solar granulation data from MHD simulations with the computed PSF, they found that the contrast of the simulated granulation matches closely the observations from SOT/SP."
 Wedemeyer-Bóhhm (2008)) used Mercury transit and eclipse images to obtain the PSF of the Hinode/SOT/Broadband Filter Imager (BFI) instrument. but did not apply the obtained PSF to deducing the true contrast in the BFI wavelength bands.," Wedemeyer-Böhhm \cite{bohm}) ) used Mercury transit and eclipse images to obtain the PSF of the Hinode/SOT/Broadband Filter Imager (BFI) instrument, but did not apply the obtained PSF to deducing the true contrast in the BFI wavelength bands."
 In this paper we obtain the PSF of the Hinode/SOT/BFI instrument also using observed Mercury. transit. images. but following the approach successfully applied to MDI images by Mathew et al. (2007)).," In this paper we obtain the PSF of the Hinode/SOT/BFI instrument also using observed Mercury transit images, but following the approach successfully applied to MDI images by Mathew et al. \cite{mathew}) )."
 We use the retrieved PSF for the deconvolution of the images observed with the Hinode/SOT/BFI instrument to recover the original intensities., We use the retrieved PSF for the deconvolution of the images observed with the Hinode/SOT/BFI instrument to recover the original intensities.
 In Sect., In Sect.
 2 we describe the method used for the retrieval of the PSF., 2 we describe the method used for the retrieval of the PSF.
 In Sect., In Sect.
 3 we present initial results showing the difference in granulation contrast before and after the image correction., 3 we present initial results showing the difference in granulation contrast before and after the image correction.
 Conclusions are given in Sect., Conclusions are given in Sect.
 4., 4.
significance in surface brightness with respect to the smooth double-8 model.,significance in surface brightness with respect to the smooth $\beta$ model.
" The jets, which have a hard non-thermal spectral energy distribution (see Marshall 2002; Wilson Yang 2002; Perlman Wilson 2005), would normally appear as bright, high pressure, hot structures in the maps, but have been masked in these images."," The jets, which have a hard non-thermal spectral energy distribution (see Marshall 2002; Wilson Yang 2002; Perlman Wilson 2005), would normally appear as bright, high pressure, hot structures in the maps, but have been masked in these images."
" At a radius of 7 arcsec (0.5 kpc) in the counter-jet direction, we observe a low ray surface brightness, hot cavity (‘A’) (see also Young 2002)."," At a radius of 7 arcsec (0.5 kpc) in the counter-jet direction, we observe a low X-ray surface brightness, hot cavity (`A') (see also Young 2002)."
" Interestingly, there is no obvious corresponding radio feature."," Interestingly, there is no obvious corresponding radio feature."
" A region of brighter, cooler gas encircles this structure and the AGN."," A region of brighter, cooler gas encircles this structure and the AGN."
 Several other low surface brightness cavities are visible in Fig., Several other low surface brightness cavities are visible in Fig.
" 8, in the jet and counter-jet directions (see also Forman 2007)."," 8, in the jet and counter-jet directions (see also Forman 2007)."
 These correspond to regions of apparent low pressure and high temperature., These correspond to regions of apparent low pressure and high temperature.
 T'wo of these cavities (labelled ‘B’ and ‘C’; both are at a radius of r~40 arcsec from the nucleus in the jet and counter-jet directions) are also filled with radio emitting plasma., Two of these cavities (labelled `B' and `C'; both are at a radius of $r\sim40$ arcsec from the nucleus in the jet and counter-jet directions) are also filled with radio emitting plasma.
 Rings of cooler gas surround these cavities., Rings of cooler gas surround these cavities.
" The eastern-most cavity (‘D’), which also has relatively low pressure, lies at the edge of the radio cocoon that surrounds the AGN."," The eastern-most cavity (`D'), which also has relatively low pressure, lies at the edge of the radio cocoon that surrounds the AGN."
" Cavity E, labelled ‘bud’ by Forman (2005), is located r~40 arcsec (3 kpc) to the south of the AGN and is associated with high temperature, low pressure gas and is filled with radio plasma."," Cavity E, labelled `bud' by Forman (2005), is located $r\sim40$ arcsec (3 kpc) to the south of the AGN and is associated with high temperature, low pressure gas and is filled with radio plasma."
 Surrounding the cavity is a rim of high pressure material that is possibly shocked gas., Surrounding the cavity is a rim of high pressure material that is possibly shocked gas.
" The southwestern edge of the bright radio emission corresponds to a high pressure, high temperature, X-ray bright ‘ridge’."," The southwestern edge of the bright radio emission corresponds to a high pressure, high temperature, X-ray bright `ridge'."
 We identify this ridge as a shock front., We identify this ridge as a shock front.
" This feature (labelled ‘Shock A’) may extend to surround most of the bright, inner radio cocoon; it is seen clearly to the"," This feature (labelled `Shock A') may extend to surround most of the bright, inner radio cocoon; it is seen clearly to the"
structure of the peaks near the maximum (clearly visible for Cve N-1) are due to the presence of the mask and partly due to the intrinsic variability of the sources.,structure of the peaks near the maximum (clearly visible for Cyg X-1) are due to the presence of the mask and partly due to the intrinsic variability of the sources.
 The few regions with negative Duxes correspond to observations where the actual background: count rate is higher than the predicted background described inre[fsec:background., The few regions with negative fluxes correspond to observations where the actual background count rate is higher than the model-predicted background described in.
. Note hat the model background. was calculated: using a set of “blank fields. whose definition is problematic given the large size of the SPL FoV. The sets of blank fields are dillercn in each of the 14 time intervals used in the background nicxlelling (see refsec:background)).," Note that the model background was calculated using a set of “blank fields”, whose definition is problematic given the large size of the SPI FoV. The sets of blank fields are different in each of the 14 time intervals used in the background modelling (see \\ref{sec:background}) )."
 For tiis reason. it is possible that the," For this reason, it is possible that the"
light cvlinder.,light cylinder.
 The error of all existing calculations comes from the improper froatmient of the singular current laver outside the Πο cylinder., The error of all existing calculations comes from the improper treatment of the singular current layer outside the light cylinder.
 Here we describe simulations of the pulsar maguctosplere which resolve all singularities we dont use uu boundary conditions. not even at the surface of the star.," Here we describe simulations of the pulsar magnetosphere which resolve all singularities – we don't use any boundary conditions, not even at the surface of the star."
 Our munerical simulations are done in the FFE (Force-Free Electrodvuamics) lait of the SFE (Strone-Ficld Electrodyuaimics)., Our numerical simulations are done in the FFE (Force-Free Electrodynamics) limit of the SFE (Strong-Field Electrodynamics).
 We describe FFE aud SEE in the next section., We describe FFE and SFE in the next section.
 In 8323. we describe the simulations.," In 3, we describe the simulations."
 Both FFE aud SFE are plasziua plysics models which describe the plasima implicitly (Cauzinov 2008)., Both FFE and SFE are plasma physics models which describe the plasma implicitly (Gruzinov 2008).
" Namely, oue solves the Maxwell equations or in the 311 split.(B=VE...(2) supplemented by some Oluu’s lav. which eives jonly."," Namely, one solves the Maxwell equations, or in the 3+1 split,, supplemented by some Ohm's law, which gives ${\bf j}$."
 Tu FFE. the Oluu’s law is =0. Ly=0.," In FFE, the Ohm's law is =0, E_0=0."
63) Tere thescalar Ey is the proper electric field. defined by ΕΞ.cdotB.. 0.," Here thescalar $E_0$ is the proper electric field, defined by ^2, 0."
1 The physical 110220iug of the FFE Oluu’s law is as follows., The physical meaning of the FFE Ohm's law is as follows.
 For any clectromaguctic field. at aux event. there is a one-parameter family ofgood frames. where E is parallel to B.," For any electromagnetic field, at any event, there is a one-parameter family of frames, where ${\bf E}$ is parallel to ${\bf B}$."
 FFE postulates. that in auygood frame. the electric field vanishes and the current flows alone the magnetic field.," FFE postulates, that in any frame, the electric field vanishes and the current flows along the magnetic field."
 Tu SFE. the Οιν law isαλ” Here Fis the dual tensor. aud c6 is the conductivity scala.," In SFE, the Ohm's law is, Here $\tilde{F}$ is the dual tensor, and $\sigma$ is the conductivity scalar."
 The physical meaning of the SFE Olun’s law is as follows., The physical meaning of the SFE Ohm's law is as follows.
 At each event. the family ofgood fraanes contains thebest frame. where thecharge density vanishes. and the current o£ flows along the conunon direction of the electric and magnetic fields.," At each event, the family of frames contains the frame, where thecharge density vanishes, and the current $\sigma E_0$ flows along the common direction of the electric and magnetic fields."
" If £j=0. the charge density p has to move at the speed of light. so that //jj,=0."," If $E_0=0$, the charge density $\rho$ has to move at the speed of light, so that $j^\mu j_\mu=0$."
 lu unnmerical simulations. one uses the 311 split. aud the FFE Ohluu's law becomes," In numerical simulations, one uses the 3+1 split, and the FFE Ohm's law becomes."
" The SFE Ον law isERAT) where κοπατε, Tn the luit of high conductivity. SPE reduces o FFE (CGaruzinovy 2008)."," The SFE Ohm's law is, where ^2, In the limit of high conductivity, SFE reduces to FFE (Gruzinov 2008)."
" This melt sccm stranec. j)ecause SEE postulates that the [-cmrent is always space-like or null-ike. jjj,x:0. wlile FFE adnutsπειες time-liketune-hke currents.curveuts. j],ji,—pepj13τοuU. But i ius out. that SEE handles the time-like curreuts by constantlv switching the direction of he uull-like current. such that the time-averagcc current becomes time-like."," This might seem strange, because SFE postulates that the 4-current is always space-like or null-like, $j^\mu j_\mu \leq 0$, while FFE admits time-like currents, $j^\mu j_\mu \equiv \rho ^2-{\bf j}^2>0.$ But it turns out, that SFE handles the time-like currents by constantly switching the direction of the null-like current, such that the time-averaged current becomes time-like."
 FFE cau be applied ouly to initial clectromague fields of special geometry with the electric ficl everywhere sinaller than aud perpendicular to the naguetic field., FFE can be applied only to initial electromagnetic fields of special geometry – with the electric field everywhere smaller than and perpendicular to the magnetic field.
 SFE applies o arbitrary initia ποια., SFE applies to arbitrary initial field.
 FFE is ideal. the clectromagnuetic euergv ds conserved.," FFE is ideal, the electromagnetic energy is conserved."
 SEE issemá-ideal. the clectromaguetic enerev ds non-dncreastue. but it remains exactly constant for all fields with £y= 0.," SFE is, the electromagnetic energy is non-increasing, but it remains exactly constant for all fields with $E_0=0$ ."
 Iun cvlindrical coordinates Ον τὸν assunüug axisviunietrie field. we unuerically iutegrate the," In cylindrical coordinates $(r,\theta ,z)$ , assuming axisymmetric field, we numerically integrate the"
remaining data are treated as bootstrap samples.,remaining data are treated as bootstrap samples.
 The standard deviation of the estimates computed from these samples serves as an estimate of (he error. less a [actor to adjust for (he smaller subsamples ancl the large overlap.," The standard deviation of the estimates computed from these samples serves as an estimate of the error, less a factor to adjust for the smaller subsamples and the large overlap."
 When estimating correlation functions. pairs or triplets etc of points have to be counted.," When estimating correlation functions, pairs or triplets etc of points have to be counted."
 By joining independently resampled blocks together to form the bootstrap sample. the block bootstrap creates artilical configurations of points across the resampling blocks and cistorts the dependence structure in (he data.," By joining independently resampled blocks together to form the bootstrap sample, the block bootstrap creates artifical configurations of points across the resampling blocks and distorts the dependence structure in the data."
 This does not matter in asymptotic arguments because (he effect becomes negligible if the range of the correlation is fixed while the resampling blocks increase in size., This does not matter in asymptotic arguments because the effect becomes negligible if the range of the correlation is fixed while the resampling blocks increase in size.
 However. Loh&Stein(2004) found that the actual coverage achieved by confidence intervals obtained using block bootstrap can be much lower than the nominal percentage level for finite samples.," However, \citet{loh02a} found that the actual coverage achieved by confidence intervals obtained using block bootstrap can be much lower than the nominal percentage level for finite samples."
 In subsaunpling. no artificial configurations of points are created.," In subsampling, no artificial configurations of points are created."
 However. while the correction weight accounts for the difference in sample sizes between (he bootstrap samples and the actual data set. it does not account lor the change in the boundary effects. due to the different resampling regions.," However, while the correction weight accounts for the difference in sample sizes between the bootstrap samples and the actual data set, it does not account for the change in the boundary effects due to the different resampling regions."
 Since subsampling uses smaller regions as (lie bootstrap observation regions. boundary effects are magnified.," Since subsampling uses smaller regions as the bootstrap observation regions, boundary effects are magnified."
 For subsampling. (here is (he temptation {ο use large subsamples to (ry. and retain more of the dependence structure. but like block bootstrap. theoretical justilication of (he method requires that the subsamples be small in size relative lo the actual data set.," For subsampling, there is the temptation to use large subsamples to try and retain more of the dependence structure, but like block bootstrap, theoretical justification of the method requires that the subsamples be small in size relative to the actual data set."
 Loh&Stein(2004) also found that subsampling can vield confidence intervals (hat attain very low empirical coverage., \citet{loh02a} also found that subsampling can yield confidence intervals that attain very low empirical coverage.
 They also found (hat the subsampling method is sensitive to the fraction of the data used lor subsampling., They also found that the subsampling method is sensitive to the fraction of the data used for subsampling.
 Loh&Stein(2004) proposed another version of spatial bootstrap. called marked point bootsirap. that. reduces the effect of joining independent blocks aud produces. confidence intervals that achieve coverage closer (ο the nominal level.," \citet{loh02a}
 proposed another version of spatial bootstrap, called marked point bootstrap, that reduces the effect of joining independent blocks and produces confidence intervals that achieve coverage closer to the nominal level."
 This is described in the next section. where we also show how it can be applied to the two- and three-point correlation function estimators commonly used in astronomy.," This is described in the next section, where we also show how it can be applied to the two- and three-point correlation function estimators commonly used in astronomy."
 Suppose NV points are observed in a region 1., Suppose $N$ points are observed in a region $A$.
 Furthermore. suppose (hat the quantity ol interest A can be estimated using an estimator ofthe form Note that each point 7 has an associated quantity $774s; o(r;.c;). the inner sum of," Furthermore, suppose that the quantity of interest $K$ can be estimated using an estimator ofthe form Note that each point $i$ has an associated quantity $\sum_{j=1, j\ne i}^N
\phi(x_i,x_j)$ , the inner sum of"
Although the FGM system of distributions provides us with convenient tool to construct the statistical model. its usefulness is restricted by the limitation of the correlation strength described above.,"Although the FGM system of distributions provides us with convenient tool to construct the statistical model, its usefulness is restricted by the limitation of the correlation strength described above."
 To overcome this drawback. many attempts have been made to extend the FGM distributions (see.e.g..Stuartetal.1994:Kotz.Balakrishnan.&Johnson2000).," To overcome this drawback, many attempts have been made to extend the FGM distributions \citep[see, e.g.,][]{stuart94,kotz00}."
. Among them. Johnson&Kotz(1977). introduced the following iterated generalization of Equation C11) where the symbol in the exponent. /2] means the maximum natural number which does not exceed 7/2.," Among them, \citet{johnson77} introduced the following iterated generalization of Equation \ref{eq:cum_fgm}) ): where the symbol in the exponent $[j/2]$ means the maximum natural number which does not exceed $j/2$."
 We set wo=1., We set $\kappa_0=1$.
 examined the dependence structure of Equation CA D) especially for the case of 4=2. and showed that the correlation can be stronger for these extension.," \citet{huang84} examined the dependence structure of Equation \ref{eq:cum_jk}) ) especially for the case of $k=2$, and showed that the correlation can be stronger for these extension."
" In the case of the one-iteration family (4= 2). we have the DF as The corresponding PDF is Then. just the same as the case of the original FGM distribution (&= 1). we obtain the covariance Huang&Kotz(1984) obtained the parameter space for &, and κο They showed that. for a positive correlation. Under these conditions. we have p<0.5072. which is considerably better than 1/3."," In the case of the one-iteration family $k=2$ ), we have the DF as The corresponding PDF is Then, just the same as the case of the original FGM distribution $k=1$ ), we obtain the covariance \citet{huang84} obtained the parameter space for $\kappa_1$ and $\kappa_2$ They showed that, for a positive correlation, Under these conditions, we have $\rho \le 0.5072$, which is considerably better than $1/3$."
 The BLF constructed with the tirst-order iterated FGM copula is expressed as The FIR-FUV BLF by Equation is shown in Figure Al.., The BLF constructed with the first-order iterated FGM copula is expressed as The FIR-FUV BLF by Equation is shown in Figure \ref{fig:fgm_lf_iter}.
 Clearly the dependence between the two luminosities is stronger than the original FGM-based BLF., Clearly the dependence between the two luminosities is stronger than the original FGM-based BLF.
" However. now it is not intuitive nor straightforward to relate these two parameters of dependence &, and 5» to the linear correlation coefficient."," However, now it is not intuitive nor straightforward to relate these two parameters of dependence $\kappa_1$ and $\kappa_2$ to the linear correlation coefficient."
half) originated in proto-GCs. and also that these proto-GCs lost about >95% of their primordial generation stars.,"half) originated in proto-GCs, and also that these proto-GCs lost about $>95$ of their primordial generation stars."
 Although we do not have direct access to events that occurred a Hubble time ago. chemical abundances allow us to put strong constraints even on those early phases of GC evolution.," Although we do not have direct access to events that occurred a Hubble time ago, chemical abundances allow us to put strong constraints even on those early phases of GC evolution."
 It is currently well known that second-generation stars are formed from the ejecta of massive stars of the primordial generation (e.g. Gratton et al., It is currently well known that second-generation stars are formed from the ejecta of massive stars of the primordial generation (e.g. Gratton et al.
 2001)., 2001).
" From our ongoing FLAMES survey we also know the current proportions of primordial and second-generation stars in GCs,", From our ongoing FLAMES survey we also know the current proportions of primordial and second-generation stars in GCs.
 The latter represent the bulk of stars in GCs (about 2/3) whereas the primordial component is still present. but at a level of only a third of the current stellar population.," The latter represent the bulk of stars in GCs (about 2/3) whereas the primordial component is still present, but at a level of only a third of the current stellar population."
 Taken together. these two observations mean that a large fraction of stars of the primordial generation must necessarily be lost from GCs.," Taken together, these two observations mean that a large fraction of stars of the primordial generation must necessarily be lost from GCs."
 Theoretical considerations about star formation efficiency. (e.g. Parmentier et al., Theoretical considerations about star formation efficiency (e.g. Parmentier et al.
 2008). violent relaxation (Lynden-Bell 1967) and gas expulsion (e.g. Baumgardt et al.," 2008), violent relaxation (Lynden-Bell 1967) and gas expulsion (e.g. Baumgardt et al."
 2008) predict that a huge mass loss occurs in early phases of the GC lifetimes., 2008) predict that a huge mass loss occurs in early phases of the GC lifetimes.
 In Carretta et al. (, In Carretta et al. (
2010) we explored the estimates of the initial mass of the primordial generation in GCs required to satisfy these two observational features.,2010) we explored the estimates of the initial mass of the primordial generation in GCs required to satisfy these two observational features.
 With suitable (and realistic) assumptions on the initial mass function of primordial and second-generation stars. mass ranges of the preferred polluters (either AGBs or FRMS). and initial-final mass relation we were able to show that a proto-GC should have lost ~90% of its primordial stellar population.," With suitable (and realistic) assumptions on the initial mass function of primordial and second-generation stars, mass ranges of the preferred polluters (either AGBs or FRMS), and initial-final mass relation we were able to show that a proto-GC should have lost $\sim 90\%$ of its primordial stellar population."
 This is a value that is not very distant from the >95% we derive in the present paper., This is a value that is not very distant from the $>95$ we derive in the present paper.
 As mentioned in Sect., As mentioned in Sect.
 2. we assumed that the diluting mass is equal to the polluting one.," 2, we assumed that the diluting mass is equal to the polluting one."
 Actually. it might be half of this value. so relaxing these constraints a bit.," Actually, it might be half of this value, so relaxing these constraints a bit."
 We conclude that. on the whole. this scenario is then quite constraining and not entirely implausible.," We conclude that, on the whole, this scenario is then quite constraining and not entirely implausible."
 Of course. a better determination of the mass loss from young stars would be highly welcomed.," Of course, a better determination of the mass loss from young stars would be highly welcomed."
of Kuiper belt objects (IKBOs). their effective streneth aud their collisional evolution (Dolinausi1969:Sterü&1999:Pan&Sari 2005).,"of Kuiper belt objects (KBOs), their effective strength and their collisional evolution \citep{D69,SC97,DF97,KL99,PS05}."
. It also provides a snapshot of an earlier stage of planet formation. which was erased clsewhere in the Solar system where planet formation proceeded all the way to completion.," It also provides a snapshot of an earlier stage of planet formation, which was erased elsewhere in the Solar system where planet formation proceeded all the way to completion."
 The cumulative size distribution of KBOs larger than R250kin is well described by a single power-laweiveu by where οςR) ds the nmuuber of objects with radi ercater than RR. aud q is the power-law index.," The cumulative size distribution of KBOs larger than $R
\gtrsim 50~\rm{km}$ is well described by a single power-lawgiven by where $N(>R)$ is the number of objects with radii greater than $R$, and $q$ is the power-law index."
 Ruiper belt surveys find that the size distribution for KBOs with radi greater than about 50 kin follows this power-law with 4~1 (eg.Trujilloetal.2001:Derusteiuetal.2001:Fuentes&Tolman2008:Fraser 2008).. which nmaplies roughly equal mass per logarithiuic mass interval.," Kuiper belt surveys find that the size distribution for KBOs with radii greater than about 50 km follows this power-law with $q \sim
4$ \citep[e.g.][]{TJL01,BTA04,FH108,FK108}, which implies roughly equal mass per logarithmic mass interval."
 This size distribution is a relic of the accretion jstorv in the I&uiper belt aud therefore provides valuable insights iuto the formation of large IKBOs (R=50 kin} (c.c.Stern1996:Davis&Farinella1997:IKeuvou2002).," This size distribution is a relic of the accretion history in the Kuiper belt and therefore provides valuable insights into the formation of large KBOs $R \gtrsim 50~\rm{km}$ ) \citep[e.g.][]{S96,DF97,K02}."
. Observations sugeest that there is a break in the power-aw size distribution at smaller KDO sizes (ee.Deru- 2010)...," Observations suggest that there is a break in the power-law size distribution at smaller KBO sizes \citep[e.g.][]{BTA04,FH108,FK108,SO09,FH10}."
 The weak in the size distribution is generally attributed to collisions that break-up small KDBOs (d.e.X50kin j and aodity their size distribution (e.g.Dohuauvi1969:I&envou&Bromley20014:PauSari 2005).," The break in the size distribution is generally attributed to collisions that break-up small KBOs $R \lesssim 50~\rm{km}$ ) and modify their size distribution \citep[e.g.][]{D69,KB04,PS05}."
.. The KBO size distribution below the break is still poorly constrained. although some eucouraeiug progress has been made recently in probing the abuudauce of sized KBOs by stellar occultations (e.g.Liuetal.2008:Schlichtingetal.2009:Biancoct 2010).," The KBO size distribution below the break is still poorly constrained, although some encouraging progress has been made recently in probing the abundance of sub-km-sized KBOs by stellar occultations \citep[e.g.][]{LC08,SO09,B10}."
. The work preseuted iu this paper focuses on the size distribution of large IKBOs (Ro250 kin). which is well coustrained by observations and which sheds light outo the formation of KBOs. protoplanets aud accretion processes that could be ongoing in other debris disks.," The work presented in this paper focuses on the size distribution of large KBOs $R \gtrsim 50~\rm{km}$ ), which is well constrained by observations and which sheds light onto the formation of KBOs, protoplanets and accretion processes that could be ongoing in other debris disks."
 Muuerical coagulation simulations have been successful iu reproducing the observed NBO size distribution., Numerical coagulation simulations have been successful in reproducing the observed KBO size distribution.
 Such siuulatious typically find that the accretion processes of KBOs viell a power-law size distribution with y~3.81.5 for 10-100 kin aud larger objects (sceuvon&Luu1999:Ikeuvou2002:IKeuvou&Bromley 2001). which is consistent with the observed power-law size distribution.," Such simulations typically find that the accretion processes of KBOs yield a power-law size distribution with $q \sim 3.8 - 4.5$ for 10-100 km and larger objects \citep{KL99,K02,KB04}, which is consistent with the observed power-law size distribution."
 Despite their success. the reason for the actual slope of the distribution has so far not been explained bv such simulations.," Despite their success, the reason for the actual slope of the distribution has so far not been explained by such simulations."
 In this paper. we offer an explanation or the slope of the NBO size distribution aud for the amount of mass in the large KDOs that are observed in todaws Ruper belt.," In this paper, we offer an explanation for the slope of the KBO size distribution and for the amount of mass in the large KBOs that are observed in today's Kuiper belt."
 Specifically we fiud a power-aw index. of q~d and a total mass in laree KBOs of ~10? of the initial planctesimal mass. which is consistent with the current observed mass in the Iuiper volt.," Specifically we find a power-law index of $q \sim 4$ and a total mass in large KBOs of $\sim 10^{-3}$ of the initial planetesimal mass, which is consistent with the current observed mass in the Kuiper belt."
" We also make a prediction for the maxima lass ratio of Kuiper belt binaries that formed by dynamical Xocesses, for example. by three body interactions. aud show that our prediction is in good agreement with the observations."," We also make a prediction for the maximum mass ratio of Kuiper belt binaries that formed by dynamical processes, for example, by three body interactions, and show that our prediction is in good agreement with the observations."
 Although our work focuses on the Kuiper dt. the results also apply to carly stages of planet ormation and protoplanctary growth iu debris disks.," Although our work focuses on the Kuiper belt, the results also apply to early stages of planet formation and protoplanetary growth in debris disks."
 Qur paper is structured as follows: Iu 82 we analytically describe the erowth of lavee KBOs. iucludiug their velocity dispersion aud derive the slope of the KBO size distribution.," Our paper is structured as follows: In 2 we analytically describe the growth of large KBOs, including their velocity dispersion and derive the slope of the KBO size distribution."
 We coufiria our analytic results iu 83 with coagulation sinulations., We confirm our analytic results in 3 with coagulation simulations.
 Ta §l. we discuss how semu-collisional accretion. binary niergeers and frequent planetesimal collisions would affect our results.," In 4, we discuss how semi-collisional accretion, binary mergers and frequent planetesimal collisions would affect our results."
 We show that our results on the KDBO erowth aud velocity dispersion have iutercsting duplications for the formation of Iuiper belt binaries aud predict the maxim mass ratio for binarics that formed by dvuamical processes i 85., We show that our results on the KBO growth and velocity dispersion have interesting implications for the formation of Kuiper belt binaries and predict the maximum mass ratio for binaries that formed by dynamical processes in 5.
 Discussion aud conclusions follow in &6., Discussion and conclusions follow in 6.
 Iu order to gain an analytic understanding of the erowth processes of huge NKBOs aud the associated velocity evolution we use the two-groups approximation (Goldreichctal.2002.20015).," In order to gain an analytic understanding of the growth processes of large KBOs and the associated velocity evolution we use the 'two-groups approximation' \citep{GLS02,GLS04}."
 The -two-eroups approximation cousists of the identification of two eroups of objects. small ones. that contain most of the total mass with mass surface density σ. aud large oues. that coutain ouly a smallfraction of the total mass with lass surface density X«e.," The `two-groups approximation' consists of the identification of two groups of objects, small ones, that contain most of the total mass with mass surface density $\sigma$, and large ones, that contain only a smallfraction of the total mass with mass surface density $\Sigma \ll \sigma $."
 We define X as the mass surface density ina sinele logarithuiic mass interval. that includes the largest bodies formed at a eiven tine.," We define $\Sigma$ as the mass surface density in a single logarithmic mass interval, that includes the largest bodies formed at a given time."
 Iu contrast σ is clefined as the total mass in small objects., In contrast $\sigma$ is defined as the total mass in small objects.
" Within the framework of the ""two-egroups approximation we arrive at the following— picture or NBO erowth.", Within the framework of the `two-groups approximation' we arrive at the following picture for KBO growth.
 Initially all the mass is in small bodies., Initially all the mass is in small bodies.
 As the small bodies start to accrete each other. huge )odies beein to form.," As the small bodies start to accrete each other, large bodies begin to form."
 To simplify the aremment. we ouly cousider the mass surface deusitv of the sia and laree bodies here. ignoring intermediate size bodiey. Or now.," To simplify the argument, we only consider the mass surface density of the small and large bodies here, ignoring intermediate size bodies for now."
 As we show later. the laree and siall bodiey. alone deteriune the velocity dispersion for bodies of a sizes aud only the large bodies erow sienificauth.," As we show later, the large and small bodies alone determine the velocity dispersion for bodies of all sizes and only the large bodies grow significantly."
 Iu he initial stage. X erows due to the accretion of sia )odies.," In the initial stage, $\Sigma$ grows due to the accretion of small bodies."
 Therefore the size of the largest bodies and the otal mass in huge bodies mereases with time., Therefore the size of the largest bodies and the total mass in large bodies increases with time.
 During his growth phase the velocity dispersion of the siia )odies increases due to viscous stirring by the larec vodics., During this growth phase the velocity dispersion of the small bodies increases due to viscous stirring by the large bodies.
 The velocity dispersion of large bodies 1s dame * dyvnandceal friction provided by the small bodies., The velocity dispersion of large bodies is damped by dynamical friction provided by the small bodies.
 X contiuues to erow until the erowth of laree KBOs by accretion of comparable size objects starts to compete with erowth by accretion of siiall bodies., $\Sigma$ continues to grow until the growth of large KBOs by accretion of comparable size objects starts to compete with growth by accretion of small bodies.
 From then on. NX remains roughly constant m a given logaritας mass interval. while the size of the laree KBOs eros linearly with time.," From then on, $\Sigma$ remains roughly constant in a given logarithmic mass interval, while the size of the large KBOs grows linearly with time."
 Tow the KBO erowth ended aud how exactly the small bodies were lost frou the I&uiper belt are still the subject of ougoime research and are unimuportaut for the purpose of this paper and we therefore will not discuss them here further., How the KBO growth ended and how exactly the small bodies were lost from the Kuiper belt are still the subject of ongoing research and are unimportant for the purpose of this paper and we therefore will not discuss them here further.
 We confi the outlined KBO erowthn analytically and with wuuerical simulations., We confirm the outlined KBO growth analytically and with numerical simulations.
 We show that the mass-ratio. S/o. is not arbitrary but an outcome of KBO erowth.," We show that the mass-ratio, $\Sigma/\sigma$, is not arbitrary but an outcome of KBO growth."
 Large KDOs viscously stir the small bodies. increasing the samall bodies velocity dispersion a.," Large KBOs viscously stir the small bodies, increasing the small bodies' velocity dispersion $u$ ."
 As a result « erows on the same timescale as A. as long as the small bodies experience no signif&cant damping by either gas or nmtual collisions. which are. most likely. not vet Huportant (see section ??)).," As a result $u$ grows on the same timescale as $R$ , as long as the small bodies experience no significant damping by either gas or mutual collisions, which are, most likely, not yet important (see section \ref{s3}) )."
 We can therefore write the, We can therefore write the
the two simulations behave very similarly. and the evolution is rather insensitive to metallicity.,"the two simulations behave very similarly, and the evolution is rather insensitive to metallicity."
 Once the gas has reached a roughly pressure-supported state in the potential of the DM halo. the subsequent evolution bifurcates. resulting in continued: collapse and. fragmentation for Lun A. and. in [Failure to do so for Run D. We now discuss these two stages in turn.," Once the gas has reached a roughly pressure-supported state in the potential of the DM halo, the subsequent evolution bifurcates, resulting in continued collapse and fragmentation for Run A, and in failure to do so for Run B. We now discuss these two stages in turn."
 In response to the initially imprinted. density. luctuations. he DAL develops a marked: substructure.," In response to the initially imprinted density fluctuations, the DM develops a marked substructure."
" The gas. does not ""feel the potential wells of these. subcondensations. iowever. since it cannot cool sulliciently during these carly evolutionary phase."," The gas does not `feel' the potential wells of these subcondensations, however, since it cannot cool sufficiently during these early evolutionary phase."
 Instead. due to adiabatie compression. Toxn?7. the gas reaches temperatures of ~103 Ix. At his point. very efficient. cooling due to the excitation of ivdrosen lines sets in (see Fig.," Instead, due to adiabatic compression, $T\propto n^{2/3}$, the gas reaches temperatures of $\sim 10^{4}$ K. At this point, very efficient cooling due to the excitation of hydrogen lines sets in (see Fig."
 1). and maintains the eas at this temperature upon further compression.," 1), and maintains the gas at this temperature upon further compression."
 At the end of the virialization process. the gas has reached. a state of rough pressure support with tvpical gas temperatures close to the virialtemperature where fe;22100 pe is the virial radius. Cis Newton's constant. Ap Boltzmann's constant. and mg the mass of a hydrogen atom.," At the end of the virialization process, the gas has reached a state of rough pressure support with typical gas temperatures close to the virialtemperature where $R_{vir}\simeq 100$ pc is the virial radius, $G$ is Newton's constant, $k_{\rmn B}$ Boltzmann's constant, and $m_{\rmn H}$ the mass of a hydrogen atom."
 To estimate the corresponding gas density. Don. We Consider the barvonic Jeans mass and assume that it has to be approximately equal to the total mass of the halo.," To estimate the corresponding gas density, $n_{vir}$, we consider the baryonic Jeans mass and assume that it has to be approximately equal to the total mass of the halo."
 Here. ny denotes the hydrogen number density.," Here, $n_{\rmn H}$ denotes the hydrogen number density."
 From imposing AM;~2.10M... one then finds meac1077 em7.," From imposing $M_{J}\sim 2\times 10^{6}M_{\odot}$, one then finds $n_{vir}\simeq 10^{2.5}$ $^{-3}$."
 Heating due to the photo-electric ellect is never important. neither during virialization. nor during the later. barvon-dominated stages.," Heating due to the photo-electric effect is never important, neither during virialization, nor during the later, baryon-dominated stages."
 From here on. the further evolution strongly depends on the level of trace metal enrichment.," From here on, the further evolution strongly depends on the level of trace metal enrichment."
 We first. discuss Run A. Cooling in this case is efficient enough to allow further collapse., We first discuss Run A. Cooling in this case is efficient enough to allow further collapse.
 In Figure 2. we show the gas morphology and the corresponding thermodynamic state abt 2=30.5.," In Figure 2, we show the gas morphology and the corresponding thermodynamic state at $z=30.5$."
 As can be seen. the eas has clissipatively settled into a disk-like central configuration.," As can be seen, the gas has dissipatively settled into a disk-like central configuration."
 This disk is horizontally supported by rotation., This disk is horizontally supported by rotation.
 In the presence of a DAL halo. one expects a contraction by a factor of 1/Ax20 [or rotational support.," In the presence of a DM halo, one expects a contraction by a factor of $1/\lambda\simeq 20$ for rotational support."
 The size of the disk. as shown in ligure 2. is in good agreement with this prediction.," The size of the disk, as shown in Figure 2, is in good agreement with this prediction."
 Lt is also evident that the disk is subject to a bar-mocde (m= 2) instability., It is also evident that the disk is subject to a bar-mode $m=2$ ) instability.
 By examining the 7ng plane (lower-Ieft. panel in Fig., By examining the $T-n_{\rmn H}$ plane (lower-left panel in Fig.
" 2). one can see that the σας elliciently. cools from ~107 Ix down to the value set by the CMB floor. fini,c=86 Ix. During this rapid cooling. the eas remains rather smooth."," 2), one can see that the gas efficiently cools from $\sim 10^{4}$ K down to the value set by the CMB floor, $T_{min}\simeq T_{\rmn CMB}=86$ K. During this rapid cooling, the gas remains rather smooth."
 The gravitationally unstable disk-material. rowever. subsequently undergoes: vigorous. fragmentation (sce Figure 3).," The gravitationally unstable disk-material, however, subsequently undergoes vigorous fragmentation (see Figure 3)."
 We next turn to Run D. and to its rather dillercnt fate.," We next turn to Run B, and to its rather different fate."
 In Figure 4. we show the situation at 228.," In Figure 4, we show the situation at $z\simeq 28$."
 In contrast to he corresponding situation for Run A (Figure 3). no further collapse. and no fragmentation has occurred.," In contrast to the corresponding situation for Run A (Figure 3), no further collapse, and no fragmentation has occurred."
 Instead. the eas remains in pressure support. and lingers at temperatures close to λε.," Instead, the gas remains in pressure support, and lingers at temperatures close to $T_{vir}$ ."
 Only much later. as the result. of slow but inexorable residual cooling. two high density clumps form," Only much later, as the result of slow but inexorable residual cooling, two high density clumps form"
the calculations of Mewe aud Iaastra (Mewe ot al.,the calculations of Mewe and Kaastra (Mewe et al.
 1986: Kaastra 1992) vields a \?/dof of 266/202 for a fitted temperature of 12.540.7 keV aud au abundance of O.1340.05., 1986; Kaastra 1992) yields a $\chi ^2$ /dof of 266/202 for a fitted temperature of $\pm$ 0.7 keV and an abundance of $\pm$ 0.05.
 These values are in agreement with the ASCA values of LO.740.6 keV aud 0.354008 (προ et al., These values are in agreement with the ASCA values of $\pm 0.6$ keV and $\pm$ 0.08 (Kubo et al.
 1998)., 1998).
 The fit shows significant residuals around 300 eV and 1 keV. The addition of a carbon line at 277 eV results iu a better fit (AZ /dof-211/199). which is sienificaut under au F test (P>99.9%)).," The fit shows significant residuals around 300 eV and 1 keV. The addition of a carbon line at 277 eV results in a better fit $\chi ^2$ /dof=244/199), which is significant under an $F$ test $>$ )."
 If real. this could tuply an overabundance of carbon.," If real, this could imply an overabundance of carbon."
 Following the ROSAT observation of a soft component. we next added a blackbody component.," Following the ROSAT observation of a soft component, we next added a blackbody component."
" This resulted iu a slightly worse ft (42 /dof-218/201) primarily due to residuals around 0.3 keV. The fitted temperature was 1004-352"" eV. which is consistent with the ROSAT value of 200410 eV. (Haberl 1995)."," This resulted in a slightly worse fit $\chi ^2$ /dof=248/201) primarily due to residuals around 0.3 keV. The fitted temperature was $\pm ^{320} _{13}$ eV, which is consistent with the ROSAT value of $\pm$ 10 eV (Haberl 1995)."
 Assiuuiue that the source is best deseribed in terms of a multiteniperature dlasmia. we replaced the dackbody. comipoueut with a second. lower temperature. MERKAL component.," Assuming that the source is best described in terms of a multi–temperature plasma, we replaced the blackbody component with a second, lower temperature, MEKAL component."
 The resulting κ fdof is 210/200 for temperatures of 12.340.6 keV and O.O540.01 keV. The fitted abundance is 1230.06. consisten with previous measurements.," The resulting $\chi ^2$ /dof is 240/200 for temperatures of $\pm$ 0.6 keV and $\pm$ 0.01 keV. The fitted abundance is $\pm $ 0.06, consistent with previous measurements."
 Whereas ROSAT reported marked variability in the soft compoucut and suggested a possible modulation period of 135 nünus. our data are consistent with a constaut mean rate throughout the observation.," Whereas ROSAT reported marked variability in the soft component and suggested a possible modulation period of 135 mins, our data are consistent with a constant mean rate throughout the observation."
 For example. iu the 0.1 to 0.5 keV band. a bestfif constaut nien rate yields ao κ ος of 61/57. as compared to 1223/6 for the 0.110 keV band.," For example, in the 0.1 to 0.5 keV band, a best–fit constant mean rate yields a $\chi ^2$ /dof of 64/57, as compared to 423/64 for the 0.1–10 keV band."
" The combined) NFI count spectu aud the best-fit twotemperature MEIAL model (fold through the appropriate iustruiuents response ""unctions) is shown iu Fig.", The combined NFI count spectrum and the best-fit two–temperature MEKAL model (folded through the appropriate instruments response functions) is shown in Fig.
 lL., 4.
 In Fig., In Fig.
 5 we show the correspouding best-ft incident photon spectrum., 5 we show the corresponding best-fit incident photon spectrum.
 The observed fux in the 10 keV band is 133410 48 ere 7? 5. which for a source distance of Lss8 pc (ESA 1997). corresponds to a bolometric- huuimositv.H of 107732 erg 1," The observed flux in the 2--10 keV band is $\times$ $^{-10}$ erg $^{-2}$ $^{-1}$, which for a source distance of 188 pc (ESA 1997), corresponds to a bolometric luminosity of $\times$ $^{32}$ erg $^{-1}$."
 The comparison of DeppoSAX results with previous results can be inisleading iu view of the lamited enerev range of carly inissious meaning that the results can be critically depeudent on assumed emission nodels which may be iuappropriate for the wide xuidwidth of BeppoSAX., The comparison of BeppoSAX results with previous results can be misleading in view of the limited energy range of early missions – meaning that the results can be critically dependent on assumed emission models which may be inappropriate for the wide bandwidth of BeppoSAX.
 For *xauple. ASC'A data are peorfectlv consistent with a powerlaw contiuuuni whereas BeppoSAX data are not. when energies above 16 ASCA upper euerey threshold are taken into account.," For example, ASCA data are perfectly consistent with a power–law continuum whereas BeppoSAX data are not, when energies above the ASCA upper energy threshold are taken into account."
 Globally. the DeppoSAX data show that the > Cas spectrum is consistent with an optically thin hermatl asma distribution which does uot require nou-thermal conrponeuts as iueht be expected for accreting neutrou star models.," Globally, the BeppoSAX data show that the $\gamma$ –Cas spectrum is consistent with an optically thin thermal plasma distribution which does not require non-thermal components – as might be expected for accreting neutron star models."
 The Fe line is a persistent feature of this source and is ecnerally attributed to a blend of Fe NNV (6.7 keV) line eimissiou and Fe NNVI (6.97 keV) enüssion produced in a highly ionized. optically thin thermal plasima.," The Fe line is a persistent feature of this source and is generally attributed to a blend of Fe XXV (6.7 keV) line emission and Fe XXVI (6.97 keV) emission produced in a highly ionized, optically thin thermal plasma."
 The nuplied temperature of ~12 keV is perfectly consistent with that derived independently for the coutinuun., The implied temperature of $\sim$ 12 keV is perfectly consistent with that derived independently for the continuum.
 Such emission is most consistent with white dif scenarios., Such emission is most consistent with white dwarf scenarios.
 Tigh mass neutron star svstenmis. ou the oicr haud. ecuerally have strong enission at 6.1 keV and only weals. if anv. e1udssion at 6.7 keV. Also. such systems eeucrallv have nou-therimal spectra which are well described by a power-law distribution with a hieh energy cut-off aud may be expected to produce cyclotron line chussion above ~LO keV. None of these are observed bx DeppoSAX.," High mass neutron star systems, on the other hand, generally have strong emission at 6.4 keV and only weak, if any, emission at 6.7 keV. Also, such systems generally have non-thermal spectra which are well described by a power-law distribution with a high energy cut-off and may be expected to produce cyclotron line emission above $\sim$ 10 keV. None of these are observed by BeppoSAX."
 Until recently. the main problem with degenerate dwarf models has been reproducing the relatively high," Until recently, the main problem with degenerate dwarf models has been reproducing the relatively high"
 , 
Structure formation in the standard inflationary A-Cold Dark Matter CACDAM) cosmological model is expected to proceed hierarchicallv.,Structure formation in the standard inflationary $\Lambda$ -Cold Dark Matter $\Lambda$ CDM) cosmological model is expected to proceed hierarchically.
 The earliest bouud. virialized structures arise on small scales. and as time progresses these objects merge aud accrete Wass. growing ever larger until cosuic acceleration at low redshift freezes out the erowth of large-scale structure.," The earliest bound, virialized structures arise on small scales, and as time progresses these objects merge and accrete mass, growing ever larger until cosmic acceleration at low redshift freezes out the growth of large-scale structure."
 The role plaved by the earliest generaions of collapsed structures in the thermal history of the universe is. at present. unclear.," The role played by the earliest generations of collapsed structures in the thermal history of the universe is, at present, unclear."
 Observatious of the spectra of Hel-redshift quasars indicate that the reionization of the intergalactic medimu was largely complete by redshift 27 (c.g.Fanetal.2006).. wlile measurements of the Thomson scattering optical depth of the cosmnüc microwave backeround suggest that reiouization occurred at 2~10 (Larsonetal.2010)..," Observations of the spectra of high-redshift quasars indicate that the reionization of the intergalactic medium was largely complete by redshift $z\approx 7$ \citep[e.g.][]{Fan06}, while measurements of the Thomson scattering optical depth of the cosmic microwave background suggest that reionization occurred at $z\sim 10$ \citep{WMAP7}."
 At hese epochs. the typical masses of colapsed dark matter halos rauge frou rare 10?AZ. objects. down to (plausibly) Earth-mass jos (Creeretal.2005).," At these epochs, the typical masses of collapsed dark matter halos range from rare $10^9 M_\odot$ objects, down to (plausibly) Earth-mass halos \citep{Green05}."
 As we diseuss below. the sallest dark matter halos are unable to attract xurvolis. resuline in au effective lower mass limit near LO?AL...," As we discuss below, the smallest dark matter halos are unable to attract baryons, resulting in an effective lower mass limit near $10^5 M_\odot$."
 Even if low-nass halos are able to accmire barvous. they may be unable to convert those baryous iuto stars 2010).. since star formation requires the presence of cold. dense gas.," Even if low-mass halos are able to acquire baryons, they may be unable to convert those baryons into stars \citep{Teg97,Bromm09,Loeb10}, since star formation requires the presence of cold, dense gas."
 Objects nassive enoueli to attract eas but whose virial temperatures are below ~104 1. termed iinilialos. caunot cool their easons hnrough atouic lines and must therefore rely upon inolectlar cooling processes.," Objects massive enough to attract gas but whose virial temperatures are below $\sim 10^4$ K, termed minihalos, cannot cool their gas through atomic lines and must therefore rely upon molecular cooling processes."
 It is unclear whether molecular πο CALL Col nünihalo gas suffickΠΙΤΑΣ to alow star formation., It is unclear whether molecular processes can cool minihalo gas sufficiently to allow star formation.
 Prior to the formation of the first stars im the Universe. the forination of molecular Πω catalyzeκα by residual free electrous left over after recombination appears iusufBcient to alow cficicnt cooling at redshifts =20 (Teemarketal.1997).," Prior to the formation of the first stars in the Universe, the formation of molecular $_2$ catalyzed by residual free electrons left over after recombination appears insufficient to allow efficient cooling at redshifts $z\lesssim20$ \citep{Teg97}."
. However. feedback. from the first uuinous Objects can chauge this resul.," However, feedback from the first luminous objects can change this result."
 Positive feedback. for example from ionizing N-ravs that strip clectrons from atoms and thereby spur molecule creaion. could lead to efficient cooling.," Positive feedback, for example from ionizing X-rays that strip electrons from atoms and thereby spur molecule creation, could lead to efficient cooling."
 Conversely. negative feedback iu the form of ultraviolet radiation im the Lyman aud Werner bands could destroy iiolecules aud suppress Πω cooling over large volumes (Yoshidaetal.2007).," Conversely, negative feedback in the form of ultraviolet radiation in the Lyman and Werner bands could destroy molecules and suppress $_2$ cooling over large volumes \citep{Yoshida07}."
. Caven his wide range of possible scenarios. it is unclear whether minihalos can formu stars and whether they mieht be mu]xαταλατ duriug the reionization of the intergalactic mecditm.," Given this wide range of possible scenarios, it is unclear whether minihalos can form stars and whether they might be important during the reionization of the intergalactic medium."
 This macertainty. however. may be viewed as ai opportuitv: anv probe that cau quantify the importance of ninibalos during recdshitts preceding and during reiouization wolid dramatically help to elucidate the plysics of star formation im the first structures that arise in the Universe.," This uncertainty, however, may be viewed as an opportunity: any probe that can quantify the importance of minihalos during redshifts preceding and during reionization would dramatically help to elucidate the physics of star formation in the first structures that arise in the Universe."
 Receutlv. Tseliakhovich&ITirata(2MLO.hereafterTII) poiuted out an naportaut effect governing the formation of 10AL. niuilalos. that had prevkmisly been overlooked.," Recently, \citet[hereafter TH]{Tsel10} pointed out an important effect governing the formation of $\sim 10^5 M_\odot$ minihalos, that had previously been overlooked."
" As we discuss below. this effect can provide a 1uiuilalo sieuature iu παν potential observables,"," As we discuss below, this effect can provide a minihalo signature in many potential observables."
 TII noticed that the relative velocity between dark matter aud barvous, TH noticed that the relative velocity between dark matter and baryons
scatter angle«ρω.,scatter angle$\phigeo$.
 The last quantity can be determined from the known source position 1.-17162)) and the scatter direction angles (X.ο).," The last quantity can be determined from the known source position 162)) and the scatter direction angles $(\chi,\psi)$."
" For a point-source the distribution of 4,,, (re. the ARM-distribution) is a narrowly peaked distribution with à maximum near 424,4,=0 and a wing for positive ο values due to incompletely absorbed events.", For a point-source the distribution of $\phiarm$ (i.e. the ARM-distribution) is a narrowly peaked distribution with a maximum near $\phiarm=0$ and a wing for positive $\phiarm$ values due to incompletely absorbed events.
 The imaging capabilities of COMPTEL rely on this sharp asymmetric distribution of ως, The imaging capabilities of COMPTEL rely on this sharp asymmetric distribution of $\phiarm$.
 The relative contributions of the peak and wing. and the width of the peak are a function. of input photon energy.," The relative contributions of the peak and wing, and the width of the peak are a function of input photon energy."
" This means that instead of fixing |;,,,,| to a value in the range 275 to 375 irrespective of the selected energies. as turned out to be the optimum range from COMPTEL studies on the Crab (Muchetal. 1995)) and Vela (Kuiperetal. 1998b)) pulsars. an energy window dependent ARM selection is more appropriate."," This means that instead of fixing $\vert\phiarm\vert$ to a value in the range $2\fdg 5$ to $3\fdg 5$ irrespective of the selected energies, as turned out to be the optimum range from COMPTEL studies on the Crab \cite{much}) ) and Vela \cite{kuiper2}) ) pulsars, an energy window dependent ARM selection is more appropriate."
 In this study we have determinedpriori the optimal value of oar] for each energy window by estimating the maximum in the Signal-to-Noise vs. μμ] relation., In this study we have determined the optimal value of $\vert\phiarm\vert$ for each energy window by estimating the maximum in the Signal-to-Noise vs. $\vert\phiarm\vert$ relation.
 The latter relation can be derived from a 3 dimensional (4. 0.47) point source model for the energy window involved and the total measured 3d-event distribution in the same energy window. heavily dominated by instrumental background events (020-050).," The latter relation can be derived from a 3 dimensional $\chi,\psi,\phibar$ ) point source model for the energy window involved and the total measured 3d-event distribution in the same energy window, heavily dominated by instrumental background events )."
 The following energy dependent criteria on [μμ] eappeared to be appropriate: 375 for the energy window 0.75-1 MeV and 275 for the energy windows 1-3. 3-10 and 10-30 MeV. The fraction of counts from a point-source within the ARM-cut is typically ~60%.," The following energy dependent criteria on $\vert\phiarm\vert$ appeared to be appropriate: $3\fdg 5$ for the energy window 0.75-1 MeV and $2\fdg 5$ for the energy windows 1-3, 3-10 and 10-30 MeV. The fraction of counts from a point-source within the ARM-cut is typically $\sim 60\%$."
 [tis also worth mentioning that the ARM cut applied in the timing analysis reduces the number of events handled in the timing analysis to typically of the number of events available for the imaging or spatial analysis. in which the full 3d-dataspace is employed.," It is also worth mentioning that the ARM cut applied in the timing analysis reduces the number of events handled in the timing analysis to typically of the number of events available for the imaging or spatial analysis, in which the full 3d-dataspace is employed."
 For the 10-30 MeV interval we have departed from the “standard” Time of Flight (TOF) and Pulse Shape Diserimination (PSD) windows (see for a description of these event parameters Schónfelderetal. 1993)) of 113-130 and 0-110 respectively. normally applied in the timing analysis (see e.g. Kuiper 19983) and have used the optimum TOF and PSD windows derived by Collmaretal.(1997) in their study on optimum parameter cuts using the Crab pulsar/nebula signature in the COMPTEL event space.," For the 10-30 MeV interval we have departed from the “standard” Time of Flight (TOF) and Pulse Shape Discrimination (PSD) windows (see for a description of these event parameters \cite{schonfelder}) ) of 113-130 and 0-110 respectively, normally applied in the timing analysis (see e.g. Kuiper 1998a) and have used the optimum TOF and PSD windows derived by \cite{collmar} in their study on optimum parameter cuts using the Crab pulsar/nebula signature in the COMPTEL event space."
 Once the event selection criteria were settled we proceeded as follows: the arrival times (recorded with an intrinsic resolution of 0.125 ms) of the events passing through our selection filters are converted to arrival times at the Solar System Barycentre (SSB) using the known instantaneous spacecraft position. the source position and the solar system ephemeris (JPL DE200 Solar System Ephemeris).," Once the event selection criteria were settled we proceeded as follows: the arrival times (recorded with an intrinsic resolution of 0.125 ms) of the events passing through our selection filters are converted to arrival times at the Solar System Barycentre (SSB) using the known instantaneous spacecraft position, the source position and the solar system ephemeris (JPL DE200 Solar System Ephemeris)."
 The pulse phase o is calculated from the following timing model: In this formula Af is given by At=#f? with ¢ the event SSB arrival time and f” the reference epoch., The pulse phase $\phi$ is calculated from the following timing model: In this formula $\Delta t$ is given by $\Delta t = t^{e} - t^{0}$ with $t^{e}$ the event SSB arrival time and $t^{0}$ the reference epoch.
 The values employed here for t?..7.7.P.oy are given in Table 2..," The values employed here for $t^{0},\nu,\nudot,\nuddot,\phi_0$ are given in Table \ref{tab_ephemerides}."
 The RMS error of the timing models listed in Table 2 1s typically 10 milli- or 1.5 ms. sufficiently accurate to keep coherency and allowing pulse phase folding over long time spans indicated by the validity range.," The RMS error of the timing models listed in Table \ref{tab_ephemerides} is typically 10 milli-periods or 1.5 ms, sufficiently accurate to keep coherency and allowing pulse phase folding over long time spans indicated by the validity range."
 The pulse phase distribution resulting from. phase-folding COMPTEL Cycle I-VI 0.75-30 MeV data is shown in Fig. 1.., The pulse phase distribution resulting from phase-folding COMPTEL Cycle I-VI 0.75-30 MeV data is shown in Fig. \ref{fig_comptel_lc_integral}.
 The modulation significance of the unbinned sample of pulse-phases is 5.10 employing a Z?-test (Buccherietal. 1983)) with 2 harmonies., The modulation significance of the unbinned sample of pulse-phases is $5.4\sigma$ employing a $Z_n^2$ -test \cite{buccheri}) ) with 2 harmonics.
 This is the first detection of pulsed emission above 0.75 MeV from PSR B1509-58., This is the first detection of pulsed emission above 0.75 MeV from PSR B1509-58.
 The pulse is roughly aligned with the pulse observed by OSSE/BATSE (Ulmeretal. 1993) and peaks at phase 0.38+0.03 (obtained from a Gaussian + background fit)., The pulse is roughly aligned with the pulse observed by OSSE/BATSE \cite{ulmer} 1993) and peaks at phase $0.38\pm0.03$ (obtained from a Gaussian + background fit).
 We have split the integral energy window of 0.75-30 MeV up into 3 smaller energy windows. 0.75-3 MeV. 3-10 MeV and 10-30 MeV and performed similar timing analyses.," We have split the integral energy window of 0.75-30 MeV up into 3 smaller energy windows, 0.75-3 MeV, 3-10 MeV and 10-30 MeV and performed similar timing analyses."
 The modulation significances (Z3-test) found for the 3 energy windows are 3.70.1.0σ and 2.10 respectively. proving the detection of pulsed emission up to at least 10. MeV. The lighteurves are shown in Fig.," The modulation significances $Z_2^2$ -test) found for the 3 energy windows are $3.7\sigma, 4.0\sigma$ and $2.1\sigma$ respectively, proving the detection of pulsed emission up to at least 10 MeV. The lightcurves are shown in ."
2. The 10-30 MeV lightcurve. having at face value à non-significant modulation. shows an indication for an enhancement in the phase range contaming the pulse at lower energies.," The 10-30 MeV lightcurve, having at face value a non-significant modulation, shows an indication for an enhancement in the phase range containing the pulse at lower energies."
 However. a narrower pulse might be visible near phase 0.85. which is absent at lower energies.," However, a narrower pulse might be visible near phase 0.85, which is absent at lower energies."
been calibrated into energy. units using the standard. star observation in order to facilitate comparison between the different bands.,been calibrated into energy units using the standard star observation in order to facilitate comparison between the different bands.
 However the calibration is only approximate due to a lack of a standard. star on the second. night. of observations., However the calibration is only approximate due to a lack of a standard star on the second night of observations.
 We can see from Figure 7. that there is enhanced brightness in the section containing the threading region in all bands in evele 29993. but only in the vellow and. blue in evele 29995.," We can see from Figure \ref{fig:partlc} that there is enhanced brightness in the section containing the threading region in all bands in cycle 29993, but only in the yellow and blue in cycle 29995."
 he section containing those parts of the stream nearest the white dwarf are also bright in evele 29993., The section containing those parts of the stream nearest the white dwarf are also bright in cycle 29993.
 However. in evele 29995 this is only seen in the blue.," However, in cycle 29995 this is only seen in the blue."
 The brightness of the different sections is consistent with the colour ratios [rom Section 4.4.., The brightness of the different sections is consistent with the colour ratios from Section \ref{sec:colourvariations}.
 In Figure 7. the threading region in cvcle 29995 is hotter than that in evele 29093 as the ratio of the vellow to red is greater for evele 290995., In Figure \ref{fig:partlc} the threading region in cycle 29995 is hotter than that in cycle 29993 as the ratio of the yellow to red is greater for cycle 29995.
 ‘This is again consistent with the colour ratios (Section +.4))., This is again consistent with the colour ratios (Section \ref{sec:colourvariations}) ).
 Llowever. the blue to vellow ratio is similar in the two eclipse ingresses suggesting that the increase has occurred in both blue and. vellow bancs.," However, the blue to yellow ratio is similar in the two eclipse ingresses suggesting that the increase has occurred in both blue and yellow bands."
 The model fits of Larrop-Mdlin (1999b) and LHarrop-Allin (1999) for one pole accretion. show a general enhancement in the threading region and owards the white dwarf.," The model fits of Harrop-Allin (1999b) and Harrop-Allin (1999) for one pole accretion, show a general enhancement in the threading region and towards the white dwarf."
 Some eclipses (for example evcle EJ23 and 3724 in Larrop-Allin 1999) show significantly &ereater brightness in the threading region of the white dwarl han others (such as the immediately preceding evcle 3, Some eclipses (for example cycle 3723 and 3724 in Harrop-Allin 1999) show significantly greater brightness in the threading region of the white dwarf than others (such as the immediately preceding cycle 3722).
 Enhanced brightness regions are also found by Vrielmann Schwope (2001) and Ixube ((2000) who apply similar mocelling techniques., Enhanced brightness regions are also found by Vrielmann Schwope (2001) and Kube (2000) who apply similar modelling techniques.
 Vrielmann Schwope (2001) apply their Accretion Stream Mapping echnique to 11. Ls and A oobservations of LL Aqr.," Vrielmann Schwope (2001) apply their Accretion Stream Mapping technique to $\beta$, $\gamma$ and $\lambda$ observations of HU Aqr."
 They find a brightness enhancement at the threading region. but not towards the white dwarf. similar to cvele 29995. so implying that this may be absent in their emission lines.," They find a brightness enhancement at the threading region, but not towards the white dwarf, similar to cycle 29995, so implying that this may be absent in their emission lines."
 Ixube ((2000) used the A line emission from UZ For. with a 3-dimensional stream model.," Kube (2000) used the $\lambda$ line emission from UZ For, with a 3-dimensional stream model."
 They found three regions of enhanced brightness: one on the ballistic accretion Low. and two on the magnetically confined section.," They found three regions of enhanced brightness: one on the ballistic accretion flow, and two on the magnetically confined section."
 They suggest that the enhancements on the magnetically confined section are caused by. irradiation of denser sections of the stream with a Large area near the accretion region. and a smaller region near to the threacding region.," They suggest that the enhancements on the magnetically confined section are caused by irradiation of denser sections of the stream with a large area near the accretion region, and a smaller region near to the threading region."
 Phis may be the case in evele 29993. where we find a bright stream near the white cdwarf. and again near the threading region.," This may be the case in cycle 29993, where we find a bright stream near the white dwarf, and again near the threading region."
 Although Ixube {find no enhancement actually at the threading region. this may be a result of an increase in the density of the stream as it approaches this point. resulting in an increase in the continuum optical depth. and hence a decrease of the A coquivalent width. ancl so is not necessarily indicative of a faint stream at this region.," Although Kube find no enhancement actually at the threading region, this may be a result of an increase in the density of the stream as it approaches this point, resulting in an increase in the continuum optical depth, and hence a decrease of the $\lambda$ equivalent width, and so is not necessarily indicative of a faint stream at this region."
" Lcating of the magnetic section. of the stream has been modelleck by Ferrario Wehlrse (1999) for a stream which is assumed to thread onto the field lines at a coupling radius r, (our £?,,) from the white chvarl. over a racial distance Ar, in the orbital plane."," Heating of the magnetic section of the stream has been modelled by Ferrario Wehrse (1999) for a stream which is assumed to thread onto the field lines at a coupling radius $r_{c}$ (our $R_{\mu}$ ) from the white dwarf, over a radial distance $\Delta r_{c}$ in the orbital plane."
 This provides an opportunity for a comparison between our observationallyv derived results. and the main points of their theoretical model results.," This provides an opportunity for a comparison between our observationally derived results, and the main points of their theoretical model results."
 Ferrario Wehrse. (1909) consider two heating mechanisms: irradiation by the X-ray component from the, Ferrario Wehrse (1999) consider two heating mechanisms: irradiation by the X-ray component from the
of these three CO features is roughly. perpendicular to the alignment of the disk (PA 30ddeg).,of these three CO features is roughly perpendicular to the alignment of the disk (PA deg).
" Thus. they could. be associated with an outllow from source C. A region of dilluse near-infrared emission is found. about 40 north and. 15 ""cast of LR""iH325AD. corresponding to PA of 20ddeg Fig. 85)."," Thus, they could be associated with an outflow from source C. A region of diffuse near-infrared emission is found about 40"" north and 15"" east of IRAS04325AB, corresponding to a PA of deg (see Fig. \ref{f3}) )."
 Thus. definedthis area is located in the extension of the axis bv the elongated emission nebula.," Thus, this area is located in the extension of the axis defined by the elongated emission nebula."
" The feature has been mentioned before in the literature. for example by 2.. and is most. pronounced at 2 to "" our Ix-band. image the feature has a size of 205m""n"," The feature has been mentioned before in the literature, for example by \citet{2002AJ....123.3370P}, and is most pronounced at 2 to $\,\mu$ m. In our K-band image the feature has a size of $20""\times 20""$."
 The proximity to. LRASOL825 ancl the location alone outflow. axis load us to believe that. the feature is physically associated with LRASOL325., The proximity to IRAS04325 and the location along the outflow axis lead us to believe that the feature is physically associated with IRAS04325.
 Under this assumption the physicaldistance from LRASOL825 would be  6000AU., Under this assumption the physical distance from IRAS04325 would be $\sim 6000$ AU.
 This patch of emission could be scattered light at the northernA end of the outllow cavity., This patch of emission could be scattered light at the northern end of the outflow cavity.
 In the LRAC bands at 3.6 and jin a 10-157. wide. dark band is visible between the LRASO4325 nebula and the emission region further north (Fig. S..," In the IRAC bands at 3.6 and $\,\mu$ m a 10-15"" wide, dark band is visible between the IRAS04325 nebula and the emission region further north (Fig. \ref{f3},"
 left panel). possibly a foreground cloud blocking the view to the source.," left panel), possibly a foreground cloud blocking the view to the source."
 At Sym the bright clilfuse pateh in. the north of IRASO4325is not visible. instead the image shows a roughly circular. 1.5« absorption feature centered 707 north and 30 cast of 18504325 (PA 23ddeg). ie. just north of the bright pateh (Fig. δ..," At $\,\mu$ m the bright diffuse patch in the north of IRAS04325 is not visible, instead the image shows a roughly circular, $1.5' \times 1.5'$ absorption feature centered 70"" north and 30"" east of IRAS04325 (PA deg), i.e. just north of the bright patch (Fig. \ref{f3},"
 right panel)., right panel).
 This dark feature has fainter extensions to the east ancl south. overlapping with I325.," This dark feature has fainter extensions to the east and south, overlapping with IRAS04325."
 Hs center is located. along the outllow axis of 325AD., Its center is located along the outflow axis of IRAS04325AB.
 Phe position agrees well with the core L1535 N-SMM seen in the submam maps of LRASOL825 presented by 2.. indicating that this feature represents an overdensity of dust.," The position agrees well with the core L1535 N-SMM seen in the submm maps of IRAS04325 presented by \citet{2000ApJ...534..880H}, indicating that this feature represents an overdensity of dust."
 Lt is possible that the northern lobe of the outllow is blocked by this core. explaining the lack of large-scale outflow features further to the NE(see below)," It is possible that the northern lobe of the outflow is blocked by this core, explaining the lack of large-scale outflow features further to the NE (see below)."
 The dark feature is only visible at S jun. and not at any other wavelength in the mid-infrared.," The dark feature is only visible at $\,\mu$ m, and not at any other wavelength in the mid-infrared."
 In the S jm image it is the only such feature within a radius of one degree.," In the $\,\mu$ m image it is the only such feature within a radius of one degree."
 This may be related to the presence of strong PALL emission bands in the other LRAC bands (e.g.7)., This may be related to the presence of strong PAH emission bands in the other IRAC bands \citep[e.g.][]{2002A&A...390.1089P}.
 lt is conceivable that we see a region of strong absorption projected against the bright PALL background.> as they are often found in the Galactic plane (e.g.?)..," It is conceivable that we see a region of strong absorption projected against the bright PAH background, as they are often found in the Galactic plane \citep[e.g.][]{1998ApJ...494L.199E}."
 In fact. the combination of submm emission and im absorption has been observed for a number of cores in infrared. clark lous (?)..," In fact, the combination of submm emission and $\,\mu$ m absorption has been observed for a number of cores in infrared dark clouds \citep{2009A&A...499..149V}."
 113504325|2402.zs has long been known to drive molecular outllows ," IRAS04325+2402 has long been known to drive molecular outflows \citep{1987ApJ...321..370H,1989ApJ...340..472T,1992ApJ...400..260M}."
Specifically. a large body of evidence is available for an outllow driven.by source AB at position angle of ddeg.," Specifically, a large body of evidence is available for an outflow drivenby source AB at position angle of deg."
. Features associated with this outllow are the elongated. emission. nebula (alsoseeninΕςΟ.2). the scattered light feature LE (Sect. 4.1)).)o," Features associated with this outflow are the elongated emission nebula \citep[also seen in HCO$^+$,][]{1998ApJ...502..315H}, the scattered light feature E (Sect. \ref{s41}) ),"
f the LLL objects 434-4366 about lddeg south-west ppc) n IRAS source at PX of ddeg (2).. and. HITTO south of 138504325 ppc) at PA of ddes (?) We searched in the Hà» images as well as in the LRAC images for more shock features along the outllow axis.," the HH objects 434-436 about deg south-west pc) of the IRAS source at PA of deg \citep{2001AJ....121.1551W}, and HH703 30' south of IRAS04325 pc) at PA of deg \citep{2003ChJAA...3..458S} We searched in the $_2$ images as well as in the IRAC images for more shock features along the outflow axis."
 In particular the Λο band 2 jii) is known to contain a number of bright emission lines of shocked. Hl» (see?.and.referencestherein)..," In particular the IRAC band 2 $\,\mu$ m) is known to contain a number of bright emission lines of shocked $_2$ \citep[see][and references therein]{2009ApJ...695L.120Y}."
 Phe group of Herbig-LHaro objects 434-436. so far only detected in the SH] line and. possibly part of a bow shock (?).. is well-visible in. Hl» and in all four. IRAC bands.," The group of Herbig-Haro objects 434-436, so far only detected in the [SII] line and possibly part of a bow shock \citep{2001AJ....121.1551W}, , is well-visible in $_2$ and in all four IRAC bands."
 In the ym image we find an aciditional knot about 1.1 NN of AD (10000AAU) at PA 14ddeg (a 43536:5. 8. |247002575.Mu (12000). Eig. S..," In the $\,\mu$ m image we find an additional knot about 1.1' north of AB AU) at PA deg $\alpha$ $4^h 35^m 36\fs5$, $\delta$ $+24^{o} 09' 25\farcs5$ (J2000), Fig. \ref{f3},"
 Left panel)., left panel).
 This feature is clearly and not seen at any other wavelength. which argues for an association with the outllow.," This feature is clearly extended and not seen at any other wavelength, which argues for an association with the outflow."
 No other obvious feature was found for PA of 20ddeg and separation from LRASOL325 up to ddeg in both directions., No other obvious feature was found for PA of deg and separation from IRAS04325 up to deg in both directions.
 There is a second large-scale outllow emanating from. IRASOL325|2402. identified by ?2..," There is a second large-scale outflow emanating from IRAS04325+2402, identified by \citet{1987ApJ...321..370H}."
 The outflow is seen in integrated CO emission spanning 12. ic. ppe if related to LRASOL325.," The outflow is seen in integrated CO emission spanning 12', i.e. pc if related to IRAS04325."
 Lt is described as well-collipated. recdshifted. and monopolar.," It is described as well-collimated, redshifted, and monopolar."
 In. clear disagreement to the first. outflow discussed above. this second flow is oriented from the ΗΛ source towards the NW at position angle around ~310 σος. roughly. perpendicular to the disk of source C. The most likely source for this second outflow is object C. This star clearly has jet activity. proven by the variety of outIlow related emission lines in the near-infrared spectrum.," In clear disagreement to the first outflow discussed above, this second flow is oriented from the IRAS source towards the NW at position angle around $\sim 310$ deg, roughly perpendicular to the disk of source C. The most likely source for this second outflow is object C. This star clearly has jet activity, proven by the variety of outflow related emission lines in the near-infrared spectrum."
 Three CO lobes are seen around this object with PA of ddeg. roughly matching the orientation reported. by ? which could belong to the outflow as well.," Three CO lobes are seen around this object with PA of deg, roughly matching the orientation reported by \citet{1987ApJ...321..370H}, which could belong to the outflow as well."
 We do not find any additional counterparts of this outflow in the HI» and the LRAC images., We do not find any additional counterparts of this outflow in the $_2$ and the IRAC images.
 We aim to reproduce the spectral energy distributions (SED) for objects AB and € with a Monte Carlo radiative transfer code., We aim to reproduce the spectral energy distributions (SED) for objects AB and C with a Monte Carlo radiative transfer code.
 In addition to the cata presented. here and in ? we make use of the Spitzer/LRS spectrum. available [or object AB (?)., In addition to the data presented here and in \citet{2008ApJ...681L..29S} we make use of the Spitzer/IRS spectrum available for object AB \citep{2008ApJS..176..184F}.
 Only the SL exposure is used. which is obtained through a 3766 wide slit oriented. roughly in N-S direction and covers the wavelength range from 5.2 to jun. This spectrum matches well with the photomery at jum. We do not use the LL spectrum (obtained through a 10766 slit) and the LRACYAILPS photometry. due to their. poor spatial resolution.," Only the SL exposure is used, which is obtained through a 6 wide slit oriented roughly in N-S direction and covers the wavelength range from 5.2 to $\,\mu$ m. This spectrum matches well with the photomery at $\,\mu$ m. We do not use the LL spectrum (obtained through a 6 slit) and the IRAC/MIPS photometry, due to their poor spatial resolution."
 Our model code computes thermal radiation. and non-spherical scattering from.dust. in a two-dimensional axisvmmoetric svstem with central source. flared disk. and lareer-seale [lattened. envelope. with a narrow evacuated bipolar outllow cavity (e.g.??).. ," Our model code computes thermal radiation and non-spherical scattering fromdust in a two-dimensional axisymmetric system with central source, flared disk, and larger-scale flattened envelope with a narrow evacuated bipolar outflow cavity \citep[e.g.][]{2003ApJ...591.1049W,2003ApJ...598.1079W}. ."
Phe central photospheres, The central photospheres
Evolved low-mass stars show photospheric CNO isotopic ratios that in many cases are not reproduced by stellar evolutionary. codes.,Evolved low-mass stars show photospheric CNO isotopic ratios that in many cases are not reproduced by stellar evolutionary codes.
 In the past vears it was recognized by many authors (Doothrovdetal.1994:Wasserbureοἱ1995:Charbonnel&DoNascimiento1993:Boothrovd&Sackmann1999) (hat these chemical anomalies derive from transport mechanisms linking (he envelope to zones where partial II-burning occurs.," In the past years it was recognized by many authors \citep{boot,wbs,char,sb99}
 that these chemical anomalies derive from transport mechanisms linking the envelope to zones where partial H-burning occurs."
" We call these phenomena ""exüra-müxing or ""deep mixing throughout this report.", We call these phenomena “extra-mixing” or “deep mixing” throughout this report.
 Nollettetal.(2003.hereafterNBW03) presented a parametric study of such mixing episodes. suitable to account for the CNO abundances measured in presolar grains of AGB origin.," \citet[][hereafter NBW03]{nol} presented a parametric study of such mixing episodes, suitable to account for the CNO abundances measured in presolar grains of AGB origin."
 The adopted formalism was based on (wo parameters. namely the rate of mass transport (M) and the temperature (Tp) of the deepest zones reached by the circulation.," The adopted formalism was based on two parameters, namely the rate of mass transport $\dot{M}$ ) and the temperature $T_P$ ) of the deepest zones reached by the circulation."
 It was also demonstrated that important composition changes can occur without introducing feedbacks on the stellar luminosity. provided 7» is kept low enough (tvpicallv. Alog7=logTi—logTp 0.08—0.1. where Zi is the temperature al which the maximum enerev of the II-burning shell is released).," It was also demonstrated that important composition changes can occur without introducing feedbacks on the stellar luminosity, provided $T_P$ is kept low enough (typically, $\Delta \log~ T = \log~T_{\rm H} - \log~T_P \gtrsim$ $-$ 0.1, where $T_{\rm H}$ is the temperature at which the maximum energy of the H-burning shell is released)."
" Subsequently, physical models for extra-mixing have been explored. which avoid the difficulties previously found with rotationally-induced mechanisms (Palaciosetal.2006)."," Subsequently, physical models for extra-mixing have been explored, which avoid the difficulties previously found with rotationally-induced mechanisms \citep{pal}."
. In particular. hvdrodyvnamical models of diffusive processes induced by variations of the mean molecular weight ji (Stothers&Simon1969).. called (Charbonnel&Zahn 2007).. were presented by Egegletonοἱal.(2006. 2008).," In particular, hydrodynamical models of diffusive processes induced by variations of the mean molecular weight $\mu$ \citep{ss69}, called \citep{cz07}, were presented by \citet{egg1,egg2}. ."
. They showed that “Le burning into !IHe and two protons successhully induces the required ji inversion (t/jo— +). thus driving mixing episodes.," They showed that $^3$ He burning into $^4$ He and two protons successfully induces the required $\mu$ inversion $\Delta \mu/\mu \simeq -$ $^{-4}$ ), thus driving mixing episodes."
 Complementarilv. Dussoοἱal.(2007)... Nordhausοἱ(2003). and Denissenkovοἱal.(2009) suggested Chat extra-mixing might be driven by magnetic buovancy. in a dynamo process operating below the envelope.," Complementarily, \citet{bwnc}, \citet{nord} and \citet{den} suggested that extra-mixing might be driven by magnetic buoyancy, in a dynamo process operating below the envelope."
 The modelbv NDBWO03 referred explicitly to AGB stars. which are known to be the," The modelby NBW03 referred explicitly to AGB stars, which are known to be the"
"slab, as a function of the different physical and geometrical parameters.","slab, as a function of the different physical and geometrical parameters."
" Having these four different methods to solve the RTE at our disposal proves to be very useful, not only to check the accuracy of the numerical results, as already mentioned, but also to understand the physical background of observed phenomena."," Having these four different methods to solve the RTE at our disposal proves to be very useful, not only to check the accuracy of the numerical results, as already mentioned, but also to understand the physical background of observed phenomena."
" In order to construct disc galaxy models we have to characterize the functions that appear in the RTE (1), sspecify the physical properties and spatial distribution of stars and dust."," In order to construct disc galaxy models we have to characterize the functions that appear in the RTE (1), specify the physical properties and spatial distribution of stars and dust."
 We will adopt a set of realistic galaxy models with a number of parameters., We will adopt a set of realistic galaxy models with a number of parameters.
 Varying these parameters will then enable us to investigate the influence of scattering and geometry on the attenuation curve., Varying these parameters will then enable us to investigate the influence of scattering and geometry on the attenuation curve.
 We will also adopt a template model to compare other models with., We will also adopt a template model to compare other models with.
" Although it has been shown that the physical properties of dust in different environments can vary greatly (Witt et 11984, Mathis Cardelli 1992), we will assume, for sake of simplicity, one single kind of dust grains."," Although it has been shown that the physical properties of dust in different environments can vary greatly (Witt et 1984, Mathis Cardelli 1992), we will assume, for sake of simplicity, one single kind of dust grains."
 This means that the spatial and wavelength dependencies of all quantities appearing in (1) are separable., This means that the spatial and wavelength dependencies of all quantities appearing in (1) are separable.
" In particular, the dust albedo and the ARF are then independent of position."," In particular, the dust albedo and the ARF are then independent of position."
 To describe general anisotropic (conservative) scattering we adopt Henyey-Greenstein scattering (Henyey Greenstein 1941)., To describe general anisotropic (conservative) scattering we adopt Henyey-Greenstein scattering (Henyey Greenstein 1941).
" The ARF corresponding to this kind of scattering is a one-parameter function parametrized by the asymmetry parameter g, which is the average of the cosine of the scattering angle."," The ARF corresponding to this kind of scattering is a one-parameter function parametrized by the asymmetry parameter $g$, which is the average of the cosine of the scattering angle."
" A closed expression and a plot of the Henyey-Greenstein ARF can be found in Appendix A of Paper I. In Section4 other kinds of scatterings such as forward and isotropic scattering, will be compared with Henyey-Greenstein scattering."," A closed expression and a plot of the Henyey-Greenstein ARF can be found in Appendix A of Paper I. In Section other kinds of scatterings such as forward and isotropic scattering, will be compared with Henyey-Greenstein scattering."
" There are two ways to determine the wavelength dependence of the albedo w, the asymmetry parameter g and the total optical depth 7o."," There are two ways to determine the wavelength dependence of the albedo $\omega$, the asymmetry parameter $g$ and the total optical depth $\tau_0$."
" On the one hand, values can be derived theoretically, by assuming a certain dust grain composition and calculating the optical properties of the dust DDraine Lee 1984)."," On the one hand, values can be derived theoretically, by assuming a certain dust grain composition and calculating the optical properties of the dust Draine Lee 1984)."
" On the other hand, optical properties can be derived empirically, usually based on a variety of observations of scattered light in the Galaxy BBruzual et 11988)."," On the other hand, optical properties can be derived empirically, usually based on a variety of observations of scattered light in the Galaxy Bruzual et 1988)."
" Our data set consists of the optical properties theoretically derived by Maccioni Perinotto (1994), displayed in Di Bartolomeo et ((1995)."," Our data set consists of the optical properties theoretically derived by Maccioni Perinotto (1994), displayed in Di Bartolomeo et (1995)."
 The adopted values are tabulated in table for the central wavelengths of various bands., The adopted values are tabulated in table for the central wavelengths of various bands.
 The vertical distribution of stars in disc galaxies is still a matter of debate., The vertical distribution of stars in disc galaxies is still a matter of debate.
 The most straightforward way to derive such a vertical distribution is to study the surface brightness of edge-on galaxies at different heights above the plane., The most straightforward way to derive such a vertical distribution is to study the surface brightness of edge-on galaxies at different heights above the plane.
 'There is a general consensus that at great heights the light distribution decreases exponentially., There is a general consensus that at great heights the light distribution decreases exponentially.
" Close to the plane of the galaxy however, dust attenuation makes the observation of the vertical distribution difficult."," Close to the plane of the galaxy however, dust attenuation makes the observation of the vertical distribution difficult."
" As a consequence, different models have been proposed."," As a consequence, different models have been proposed."
 The most popular models are an isothermal sheet distribution (van der Kruit Searle 1981) and an exponential profile (Wainscoat et 11989)., The most popular models are an isothermal sheet distribution (van der Kruit Searle 1981) and an exponential profile (Wainscoat et 1989).
" In order to allow a wide range in vertical density distributions, we adopt a two-parameter family of stellar emissivity profiles which were adapted from van der Kruit (1988), where the function B(«,y) in the represents the Beta function (Abramowitz Stegun 1972)."," In order to allow a wide range in vertical density distributions, we adopt a two-parameter family of stellar emissivity profiles which were adapted from van der Kruit (1988), where the function $B(x,y)$ in the represents the Beta function (Abramowitz Stegun 1972)."
 The first factor is determined such that the normalization condition (5)) is, The first factor is determined such that the normalization condition \ref{normeta}) ) is
the z~0.685 absorber is given by Murphyetal.(2008a)..,the $z \sim 0.685$ absorber is given by \citet{murphy08}.
 These include the following: (1) the assumption that different, These include the following: (1) the assumption that different
come in several variants. and may be finetuned. from the web-page of Dr. For our purposes. we restrict ourselves to mocdoels with a Salpeter initial mass function. with the assumption of a single. instantaneous burst of star formation.,"come in several variants, and may be fine–tuned from the web-page of Dr. For our purposes, we restrict ourselves to models with a Salpeter initial mass function, with the assumption of a single, instantaneous burst of star formation."
 However. the erids used in this study diller from the original Worthey 994) models in one important respect. which is in their Eeeatment of the horizontal branches (M1Bs) for metal-poor αςobular clusters.," However, the grids used in this study differ from the original Worthey (1994) models in one important respect, which is in their treatment of the horizontal branches (HBs) for metal-poor globular clusters."
 The morphology of the LIB now follows he observed. behaviour of the GGCSs. in that they become more extended. toward. the blue. for. more. metal-poor elobular clusters. as opposed. to assuming a red clump at he base of the LLB irrespective of metallicity.," The morphology of the HB now follows the observed behaviour of the GGCs, in that they become more extended toward the blue for more metal-poor globular clusters, as opposed to assuming a red clump at the base of the HB irrespective of metallicity."
 The CGGCSs AIS and M92 were used as templates for this behaviour (e.g. Aaronson LOTS - for further discussion see Worthey 1993)., The GGCs M3 and M92 were used as templates for this behaviour (e.g. Aaronson 1978 - for further discussion see Worthey 1993).
 This change significantly increases the predicted L3 index by upwards of 0.5 aab Fel] < -0.5 dex., This change significantly increases the predicted $\beta$ index by upwards of 0.5 at [Fe/H] $\leq$ -0.5 dex.
 Pig., Fig.
 10. illustrates this elfect and its importance with regard to the predicted ages for elobular clusters. of which a substantial population have sub-solar abundances.," \ref{fig:grids} illustrates this effect and its importance with regard to the predicted ages for globular clusters, of which a substantial population have sub-solar abundances."
 A globular. cluster with a measured. F05270 index of 1.5 and 1 index of 24 wavoulcd be assigned an age of S Gyr according to the old models. but is predicted to be z 17 Gyr old by the models using the new LLB morphology.," A globular cluster with a measured Fe5270 index of 1.5 and $\beta$ index of 2.4 would be assigned an age of 8 Gyr according to the old models, but is predicted to be $\geq$ 17 Gyr old by the models using the new HB morphology."
 As a case in point. it is interesting to compare the 1112 indices of GGC's at the same metallicity. but with cillering WB morphologies.," As a case in point, it is interesting to compare the $\beta$ indices of GGCs at the same metallicity, but with differing HB morphologies."
 One of our calibrating GGC's is ALLS (NGC 6205). for which we have measured L3 — 2.40A.. and has a HB ratio of approximately unity (ellectively it," One of our calibrating GGCs is M13 (NGC 6205), for which we have measured $\beta$ = 2.40, and has a HB ratio of approximately unity (effectively it"
phase zero correspouds to the inferior conjunctiou of the secoudary star.,phase zero corresponds to the inferior conjunction of the secondary star.
 The light curve is similar to that found by Woudt.Warner.&Pretorius(2001)., The light curve is similar to that found by \citet{woudtwarner}.
. Mininun light corresponds closely with iuferior conjunction. as expected for a heating effect.," Minimum light corresponds closely with inferior conjunction, as expected for a heating effect."
 The 8—V aud V—/ colors are a also modulated. with the star bluest at maximum light.," The $B-V$ and $V-I$ colors are a also modulated, with the star bluest at maximum light."
 The curves in Fig., The curves in Fig.
 | are from a model described later., 4 are from a model described later.
 We rectified all the spectra aid. created the phase-averaged greyscale representatiou slow in Fig., We rectified all the spectra and created the phase-averaged greyscale representation shown in Fig.
 5., 5.
 The most remarkable feature is the complete absence ofeng eiilssion lines., The most remarkable feature is the complete absence of emission lines.
 Cirevscale represeutations ofthis kind cau sometimes brine out subtle spectral features. but this looks remarkably ordinary.," Greyscale representations of this kind can sometimes bring out subtle spectral features, but this looks remarkably ordinary."
 There is also uo strong modulation of the spectrum arouud the orbit., There is also no strong modulation of the spectrum around the orbit.
 The coverage is unfortunately uouuniform (refer to Fig., The coverage is unfortunately nonuniform (refer to Fig.
 3): for a portion of the figure around. phase 1. ouly one observation coutributes. so the data remain unchauged with phase.," 3); for a portion of the figure around phase 1, only one observation contributes, so the data remain unchanged with phase."
 However. coverage is deusest ou the clesceucling side of the velocity curve. which corresponds to superior conjunction of the secondary.," However, coverage is densest on the descending side of the velocity curve, which corresponds to superior conjunction of the secondary."
 This is the portion of the orbit where the heate [ace of the secoudary is turued towar is. and we still do uot see any emission lines.," This is the portion of the orbit where the heated face of the secondary is turned toward us, and we still do not see any emission lines."
 To estimate the mean spectral type of the secoucdary. we used the spectral decompositioi »xocedure outlined in Thorsteusen.Fenton.&Taylor(2001).. basically subtracting scaled versious ol spectral-type standard stars away from the mean spectrum. aud lookiug for good cancellation of he late-type features.," To estimate the mean spectral type of the secondary we used the spectral decomposition procedure outlined in \citet{longp03}, basically subtracting scaled versions of spectral-type standard stars away from the mean spectrum, and looking for good cancellation of the late-type features."
 The Ix- aud M-dwarf library spectra taken with the same instrument prove o be too cool to match. so we used Ci-type library spectra from Jacoby. (1981)..," The K- and M-dwarf library spectra taken with the same instrument proved to be too cool to match, so we used G-type library spectra from \citet{jacoby}."
 These matched. reasonably well arouud mid-G. but with a siguificaut. mismatch at the sodium D lines. which are stronger than they should be for the spectral type.," These matched reasonably well around mid-G, but with a significant mismatch at the sodium D lines, which are stronger than they should be for the spectral type."
 The decomposition was cousistent withaff the light coming from the secoucdary star — there was uo need to include any contribution from a hot component., The decomposition was consistent with the light coming from the secondary star – there was no need to include any contribution from a hot component.
 This conclusion is corroborated by the colors in Table 2. anc the V—H and V—J colors found by combining the present data with the / auc A maeuituces from the 2MAÀSS All Sky Data Release.," This conclusion is corroborated by the colors in Table 2, and the $V-H$ and $V-J$ colors found by combining the present data with the $J$ and $H$ magnitudes from the 2MASS All Sky Data Release."
 Pickles(1908). tablates normal Cidwarf colors in many passbaucls. aud the observed colors are all consistent with a type between G5 aud G7.," \citet{pickles}
 tabulates normal G-dwarf colors in many passbands, and the observed colors are all consistent with a type between G5 and G7."
 Remarkably. this is even true for the Ü-band. in which one might expect to start seeing a lot compouent if one were present.," Remarkably, this is even true for the $U$ -band, in which one might expect to start seeing a hot component if one were present."
 Although the pliase-averaged spectrum is not sensitive enough to show spectraltype variation. the color modulation correspouds to a hall-amplitude of around 3 subtypes. correspoucine to 7180 kelvin arouid mic-C. The remarkable light. auc color curve of this system motivated us to construct a light-curve mocleling program.," Although the phase-averaged spectrum is not sensitive enough to show spectral-type variation, the color modulation corresponds to a half-amplitude of around 3 subtypes, corresponding to $\sim
180$ kelvin around mid-G. The remarkable light and color curve of this system motivated us to construct a light-curve modeling program."
 In our model. the secondary ills its Roche critical lobe. as CV secoucdaries eenerally do: although mass trausfer was not evident curing our observations. the secoudary should still nearly. fill its Roche lobe. since tlie system was actively transferring mass within the last few years aud the Welvin-Helinholtz relaxation time of tlie secondarys envelope should be much louger than that.," In our model, the secondary fills its Roche critical lobe, as CV secondaries generally do; although mass transfer was not evident during our observations, the secondary should still nearly fill its Roche lobe, since the system was actively transferring mass within the last few years and the Kelvin-Helmholtz relaxation time of the secondary's envelope should be much longer than that."
5truei Strucin clures clures clures clures cur1) clussilü ον CLUSSS ciusshbxlO 1102 ciutir clurd cutis clures ,"5truein 8truein cmr8 cmr8 cmr8 cmr8 cmr10 cmssi10 cmss10 cmss8 cmssbx10 2 cmti7 cmr6 cmti8 cmr8 \def\ref{\par\noindent\hangindent 15pt}
 "
This discrepancy between models aud helioseisiiic inferences has prompted a muuber of authors to revise the plwsical inputs of SSAMs (Moutalbáu 2009).. aud to question the revision of the solar abundances. particularly those of C. N. O. Ne and Ar whose fractional abuudauces cannot be determined from micteoritic samples (Antia& 2008).,"This discrepancy between models and helioseismic inferences has prompted a number of authors to revise the physical inputs of SSMs \citep{montalban,basu04,bbps05,guzik06,jcd09}, and to question the revision of the solar abundances, particularly those of C, N, O, Ne and Ar whose fractional abundances cannot be determined from meteoritic samples \citep{ab05,ab06,bbs05,dp06,ba08}."
. Verv recently. Asplundetal.(2009.here-afterAGSSO9) have done a complete revision of the solar plotospheric abuudauces for nearly all elements. including a new 3D hydrodyuanical solar atmosphere model with improved radiative transfer and opacities (Trampedachctal.2009).," Very recently, \citet[hereafter AGSS09]{agss09} have done a complete revision of the solar photospheric abundances for nearly all elements, including a new 3D hydrodynamical solar atmosphere model with improved radiative transfer and opacities \citep{tramp09}."
. The predictions from this 3D model have been shown to agree remarkably well with various observational constraints. includiue the atmospheric thermal structure as judged from contiuuuua ceuter-to-linh variation aud detailed line profile shapes (Pereiractal. 2009a.b)..," The predictions from this 3D model have been shown to agree remarkably well with various observational constraints, including the atmospheric thermal structure as judged from continuum center-to-limb variation and detailed line profile shapes \citep{pereira09a,pereira09b}. ."
" The newly determined solar abundances lead to (Z/N).= 0.0178. higher than the ACSOS value but still well below older determinations. e.g. CSOs,"," The newly determined solar abundances lead to $(Z/X)_{\odot}=0.0178$ , higher than the AGS05 value but still well below older determinations, e.g. GS98."
" In this Letter we present a series of new SSAL caleulatious using solu compositions frou. GS9s, AGSOS. and the newly determined solar abunudauces by ACSSO9,"," In this Letter we present a series of new SSM calculations using solar compositions from GS98, AGS05, and the newly determined solar abundances by AGSS09."
 Allthe models incorporate new refinements m the input physics. so that models preseuted here with the older compositions (GSOS and AGSOS) represent. updated versions of previous solar model calenlatious (Bahealletal. 2005).," All the models incorporate new refinements in the input physics, so that models presented here with the older compositions (GS98 and AGS05) represent updated versions of previous solar model calculations \citep{bs05}."
. For each model. we compare our results with helioseimmological deteriinatious of solar properties and also give the predicted solar neutrino fluxes.," For each model, we compare our results with helioseismological determinations of solar properties and also give the predicted solar neutrino fluxes."
 Additionally. aud motivated by the new AGSSOO. composition. we determine the factor by which radiative opacities in the solar interior should be increased to solve the solar abundance problem following the scheme presented by Cliisteuscu-Dalseaardetal.(2009).," Additionally, and motivated by the new AGSS09 composition, we determine the factor by which radiative opacities in the solar interior should be increased to solve the solar abundance problem following the scheme presented by \citet{jcd09}."
. Solar models in this work have beeu computed withE a; modifiedfe versionOpe) of° GARSTEC1ISTEC (WeissΌλος&Schluttl2008) that uses the nuclear OLOYOV ecneration routineeportenengy., Solar models in this work have been computed with a modified version of GARSTEC \citep{garstec} that uses the nuclear energy generation routine.
P... Eleweout diffision in the solar interior is included according to Thouletal.(1991)., Element diffusion in the solar interior is included according to \citet{tbl94}.
". Radiative opacities are from the Opacity Project. complemented at low temperatures with those frou, Fergusonctal.(2005)."," Radiative opacities are from the Opacity Project, complemented at low temperatures with those from \citet{lowt}."
. Specific sets of opacities have been computed for cach of the solar compositious used in this paper (see below)., Specific sets of opacities have been computed for each of the solar compositions used in this paper (see below).
" With respect to orevious works. ce. Balealletal.(2005,2006).. i6 changes in the input plysics are: a revised version of the OPAL equation of (EOS) iat corrects errors in the 2002 OPAL EOS tables rom) Rogers&Nayfonov(2002) (our previous choice). and updated values of two iuportaut melear astrophysical factors. $5, (Costantinietal.2008) and 5,44 (Martaetal.2008}.. the latest determinations by the LUNA experiment."," With respect to previous works, e.g. \citet{bs05,montecarlo}, the changes in the input physics are: a revised version of the OPAL equation of (EOS) that corrects errors in the 2002 OPAL EOS tables from \citet{opal01} (our previous choice), and updated values of two important nuclear astrophysical factors, $_{34}$ \citep{s34} and $_{1,14}$ \citep{s114}, the latest determinations by the LUNA experiment."
 We lave computed solar models uxiug three different basic solar abundances., We have computed solar models using three different basic solar abundances.
 Two models eniplov previous solar abundance compilations (GS98 and ACSO5) iud show small differences witli respect to models with the same abundances oeseuted: clsewhere. c.g. Dahlicalletal.(2005).," Two models employ previous solar abundance compilations (GS98 and AGS05) and show small differences with respect to models with the same abundances presented elsewhere, e.g. \citet{bs05}."
. The changes originate from the use of the updatec EOS aud cross-sections for unclear reactions nentioucd above., The changes originate from the use of the updated EOS and cross-sections for nuclear reactions mentioned above.
 A third SSM has been computcc adopting the new solar composition determines wv AGSSOD., A third SSM has been computed adopting the new solar composition determined by AGSS09.
 The most iniportant. results in this work are related to this model, The most important results in this work are related to this model.
 The choice of he abnudauce scale (neteoritie or photospheric} deserves a short discussion., The choice of the abundance scale (meteoritic or photospheric) deserves a short discussion.
 While ACGSSO9 fin he average difference between photospheric aux neteoritic abundauces to be 0.00+0.01 dex. a ow clemcuts relevant to detailed solu modcling show comparable or slightlv larger deviations.," While AGSS09 find the average difference between photospheric and meteoritic abundances to be $0.00 \pm 0.04$ dex, a few elements relevant to detailed solar modeling show comparable or slightly larger deviations."
" This is the case for Mg. Ca, and Fe for which differences between the two scales are 0.07. 0.05. aud 0.05 dex respectively. photospleric values being larger."," This is the case for Mg, Ca, and Fe for which differences between the two scales are 0.07, 0.05, and 0.05 dex respectively, photospheric values being larger."
 Given the historical robustuess aud higher accuracyof metcoritic deteriiuations of abundance ratios. and the present execlleut overall agreement with photospherie abundances.," Given the historical robustness and higher accuracyof meteoritic determinations of abundance ratios, and the present excellent overall agreement with photospheric abundances,"
"For the various solutions attempted, xà“educed 81€ found the same (Table A2)).","For the various solutions attempted, $\chi^2_\mathrm{reduced}$ are found the same (Table \ref{tab:WASP2comp}) )."
" We therefore choose the priorless, circular adjustment as our solution."," We therefore choose the priorless, circular adjustment as our solution."
" Compared to ?, parameters have only changed little."," Compared to \citet{West:2009p2783}, parameters have only changed little."
 Thanks to the higher number of points we give an upper limit on eccentricity: e«0.087 (Fig., Thanks to the higher number of points we give an upper limit on eccentricity: $e < 0.087$ (Fig.
" 5cc shows results consistent with zero); there is no evident long term evolution in the radial velocities, which is constrained within: |y|«11 ! yyr!"," \ref{fig:WASP15dis}c c shows results consistent with zero); there is no evident long term evolution in the radial velocities, which is constrained within: $| \dot{\gamma} | < 11$ $^{-1}$ $^{-1}$."
 The projected spin-orbit angle is found rather large with B=139.6°*}3 making WASP-15b appear as a retrograde planet with a very clear detection.," The projected spin-orbit angle is found rather large with $\beta = 139.6^{\circ\,+5.2}_{\,\,\,\,-4.3}$ making WASP-15b appear as a retrograde planet with a very clear detection."
 Vsin/is found within 1c of the spectrally analysed value of from? at 4.27*026-0.36 ss! and as such constitutes a precise independent measurement.," $V\sin I$is found within $1\,\sigma$ of the spectrally analysed value of from \citet{West:2009p2783} at $4.27^{+0.26}_{-0.36}$ $^{-1}$ and as such constitutes a precise independent measurement."
" X2tuceq=1.51+0.19 for the spectroscopy, indicating a good fit of the Keplerian as well as of the Rossiter-McLaughlin effect, the best fit in this paper."," $\chi^2_ \mathrm{reduced}=1.51\pm0.19$ for the spectroscopy, indicating a good fit of the Keplerian as well as of the Rossiter-McLaughlin effect, the best fit in this paper."
 Full results can be seen in Table 3.., Full results can be seen in Table \ref{tab:params}.
" On 2009 May 22, 11 CORALIE spectra were obtained at a cadence of 2030s with an average precision of 33.67 ss! to confirm the detection of retrograde orbital motion announced by ?.."," On 2009 May 22, 11 CORALIE spectra were obtained at a cadence of 2030s with an average precision of $33.67$ $^{-1}$ to confirm the detection of retrograde orbital motion announced by \citet{Anderson:2010p5177}."
 The sequence was stopped when airmass reached 2., The sequence was stopped when airmass reached 2.
 HARPS was subsequently used and on 2009 July 5 a sequence of 42 spectra was acquired with a cadence of 630s during transit., HARPS was subsequently used and on 2009 July 5 a sequence of 42 spectra was acquired with a cadence of 630s during transit.
 They have a mean precision of 19.02 mmss'!., They have a mean precision of $19.02$ $^{-1}$.
 In addition to these and to data already published 12 CORALIE spectra and 15 HARPS spectra were obtained., In addition to these and to data already published 12 CORALIE spectra and 15 HARPS spectra were obtained.
 All the spectroscopic data is presented in the appendices., All the spectroscopic data is presented in the appendices.
" The photometry includes five timeseries of data in the WASP bandpass, and one C2 Euler I band transit (?).."," The photometry includes five timeseries of data in the WASP bandpass, and one $C2$ $Euler$ $I$ band transit \citep{Anderson:2010p5177}. ."
 The model had to adjust up to 10 free floating parameters and 10 adjustment parameters (6 photometric normalisation, The model had to adjust up to 10 free floating parameters and 10 adjustment parameters (6 photometric normalisation
The solar five-minute oscillations have provided à wealth of information on the internal structure of the Sun.,The solar five-minute oscillations have provided a wealth of information on the internal structure of the Sun.
 These results stimulated various attempts to obtain similar. observations for other solar-type stars., These results stimulated various attempts to obtain similar observations for other solar-type stars.
 In past years. the spectrographs developed for extra-solar planet search have finally achieved the accuracy needed to detect solar-like oscillations on other stars (seee.g.2).," In past years, the spectrographs developed for extra-solar planet search have finally achieved the accuracy needed to detect solar-like oscillations on other stars \citep[see e.g.][]{bed08}."
 In addition to. these. ground-based observations. photometric measurements of solar-like oscillations are also obtained from space. thanks to the CoRoT and the Kepler space missions.," In addition to these ground-based observations, photometric measurements of solar-like oscillations are also obtained from space, thanks to the CoRoT and the Kepler space missions."
 All these observations of oscillations for solar-type stars stimulate the theoretical study of the effects of various physical processes on the asteroseismic properties of these stars., All these observations of oscillations for solar-type stars stimulate the theoretical study of the effects of various physical processes on the asteroseismic properties of these stars.
 Rotation is one of the key processes that influences all outputs of stellar models with a specially strong impact on the physies and evolution of massive stars e.g. 22)..," Rotation is one of the key processes that influences all outputs of stellar models with a specially strong impact on the physics and evolution of massive stars \citep[see e.g.][]{zah92, mae09}."
 In this work. we study the effects of rotational mixing on the evolution and asteroseismic properties of solar-type stars by comparing stellar models including shellular rotation. to non-rotating models.," In this work, we study the effects of rotational mixing on the evolution and asteroseismic properties of solar-type stars by comparing stellar models including shellular rotation to non-rotating models."
 The influence of internal magnetic fields is also discussed in the context of a dynamo that possibly occurs in the radiative zone by computing stellar models including the Tayler-Spruit dynamo (?).., The influence of internal magnetic fields is also discussed in the context of a dynamo that possibly occurs in the radiative zone by computing stellar models including the Tayler-Spruit dynamo \citep{spr02}.
 The modelling of rotation is presented in Sect., The modelling of rotation is presented in Sect.
 2., 2.
 The effects of rotational mixing and internal magnetic fields on the evolution and asteroseismic properties of solar-type stars are discussed in Sect., The effects of rotational mixing and internal magnetic fields on the evolution and asteroseismic properties of solar-type stars are discussed in Sect.
 43. while the conclusior is given in Sect.," 3, while the conclusion is given in Sect."
 4., 4.
 In this section. we briefly summarise the basic physical ingredients of numerical models of rotating stars.," In this section, we briefly summarise the basic physical ingredients of numerical models of rotating stars."
 Meridional circulation is generated in the radiative zone of a rotating star às a result of the thermal imbalance inducec by the breaking of the spherical symmetry (?2).. structural adjustments and surface extraction of angular momentum (?)..," Meridional circulation is generated in the radiative zone of a rotating star as a result of the thermal imbalance induced by the breaking of the spherical symmetry \citep{edd25, vog26}, structural adjustments and surface extraction of angular momentum \citep{dec09}."
 Transporting matter and angular momentum. this circulation creates differential rotation in the radiative zones. which makes the stellar interior highly turbulent.," Transporting matter and angular momentum, this circulation creates differential rotation in the radiative zones, which makes the stellar interior highly turbulent."
 This turbulence is assumed to be much stronger in the horizontal than in the vertical direction (?2).," This turbulence is assumed to be much stronger in the horizontal than in the vertical direction \citep{tas83, zah92}."
. The horizontal turbulent coupling favours ài essentially constant angular velocity Q on the isobars., The horizontal turbulent coupling favours an essentially constant angular velocity $\Omega$ on the isobars.
 With this hypothesis of shellular rotation. every quantity depends solely on pressure and can be split into à mean value and its latitudinal perturbation where P>(cos0) is the second Legendre polynomial.," With this hypothesis of shellular rotation, every quantity depends solely on pressure and can be split into a mean value and its latitudinal perturbation where $P_2(\cos \theta)$ is the second Legendre polynomial."
 In the framework of shellular rotation. the transport of angular momentum obeys an advection-diffusion equation (22): where r is the characteristic radius of the isobar. p the mean density on an isobar. O(r) the mean angular velocity at level r and D is the diffusion coefhicient associated to the transport of," In the framework of shellular rotation, the transport of angular momentum obeys an advection-diffusion equation \citep{zah92, mae98}: where $r$ is the characteristic radius of the isobar, $\rho$ the mean density on an isobar, $\Omega(r)$ the mean angular velocity at level $r$ and $D$ is the diffusion coefficient associated to the transport of"
progressively more tangential. but it is impossible to drive the svstem at frequencies higher than the maximum response [requcney of apy. corresponding to completely vertical oscillations.,"progressively more tangential, but it is impossible to drive the system at frequencies higher than the maximum response frequency of $\omega_{\rm BV}$, corresponding to completely vertical oscillations."
 This thus implies that waves driven at frequencies w«vpy can be resonantly excited. and. must propagate inward toward the cluster center (as can be seen from their group velocity: 2)). where they will be trapped. reflected: ancl focused. inside the resonance radius where way=w.," This thus implies that waves driven at frequencies $\omega < \omega_{\rm BV}$ can be resonantly excited, and must propagate inward toward the cluster center (as can be seen from their group velocity; \citet{balbus90}) ), where they will be trapped, reflected and focused inside the resonance radius where $\omega_{\rm BV}=\omega$."
 A linear analysis by ? showed that most of the power in g-modes is in the longestwavelongtlst., A linear analysis by \citet{balbus90} showed that most of the power in $g$ -modes is in the longest.
. Note that both z (which depencds on the orbital frequencies of galaxies) and wpy are sensitive to the gravitational potential. which is instrumental in determining if e&-mocoes will be excited.," Note that both $\omega$ (which depends on the orbital frequencies of galaxies) and $\omega_{\rm BV}$ are sensitive to the gravitational potential, which is instrumental in determining if g-modes will be excited."
 Turbulence in the Iluid has to compete with buovaney forces arising from. stable stratification., Turbulence in the fluid has to compete with buoyancy forces arising from stable stratification.
 One can show that the ratio of tangential ancl racial velocities is given by (6.8... see discussion in §22 of ?)): where wp=erfh is the eddy turnover frequency al a given scale. and Fr is the Froude number. which compares inertial ancl gravitational forces (Iuαμ is the Richarcson number)," One can show that the ratio of tangential and radial velocities is given by (e.g., see discussion in 2 of \citet{ruszkowski10}) ): where $\omega_{\rm L}=v/L$ is the eddy turnover frequency at a given scale, and Fr is the Froude number, which compares inertial and gravitational forces ${\rm Ri} \sim 1/{\rm Fr}^{2}$ is the Richardson number)."
 Ifa<way. then turbulence is fundamentally 2D. and for instance it is dilficult to rearrange maenetic fields in the racial direction.," If $\omega \ll \omega_{\rm BV}$, then turbulence is fundamentally 2D, and for instance it is difficult to rearrange magnetic fields in the radial direction."
" However. the level of turbulence required to overcome stable stratification is weak: for typical cluster conditions the critical turbulent. velocity is (7): where gx is the gravitational acceleration in units of 10ems""- 4o ds a characteristic scale height in units of 10 kpe. and H4. is the eritical Richardson number: H4.~1/4 is typical for hydrodynamic Low."," However, the level of turbulence required to overcome stable stratification is weak; for typical cluster conditions the critical turbulent velocity is \citep{sharma09b}: where $g_{-8}$ is the gravitational acceleration in units of $10^{-8} \, {\rm cm^{2} s^{-1}}$, $r_{10}$ is a characteristic scale height in units of $10$ kpc, and $Ri_{c}$ is the critical Richardson number; $Ri_{c} \sim 1/4$ is typical for hydrodynamic flow."
 At first blush. the requirement for brc1 migh seen to be at odds. with the requirement that w=<wpy lor g modes to be excited.," At first blush, the requirement for ${\rm Fr} \gsim 1$ might seem to be at odds with the requirement that $\omega < \omega_{\rm BV}$ for $g$ modes to be excited."
 However. note that. lor homogeneous Wolmogoroy turbulence. wpxL ο.” therefore. conceivable that low [requenev. e-moces can be excited on large scales. while high-frequency: small-scale modes can overcome stabilizing buovancy forces.," However, note that for homogeneous Kolmogorov turbulence, $\omega_{\rm L} \propto L^{-2/3}$; it is therefore conceivable that low frequency g-modes can be excited on large scales, while high-frequency small-scale modes can overcome stabilizing buoyancy forces."
 Since our background state is not homogeneous. we have to resort to 3D simulations to νο if this expectation is indeed satisfied.," Since our background state is not homogeneous, we have to resort to 3D simulations to verify if this expectation is indeed satisfied."
 his is à major goal of this paper., This is a major goal of this paper.
 CG-modes./ excite vorticity., G-modes excite vorticity.
 An easy. way to see this is to examine the vorticity evolution form of the momentum equation for g-waves (1.0. assuming 07P« dpfp) (7): where Q is the vorticity. and to note that k is in general non-radial. so that ko.g is non-zero (indeed. we see in Fig.," An easy way to see this is to examine the vorticity evolution form of the momentum equation for $g$ -waves (i.e., assuming $\delta P/P \ll \delta \rho/\rho$ ) \citep{lufkin95}: where ${\bf \Omega}$ is the vorticity, and to note that ${\bf k}$ is in general non-radial, so that ${\bf k} \times {\bf g}$ is non-zero (indeed, we see in Fig."
 2 that since wfwpy rises toward the center. that. e-mocdes become progressively more tangentially biased there).," \ref{fig:frequencies} that since $\omega/\omega_{\rm BV}$ rises toward the center, that g-modes become progressively more tangentially biased there)."
 Εις implies that vorticity is a good tracer of e-mocles. a fact which we shall exploit.," This implies that vorticity is a good tracer of g-modes, a fact which we shall exploit."
 It also means that e-moces could conceivably drive an ellicicnt dynamo., It also means that g-modes could conceivably drive an efficient dynamo.
 Phere is a well-known analogy between the vorticity equation: where ois the viscosity. and the relation for the magnetic field in the Dux-freezing limit. where 5 is the electricity resistivity.," There is a well-known analogy between the vorticity equation: where $\nu$ is the viscosity, and the relation for the magnetic field in the flux-freezing limit, where $\eta$ is the electricity resistivity."
 This. together with he fact that the divergence of B and Q both vanish. leads to he expectation that their growth might berelated?.," This, together with the fact that the divergence of ${\bf B}$ and ${\bf \Omega}$ both vanish, leads to the expectation that their growth might be."
. There mve been a number of studies pointing out that turbulent motions could eive rise to magnetic fields in clusters (e.g. ??77)).," There have been a number of studies pointing out that turbulent motions could give rise to magnetic fields in clusters (e.g., \citet{ruzmaikin89,subramanian06,ryu08,cho09}) )."
 This subject is rich ancl bevond the scope of this »iper: we shall merely compare the erowth of vorticity and magnetic fields in our simulations. to see how well they track one another.," This subject is rich and beyond the scope of this paper; we shall merely compare the growth of vorticity and magnetic fields in our simulations, to see how well they track one another."
 A reasonable expectation is that the magnetic iclds achieve equipartition with turbulence (e.g... 7.. and references therein): where roan is the rms turbulent velocity on large scales.," A reasonable expectation is that the magnetic fields achieve equipartition with turbulence (e.g., \citet{schekochihin07}, and references therein): where $v_{\rm turb}$ is the rms turbulent velocity on large scales."
 The above estimate is consistent with observed pii fields (?).. though there are considerableuncertaünties?.," The above estimate is consistent with observed $\sim \mu$ G fields \citep{carilli}, though there are considerable."
. The Lact that trapping of g-modes can give rise to volume-filling turbulence would then be instrumental in allowing volume-lilling magnetic fields., The fact that trapping of $g$ -modes can give rise to volume-filling turbulence would then be instrumental in allowing volume-filling magnetic fields.
 Magnetic tension can inhibit the LIBL(72).., Magnetic tension can inhibit the HBI\citep{quataert08}.
 For perturbation scales comparable to the radius Γιο... A= 2r) we obtain a critical value: [or suppression. where the fiducial values are measured from our simulated. cluster at à. radius of r= 30kpc.," For perturbation scales comparable to the radius $r$ (i.e., $\lambda =2r$ ) we obtain a critical value: for suppression, where the fiducial values are measured from our simulated cluster at a radius of $r=30$ kpc."
 Due to the similarity between the field. values in equation (8)) and (9)). it has been suggested. that magnetic. fields amplified by turbulence. can prevent the onset of. the LIBI (c.g..see discussion in. ?..," Due to the similarity between the field values in equation \ref{eqn:B_field_equi}) ) and \ref{eqn:B_field_hbi}) ), it has been suggested that magnetic fields amplified by turbulence can prevent the onset of the HBI (e.g.,see discussion in \citet{kunz10}. ."
 Note that their version of equation (9)) vields somewhat lower B-ficlels than ours. for," Note that their version of equation \ref{eqn:B_field_hbi}) ) yields somewhat lower B-fields than ours, for"
fitting.,fitting.
 There is no correlation of the differeuces with Cepheic Lanctallicity. but that is a particularly challenging test to make with the Table 1 calibrators because of the small spread in metallicities for nearby Cepheids (seeTurner&Burke 2002).," There is no correlation of the differences with Cepheid metallicity, but that is a particularly challenging test to make with the Table \ref{tab3} calibrators because of the small spread in metallicities for nearby Cepheids \citep[see][]{tb02}."
. Tu the case of Cepheids with measured trigonomoetric parallaxes. it is necessary to have reliabe reddenimgs to correct the magnitudes aud colors for the effects of intervening interstellar extinction.," In the case of Cepheids with measured trigonometric parallaxes, it is necessary to have reliable reddenings to correct the magnitudes and colors for the effects of intervening interstellar extinction."
 Iu general. such information is available from the sudies ci earlier (Turneretal.1987:Turner2001:BeIxovtvukhetal.," In general, such information is available from the studies cited earlier \citep{te87,tu01,bn02,bn07,lc07,ko08}."
 2008).. Table 1 sunnuudzes available data for MST€'eplieids., Table \ref{tab4} summarizes the available data for Cepheids.
 The resulting. data for LST Copheids are plotted iu Fig. 5..," The resulting data for Cepheids are plotted in Fig. \ref{fig5},"
 and aeree well with the rezts of Fig., and agree well with the results of Fig.
 3 derived for cluster Cepheids., \ref{fig3} derived for cluster Cepheids.
 Iudividial HST Ceoes deviate from the relationship of Fie., Individual Cepheids deviate from the relationship of Fig.
 3 as expected from their location in he iustadlitv strip. ie. X Ser falls above 1ο relationship because it lies ou the hot side of 1C strip. whereas (6 Car fals below the relationship )ocause 1 lies on the coc side of the strip.," \ref{fig3} as expected from their location in the instability strip, i.e. X Sgr falls above the relationship because it lies on the hot side of the strip, whereas $\ell$ Car falls below the relationship because it lies on the cool side of the strip."
 Ax doie for cluster ορια». the deviations AMMy(observe)My(predicted) are otted in Fig.," As done for cluster Cepheids, the deviations $\Delta M_V = M_V({\rm observed})-M_V({\rm predicted})$ are plotted in Fig."
 6 as a function of pulsation 21ος. with the ΤΟΥ bars again representing quadratic suus of the aicertaiuties im extinction and distauce imnocdulus.," \ref{fig6} as a function of pulsation period, with the error bars again representing quadratic sums of the uncertainties in extinction and distance modulus."
 The mean deviation for theMST Cepheid parallaxes is |0.00.+0.03. which implies that the data confini the distauce scale. tied to the period-racius relation usec i conjunction with effective temperatures and bolometric corrections obtainec from stellar atmospheres.," The mean deviation for the Cepheid parallaxes is $+0.00\pm0.03$, which implies that the data confirm the distance scale tied to the period-radius relation used in conjunction with effective temperatures and bolometric corrections obtained from stellar atmospheres."
 I should be note. however. that no Lutz-Ixelker corrections were applied. te» the parallaxes in this case.," It should be noted, however, that no Lutz-Kelker corrections were applied to the parallaxes in this case."
 The raΠο behind such hnuuiuositv acjustineuts is souewhat uncear (Sith.2003).. despite areuieuts otherwise (Benedictetal. 2007).," The rationale behind such luminosity adjustments is somewhat unclear \citep{sm03}, despite arguments otherwise \citep{bn07}."
. The adjusmeuts are typically simall. aud iu the preseut instance woulcL shift all of the data iu Fie.," The adjustments are typically small, and in the present instance would shift all of the data in Fig."
 6 below t1e null relationship., \ref{fig6} below the null relationship.
 Au alternate imethod of conrparius Προ huuiuosities for caibratiug Cepheids is by plotting tlrear derived paraaxes with those mferred empirically. as preseuted in Fig. 7..," An alternate method of comparing implied luminosities for calibrating Cepheids is by plotting their derived parallaxes with those inferred empirically, as presented in Fig. \ref{fig7}."
 The sanall scatter in the daa of Fig., The small scatter in the data of Fig.
 T οuphasizes the good. agreement heween cluster aud piiidlaxes with predictions from οupirical relations., \ref{fig7} emphasizes the good agreement between cluster and parallaxes with predictions from empirical relations.
LST pavallaxcs for οςpleid calibrators agree wit1 enipirical predictions WIuu the stated uncertainties of the former in 7 of ]ϐ cases. or TOM. with al three outliers Wing wiin 1.30 of the predicte values.," parallaxes for Cepheid calibrators agree with empirical predictions within the stated uncertainties of the former in 7 of 10 cases, or $70\%$, with all three outliers lying within $1.3\sigma$ of the predicted values."
 In the case of cluster parallaxes for Cooed calibrators. 16 of 2| or GTM. agree with «qupirical predictions wiiu he stated 1ncertainies. with all of the oulors lug withiu ~3s of the predicted values except or XCre.," In the case of cluster parallaxes for Cepheid calibrators, 16 of 24, or $67\%$, agree with empirical predictions within the stated uncertainties, with all of the outliers lying within $\sim 3\sigma$ of the predicted values except for XCyg."
 Theobxvved percentages of Cajumxators line wituu lo of the predicted values, Theobserved percentages of calibrators lying within $1\sigma$ of the predicted values
"We note that when using a MW reddening law, even the best fit does not provide a good fit to the H-band (see Fig. 2)).","We note that when using a MW reddening law, even the best fit does not provide a good fit to the H-band (see Fig. \ref{fig:wirac_sb_mw}) )."
" Similarly, the stellar population models extinguished with the Calzetti reddening law overestimate the K-bandflux."," Similarly, the stellar population models extinguished with the Calzetti reddening law overestimate the $K$ -band."
" The reason for the imperfect fits to the H-band flux is possibly emission lines such as Ραβ and He I from the ionised interstellar gas, which fall into the H-band at the redshift of this galaxy."," The reason for the imperfect fits to the $H$ -band flux is possibly emission lines such as $\beta$ and He I from the ionised interstellar gas, which fall into the $H$ -band at the redshift of this galaxy."
 The SED fits show that the optical and near-infrared emission from the galaxy is dominated by a very young stellar population., The SED fits show that the optical and near-infrared emission from the galaxy is dominated by a very young stellar population.
 The young age of the dominant stellar population prevents us from distinguishing between models with different SFR e-folding times and hence does not allow us to determine the SFR history of the galaxy., The young age of the dominant stellar population prevents us from distinguishing between models with different SFR e-folding times and hence does not allow us to determine the SFR history of the galaxy.
" The age of the dominant stellar population is 6 Myr, if the metallicity is fixed to Z = 0.04, and slightly older, ~30 Myr, if the metallicity evolves in proportion to the age of the stellar population."," The age of the dominant stellar population is $\sim$ 6 Myr, if the metallicity is fixed to Z = 0.04, and slightly older, $\sim$ 30 Myr, if the metallicity evolves in proportion to the age of the stellar population."
 The MW-like extinction provides better fits to the data than the Calzetti reddening., The MW-like extinction provides better fits to the data than the Calzetti reddening.
 The best-fit extinction value is in the range Ay~ 1.8 — 2.6 mag depending on the galaxy template library used., The best-fit extinction value is in the range $_V \sim$ 1.8 – 2.6 mag depending on the galaxy template library used.
" In principle, there is a degeneracy between the dust extinction in a galaxy and the age and metallicity of the mean stellar population of a galaxy, since all three redden the colour of the galaxy."," In principle, there is a degeneracy between the dust extinction in a galaxy and the age and metallicity of the mean stellar population of a galaxy, since all three redden the colour of the galaxy."
" However, it is also known that metal-poor galaxies have less dust content and lower global infrared emission (Calzettietal.2010;Cannon2005,2006;Wal-teretal. 2007).."," However, it is also known that metal-poor galaxies have less dust content and lower global infrared emission \citep{cal10,can05,can06,wal07}."
" This is supported by our finding that the dust extinction and the age values obtained by fitting the solar/super-solar metallicity models and the evolving metallicity models roughly agree with each other, indicating that either the metallicity is high or it does not have a significant effect on the determination of the dust extinction for this galaxy, or both."," This is supported by our finding that the dust extinction and the age values obtained by fitting the solar/super-solar metallicity models and the evolving metallicity models roughly agree with each other, indicating that either the metallicity is high or it does not have a significant effect on the determination of the dust extinction for this galaxy, or both."
" In other words, the galaxy is highly extinguished according to the fits by synthetic stellar population models, independent of the metallicity of the models."," In other words, the galaxy is highly extinguished according to the fits by synthetic stellar population models, independent of the metallicity of the models."
" The age and dust extinction values we obtained agree with the spectroscopic measurements of Levesqueetal.(2010) who found an age of 7.8+0.9 Myr using the Hg emission line equivalent width and E (B — V) = 0.64 using the H,/Hg line ratio.", The age and dust extinction values we obtained agree with the spectroscopic measurements of \citet{leve10} who found an age of $\pm{0.9}$ Myr using the $_{\beta}$ emission line equivalent width and E (B – V) = 0.64 using the $_{\alpha}$ $_{\beta}$ line ratio.
" For a MW-like total-to-selective extinction ratio Ry — 3.1, E (B — V) = 0.64 corresponds to Ay = 1.98 mag, which is in agreement with the Ay values from our SED fits."," For a MW-like total-to-selective extinction ratio $_V$ = 3.1, E (B – V) = 0.64 corresponds to $_V$ = 1.98 mag, which is in agreement with the $_V$ values from our SED fits."
 Levesqueetal.(2010) also measured the metallicity of the host galaxy based on the spectroscopic line ratio of [NII]46584/[OII]| 43727 and found a super-solar metallicity of log(O/H) + 12 = 9.0+0.1., \citet{leve10} also measured the metallicity of the host galaxy based on the spectroscopic line ratio of $\lambda$ $\lambda$ 3727 and found a super-solar metallicity of log(O/H) + 12 = $\pm{0.1}$.
" The age (and extinction) value obtained from either our SED fits or the spectrum, by Levesqueetal.(2010),, do not agree with that of Savaglioetal.(2009)."," The age (and extinction) value obtained from either our SED fits or the spectrum, by \citet{leve10}, do not agree with that of \cite{sandra}."
". The reason for this disagreement is probably that they fit the SED of this host using only the B-, R-, and K-band magnitudes available in the literature, where the B-band magnitude has a large uncertainty"," The reason for this disagreement is probably that they fit the SED of this host using only the $B$ -, $R$ -, and $K$ -band magnitudes available in the literature, where the $B$ -band magnitude has a large uncertainty"
 =1. a230°. 5000kmst. ~GOOAL.vr.L|. oc0.2. , $ \ga 1$ $\alpha \ga 30^\circ$ $\sim 5000 \km \s^{-1}$ $\sim 600 M_\odot \yr^{-1}$ $\delta \simeq 0.2$ 
A comprehensive theory of star formation is necessary for understanding processes spanning the entire range of cosmic evolution. from the formation and evolution of galaxies to the formation of planets.,"A comprehensive theory of star formation is necessary for understanding processes spanning the entire range of cosmic evolution, from the formation and evolution of galaxies to the formation of planets."
 Thus. observing the formation of stars ts one of the prime science objectives of the citeherschel..," Thus, observing the formation of stars is one of the prime science objectives of the \\cite{herschel}."
 With its large (3.5 m) primary mirror. us able to survey a substantial fraction of the current star formation in the Galaxy with unprecedented efficiency and sensitivity.," With its large (3.5 m) primary mirror, is able to survey a substantial fraction of the current star formation in the Galaxy with unprecedented efficiency and sensitivity."
 The result will be an explosion of far-IR and mm data on star formation regions., The result will be an explosion of far-IR and sub-mm data on star formation regions.
 lis particularly suited for carrying out these surveys because the spectral energy distributions (SEDs) of protostars peaks in the far-IR and sub-mm region., is particularly suited for carrying out these surveys because the spectral energy distributions (SEDs) of protostars peaks in the far-IR and sub-mm region.
 A large number of guaranteed- and open- time key (legacy) pprograms are. thus. focused on star formation regions.," A large number of guaranteed- and open- time key (legacy) programs are, thus, focused on star formation regions."
 These include PACS (photodetector array camera spectrometer. Poglitschetαἱ. 2010)) and SPIRE (spectral imaging reciever. Griffinerαἱ. 2010)) imaging surveys of the Gould belt (Andreefaf. 2010)). and the Herschel Orion protostar survey (HOPS) and DIGIT programs. among others.," These include PACS (photodetector array camera spectrometer, \cite{PACS}) ) and SPIRE (spectral imaging reciever, \cite{SPIRE}) ) imaging surveys of the Gould belt \cite{andre2010}) ), and the Herschel Orion protostar survey (HOPS) and DIGIT programs, among others."
 These surveys will detect hundreds of thousands of protostars., These surveys will detect hundreds of thousands of protostars.
 For our purposes. protostars are low-mass stars In the earliest stages of their evolution.," For our purposes, protostars are low-mass stars in the earliest stages of their evolution."
 They are less than a few x 10? yrs old and are still surrounded by an infalling envelope., They are less than a few $\times$ $^5$ yrs old and are still surrounded by an infalling envelope.
 The SEDs of these protostars will be complex mixture of their intrinsic emission coupled with reprocessing and emission from their immediate environment., The SEDs of these protostars will be complex mixture of their intrinsic emission coupled with reprocessing and emission from their immediate environment.
 Radiative transfer models are an important tool in understanding and interpretting the observed flux densities of protostars., Radiative transfer models are an important tool in understanding and interpretting the observed flux densities of protostars.
 Model SEDs can provide crucial constraints on the most important physical parameters of a protostellar system., Model SEDs can provide crucial constraints on the most important physical parameters of a protostellar system.
 Because protostars can encompass a wide rage of parameter space it Is often necessary to compare observations against a large number of different models to derive a reasonable solution and to understand the degeneracies involved., Because protostars can encompass a wide rage of parameter space it is often necessary to compare observations against a large number of different models to derive a reasonable solution and to understand the degeneracies involved.
 Robitailleerαἰ.2006 constructed a grid of 20.000 individual models for SED fitting: however. these models used an ism model for the envelope. which is not accurate at far-IR wavelengths.," \cite{robitaille2006} constructed a grid of 20,000 individual models for SED fitting; however, these models used an ism model for the envelope, which is not accurate at far-IR wavelengths."
" This is because reprocessing by dust is especially important at Herscheflss wavelengths as this reprocessed light forms the bulk of the protostars'"" SED.", This is because reprocessing by dust is especially important at s wavelengths as this reprocessed light forms the bulk of the protostars' SED.
 In this contribution. we have generated a grid of 20.160 SEDs from 2.016 individual models focused primarily on the parameter space appropriate for young stars. and for the bbroad-band filters.," In this contribution, we have generated a grid of 20,160 SEDs from 2,016 individual models focused primarily on the parameter space appropriate for young stars, and for the broad-band filters."
 We use the Monte Carlo radiative transfer code developed by Whitneyeral(2003)... which is adapted to include the dust mixture properties from Tobin @/(2008) to calculate the model SEDs.," We use the Monte Carlo radiative transfer code developed by \cite{whitney2003}, which is adapted to include the dust mixture properties from Tobin (2008) to calculate the model SEDs."
 For convenience. we briefly summarize the maim components here.," For convenience, we briefly summarize the main components here."
 The code comprises four physical components: (1) a central object. G, The code comprises four physical components: (i) a central object. (
i) À flared disk. (,ii) A flared disk. (
111) A rotating collapsing envelope. and (iv) a bipolar cavity.,"iii) A rotating collapsing envelope, and (iv) a bipolar cavity."
 These components are illustrated in Fig. 1..., These components are illustrated in Fig. \ref{FigPars} .
" The startdisk system emits energy packets (""photons"") that are absorbed or scattered by the disk and/or envelope. subsequently determining the emergent SEDof the system."," The star+disk system emits energy packets (""photons"") that are absorbed or scattered by the disk and/or envelope, subsequently determining the emergent SEDof the system."
 Our adopted dust model uses the methodology described by D'Alessioeral.(2001). with additional optical constants for graphite from Draine&Lee (1984).., Our adopted dust model uses the methodology described by \cite{dustmodel} with additional optical constants for graphite from \cite{dustgrains}. .
 The dust grains used here, The dust grains used here
he source has not varied intrinsically. and that just. the oreground. absorption bas varied.,"the source has not varied intrinsically, and that just the foreground absorption has varied."
 The non-cetection with Swift in March. of 2010 argues (albeit only at the ~ 36 evel) against a change in absorption as the reason for the acing seen in the Chandra observations. unless that change is rather long lived.," The non-detection with Swift in March of 2010 argues (albeit only at the $\sim$ $\sigma$ level) against a change in absorption as the reason for the fading seen in the Chandra observations, unless that change is rather long lived."
 It should be noted that such a long-lived change might be expected for the case for a disk wind from a orecessing disk(i£ e.g. theinclination angle of the disk wind changed from one from not intercepting the line of sight to one intercepting it). and that the one Galactic X-ray binary with à strong. persistent disk wind. SS 433 (Blundell et al.," It should be noted that such a long-lived change might be expected for the case for a disk wind from a precessing disk (if e.g. the inclination angle of the disk wind changed from one from not intercepting the line of sight to one intercepting it), and that the one Galactic X-ray binary with a strong, persistent disk wind, SS 433 (Blundell et al."
 2001)is well known to have a strong precession (e.g.Margon 1984)., 2001) is well known to have a strong precession (e.g. Margon 1984).
" If the N-rav. variability is due to real changes in the central engine Luminosity, then the O LL] luminosity should respond to those changes on a light travel time: if it is due to changes in the absorption. the response of O LI] should be much weaker. since most of the photoionizing emission is directed. along lines of sight other than the one between the source and the Earth."," If the X-ray variability is due to real changes in the central engine luminosity, then the [O III] luminosity should respond to those changes on a light travel time; if it is due to changes in the absorption, the response of [O III] should be much weaker, since most of the photoionizing emission is directed along lines of sight other than the one between the source and the Earth."
 An approved. ||Gemini campaign will provide the first. test of whether the X-ray source is still on. and whether the ο IHE] luminosity: has responded to any changes in X-ray Luminosity.," An approved + campaign will provide the first test of whether the X-ray source is still on, and whether the [O III] luminosity has responded to any changes in X-ray luminosity."
 We note that we have done these calculations assuming that the absorbing material has the cosmic abundances of Morrison AleCammon (1983). which are embedded within WS3PIAMIAIS. rather than the nearly hvelrogen-[ree abundances expected. on the basis of the optical spectra of RZ 2109.," We note that we have done these calculations assuming that the absorbing material has the cosmic abundances of Morrison McCammon (1983), which are embedded within W3PIMMS, rather than the nearly hydrogen-free abundances expected on the basis of the optical spectra of RZ 2109."
 Since the extinction in the soft X-rays is predominantly due to carbon. anc oxygen. it ds. not intrinsically problematic that there is no hydrogen present.," Since the extinction in the soft X-rays is predominantly due to carbon and oxygen, it is not intrinsically problematic that there is no hydrogen present."
 The column densities of carbon and oxygen. will be nearly the same in a hydrogen-free absorber as they would be in à solar composition absorber with the fitted Ng., The column densities of carbon and oxygen will be nearly the same in a hydrogen-free absorber as they would be in a solar composition absorber with the fitted $N_H$.
 We have reported large zumplitude N-ray variability. [rom XMAMU 122939.7|075338. the first. strong candidate [ου being a BIL X-ray binary in a elobular cluster.," We have reported large amplitude X-ray variability from XMMU 122939.7+075333, the first strong candidate for being a BH X-ray binary in a globular cluster."
 We have shown that the combination of X-rav luminositv. X-ray variability on both short and long timescales. ancl optical line emission are all consistent with the idea that this svstem is. rather than being an A-rayv binary. a hierarchical triple system with its inner binary composed. of a WD and a stellar mass DII.," We have shown that the combination of X-ray luminosity, X-ray variability on both short and long timescales, and optical line emission are all consistent with the idea that this system is, rather than being an X-ray binary, a hierarchical triple system with its inner binary composed of a WD and a stellar mass BH."
 Better sampling of the long timescale X-pav variability. of the system is needed to test. this. idea more thoroughly., Better sampling of the long timescale X-ray variability of the system is needed to test this idea more thoroughly.
 We have also shown that in the proposed scenario in which the system has an intermediate mass DII accretor has serious problems reproducing both the short and lone term variability., We have also shown that in the proposed scenario in which the system has an intermediate mass BH accretor has serious problems reproducing both the short and long term variability.
 TIAL thanks the European Union for support under LPT erant 215212: Black Ποιο Universe., TJM thanks the European Union for support under FP7 grant 215212: Black Hole Universe.
 AI thanks NASA for support under Chandra. grant GOO-LLILIA and HIST archival program LIST-AR-11264., AK thanks NASA for support under Chandra grant GO0-11111A and HST archival program HST-AR-11264.
 SEZ thanks NASA for support under grants NNNOSAJGOG and. Chandra. CO0-11105X., SEZ thanks NASA for support under grants NNX08AJ60G and Chandra GO0-11105X.
 ‘This research is supported in part by an NSE Faculty Early Career Development (CAREER) award (AS'T-OS47109) to WLR., This research is supported in part by an NSF Faculty Early Career Development (CAREER) award (AST-0847109) to KLR.
 We thank the Swift. team for awarding target 7 opportunity observations to look at XMNMU 1229397|075333., We thank the Swift team for awarding target of opportunity observations to look at XMMU 122939.7+075333.
 ‘PIAL thanks Cole Miller and Lan AMellardy for useful discussions., TJM thanks Cole Miller and Ian McHardy for useful discussions.
 We thank an anonymous referee for a brief report with a lew very. useful suggestions that have hopefully improved the clarity of the paper., We thank an anonymous referee for a brief report with a few very useful suggestions that have hopefully improved the clarity of the paper.
The (High Accuracy Radial Velocity Planet Searcher) program has been on-going since 2003 at the ESO 3.6 meter telescope located at La Silla Observatory in Chile (Pepe 2002)).,The (High Accuracy Radial Velocity Planet Searcher) program has been on-going since 2003 at the ESO 3.6 meter telescope located at La Silla Observatory in Chile (Pepe \cite{pepeetal2002}) ).
" Thanks to its high accuracy of <1 m/s and its long time stability, has in particular detected many low mass planets, starting with uw Arae b at the beginning of the program(Santos et al. 2004))"," Thanks to its high accuracy of $\lesssim 1$ m/s and its long time stability, has in particular detected many low mass planets, starting with $\mu$ Arae b at the beginning of the program(Santos et al. \cite{santosetal2004}) )"
 to the recent two Earth-mass planet around (Mayor et al. [2009))., to the recent two Earth-mass planet around (Mayor et al. \cite{mayoretal2009}) ).
" As such low mass planets seem to be very abundant (Lovis et al. 2009)),"," As such low mass planets seem to be very abundant (Lovis et al. \cite{lovisetal2009}) ),"
 helps significantly to increase the number of known extrasolar planets., helps significantly to increase the number of known extrasolar planets.
" The latter is raising rapidly in time {, roughly as £2? since the discovery of 51 Peg b by Mayor Queloz (1995)) fifteen years ago."," The latter is raising rapidly in time $t$, roughly as $t^{2..3}$ since the discovery of 51 Peg b by Mayor Queloz \cite{mayorqueloz1995}) ) fifteen years ago."
 These detections of extrasolar planets have enormously stimulated the research on planet formation., These detections of extrasolar planets have enormously stimulated the research on planet formation.
" They have shown the importance of mechanisms which were previously underestimated in their importance from the shape of our own solar system alone, like for example orbital migration which was known on purely theoretical bases for along time (Goldreich Tremaine, [[980)), overthrowing the idea that giant planets can only be found beyond a few astronomical units (Boss [1995))."," They have shown the importance of mechanisms which were previously underestimated in their importance from the shape of our own solar system alone, like for example orbital migration which was known on purely theoretical bases for along time (Goldreich Tremaine, \cite{goldreichtremaine1980}) ), overthrowing the idea that giant planets can only be found beyond a few astronomical units (Boss \cite{boss1995}) )."
 The quickly growing number of extrasolar planets has allowed to derive many important distributions of physical properties and orbital elements., The quickly growing number of extrasolar planets has allowed to derive many important distributions of physical properties and orbital elements.
" We know now distributions of masses, semi-major axes or eccentricities of giant planets within a few AU around solar like stars (e.g. Udry Santos [2007)), and see correlations between stellar and planetary parameters."," We know now distributions of masses, semi-major axes or eccentricities of giant planets within a few AU around solar like stars (e.g. Udry Santos \cite{udrysantos2007}) ), and see correlations between stellar and planetary parameters."
" The most important example is the “metallicity effect"" i.e. the increase of giant planet frequency with stellar [Fe/H], see e.g. Santos et al. (2001))"," The most important example is the “metallicity effect” i.e. the increase of giant planet frequency with stellar [Fe/H], see e.g. Santos et al. \cite{santosetal2001}) )"
 or Fischer Valenti (2005))., or Fischer Valenti \cite{fischervalenti2005}) ).
" By varying initial conditions of planetary formation models in a Monte Carlo way (Ida Lin [2004]), one can try to derive these statistical distributions also from theoretical formation models and compare them with the observed ones."," By varying initial conditions of planetary formation models in a Monte Carlo way (Ida Lin \cite{idalin2004}) ), one can try to derive these statistical distributions also from theoretical formation models and compare them with the observed ones."
" This young method of planetary population synthesis (Mordasini et al. {2009al, 2009b))"," This young method of planetary population synthesis (Mordasini et al. \cite{mordasinietal2009a}, \cite{mordasinietal2009b}) )"
" allows to use the full wealth of observational data to constrain theoretical models and to improve our understanding of planet formation, as demonstrated here for the specific case of intermediate mass planets."," allows to use the full wealth of observational data to constrain theoretical models and to improve our understanding of planet formation, as demonstrated here for the specific case of intermediate mass planets."
" In this paper we report the discovery of two types of planets, namely of one Neptunian planet and of two intermediate mass planets (about 31 and 42 Ma) without analogue in the solar system."," In this paper we report the discovery of two types of planets, namely of one Neptunian planet and of two intermediate mass planets (about 31 and 42 $\mearth$ ) without analogue in the solar system."
 We discuss the formation of the latter objects in the context of the core accretion formation model at the end of the paper., We discuss the formation of the latter objects in the context of the core accretion formation model at the end of the paper.
" Such intermediate mass planets are interesting, as they provide observational constraints on the rate at which gas can be accreted by planets starting runaway gas accretion."," Such intermediate mass planets are interesting, as they provide observational constraints on the rate at which gas can be accreted by planets starting runaway gas accretion."
 The paper is organized as follows:In section ?? we discuss the host star properties., The paper is organized as follows:In section \ref{sec:hoststarcharacteristics} we discuss the host star properties.
 Radial velocity measurements and orbital solutions are presented in section ??.., Radial velocity measurements and orbital solutions are presented in section \ref{sec:measurements}. .
" In section ??,, we summarize our discoveries and in section ?? we discuss them."," In section \ref{sec:summary}, , we summarize our discoveries and in section \ref{sec:discussion} we discuss them."
Combining the unique BLAST FIR data with previous observations and our spectroscopic redshift identifications allows a full characterisation of FIR SEDs for 250um--bright HyLIRGs.,Combining the unique BLAST FIR data with previous observations and our spectroscopic redshift identifications allows a full characterisation of FIR SEDs for -bright HyLIRGs.
" Since mmapping has the advantage of sampling blackbody emission near its peak at z~2, UULIRG/HyLIRG selection is far less biased towards certain SED shapes, making 250um--bright galaxies a much cleaner, unbiased subset all high-redshift ULIRGs."," Since mapping has the advantage of sampling blackbody emission near its peak at $\sim$ 2, ULIRG/HyLIRG selection is far less biased towards certain SED shapes, making -bright galaxies a much cleaner, unbiased subset all high-redshift ULIRGs."
 The seven galaxies with secure redshifts suggest that these 250m-bright galaxies have roughly 1/5 the volume density of similarly luminous SMGs., The seven galaxies with secure redshifts suggest that these 250m-bright galaxies have roughly 1/5 the volume density of similarly luminous SMGs.
" We exclude the sources which only have tentative redshift identifications from this analysis, although we note that they would not skew or affect the interpretations we draw from the entire sample."," We exclude the sources which only have tentative redshift identifications from this analysis, although we note that they would not skew or affect the interpretations we draw from the entire sample."
" We estimate this lower limit to p250 for our sample by taking the redshift ranges z=1.3—1.7 and z=2.0—2.6, given the gap in the atmospheric opacity between H and K-bands."," We estimate this lower limit to $\rho_{250}$ for our sample by taking the redshift ranges $z=1.3-1.7$ and $z=2.0-2.6$, given the gap in the atmospheric opacity between $H$ and $K$ -bands."
" We treat the D10 and I10 sample separately as the relative selection depths differ (S250 >33mmJy and S259>59 mmJy respectively), finding >8x10 $hh? MMpc and >5x1079 hh? MMpc? respectively."," We treat the D10 and I10 sample separately as the relative selection depths differ $S_{250}>$ mJy and $S_{250}>$ mJy respectively), finding $>8\times10^{-6}$ $^3$ $^{-3}$ and $>5\times10^{-6}$ $^3$ $^{-3}$ respectively."
" Of the spectroscopically5 identified SMG samples in the literature etal. 2005),, oof the sources have Lrrr>8x1013 (a cutoff corresponding approximately to the BLAST ddepth), which implies a luminosity-limited volume density of 2.5x107? hh? MMpc? for SMGs."," Of the spectroscopically identified SMG samples in the literature \citep[e.g.][]{chapman05a}, of the sources have $_{FIR} >
8\times10^{12}$ (a cutoff corresponding approximately to the BLAST depth), which implies a luminosity-limited volume density of $2.5\times10^{-5}$ $^3$ $^{-3}$ for SMGs."
" As much deeper, more uniform ddata become available fromHerschel, the overlap with the SMG population is being explored more fully (e.g.Elbazetal.2010).."," As much deeper, more uniform data become available from, the overlap with the SMG population is being explored more fully \citep[e.g.][]{elbaz10a}."
" Of our nine spectroscopic sources, only four have been detected as SMGs in Weifetal.(2009).."," Of our nine spectroscopic sources, only four have been detected as SMGs in \citet{weiss09b}."
" While 250um--bright sources at high-z are more rare than SMGs, the fact that ((5/9) of our sample are submm-faint (with (Sazo) 22mmjJy) highlights that the SMG population represents only a subset of high-redshift ULIRG activity, as Caseyetal.(2009),, Chapmanetal.(2004) and Blainetal.(2004) suggest."," While -bright sources at $z$ are more rare than SMGs, the fact that (5/9) of our sample are submm-faint (with $\langle S_{\rm 870}\rangle$ mJy) highlights that the SMG population represents only a subset of high-redshift ULIRG activity, as \citet{casey09a}, \citet{chapman04a}
 and \citet{blain04a} suggest."
" The addition of 250um--selected, submm-faint galaxies to the previously-known HyLIRG population could imply that the volume density of known high-z HyLIRGs would increase from the SMG estimate roughly by,11296."," The addition of -selected, submm-faint galaxies to the previously-known HyLIRG population could imply that the volume density of known $z$ HyLIRGs would increase from the SMG estimate roughly by."
". However, more spectral observations of similar 250um--bright objects from are needed to boost these statistics and understand the actual level of contribution."," However, more spectral observations of similar -bright objects from are needed to boost these statistics and understand the actual level of contribution."
" The dderived star formation rates of the BLAST HyLIRG sample underestimate the FIR SFRs by ~10x, as is often the case with rest-UV or rest-optical emission line star-formation indicators in dust-obscured starburst galaxies."," The derived star formation rates of the BLAST HyLIRG sample underestimate the FIR SFRs by $\sim$ $\times$, as is often the case with rest-UV or rest-optical emission line star-formation indicators in dust-obscured starburst galaxies."
" However, we note near-IR spectroscopic observations of SMGs in Takataetal.(2006) measured internal extinction factors of Ay 22.9-Ε0.5 using Ho//H ratios."," However, we note near-IR spectroscopic observations of SMGs in \citet{takata06a} measured internal extinction factors of $A_{V}$ $\pm$ 0.5 using $\beta$ ratios."
" When correcting the Ha--inferred SFRs in Table 2 for this dust extinction the FIR-inferred SFRs are recovered, averaging to ~2000 yyr|."," When correcting the -inferred SFRs in Table \ref{tab:halpha} for this dust extinction the FIR-inferred SFRs are recovered, averaging to $\sim$ $^{-1}$."
 This indicates that dust obscuration is significant in the near-IR and must be corrected for to understand the true nature of the ultraluminous activity in these galaxies., This indicates that dust obscuration is significant in the near-IR and must be corrected for to understand the true nature of the ultraluminous activity in these galaxies.
" Placing our mmetallicity measurements in a larger galaxy evolution context, the metallicities of this sample (measured by converting to (O/H), i.e. (12+ log(O/H)) 88.65), agree within uncertainties with the observed metallicities of the most massive z~2 galaxies, (12+ log(O/H))~ 88.55+0.07, in Erbetal.(2006).."," Placing our metallicity measurements in a larger galaxy evolution context, the metallicities of this sample (measured by converting to $\langle{\rm O/H}\rangle$, i.e. $\langle12\,+\,\log($ $)\rangle$ 8.65), agree within uncertainties with the observed metallicities of the most massive $\sim$ 2 galaxies, $\langle12\,+\,\log($ $)\rangle\,\sim$ $\pm$ 0.07, in \citet{erb06a}."
" The mean rratio for this sample, 0.29+0.23, agrees within uncertainty with the Swinbanketal.(2004) SMGs, 0.41+0.38."," The mean ratio for this sample, $\pm$ 0.23, agrees within uncertainty with the \citet{swinbank04a} SMGs, $\pm$ 0.38."
" While evolutionary conclusions should not be drawn from these data alone, the results are consistent with conjecture that the ULIRG phenomenon occurs at the early stages of a burst in star formation triggered by the merger of two typical massive galaxies at z--2."," While evolutionary conclusions should not be drawn from these data alone, the results are consistent with conjecture that the ULIRG phenomenon occurs at the early stages of a burst in star formation triggered by the merger of two typical gas-rich massive galaxies at $\sim$ 2."
" Figure 6 shows dust temperature (Tuus) against FIR luminosity, with BLAST"," Figure \ref{fig:lfirtd} shows dust temperature $T_{dust}$ ) against FIR luminosity, with BLAST"
orbital nueration that is often invoked to explain the cohbunon existence of giant planets well within the canonical “snow luc.”,orbital migration that is often invoked to explain the common existence of giant planets well within the canonical “snow line.”
 Additionally. gravitational interactions iuuoug resonant planets— can also place— constraüiuts —ou both the system inclination with respect to the sky as well as mutual inclinations between the planets. aud thereby remove the sin/ ambiguity aud provide absolute measurements of the planet masses (27)..," Additionally, gravitational interactions among resonant planets can also place constraints on both the system inclination with respect to the sky, as well as mutual inclinations between the planets, and thereby remove the $\sin{i}$ ambiguity and provide absolute measurements of the planet masses \citep{rivera05,correia10}."
 Duteractions observed in certain types of multiplauet svstenis cau reveal the interior structures of eas giaut planets in vivid detail., Interactions observed in certain types of multiplanet systems can reveal the interior structures of gas giant planets in vivid detail.
 Iu the dramatic case of the system of plauets around TAT-P-13. the iuner planet transits its host star and experiences additional gravitational perturbations roni an outer planet neu d AU (77)..," In the dramatic case of the system of planets around HAT-P-13, the inner planet transits its host star and experiences additional gravitational perturbations from an outer planet near 1 AU \citep{bakos09,winn10}."
 Depending ou he inclinations of the planets in the system. precise ollow-up incasurcincuts may provide estimates of the idal Love ummber iud Q value of the inner planet to a üieher precision than is possible for Jupiter (27?)..," Depending on the inclinations of the planets in the system, precise follow-up measurements may provide estimates of the tidal Love number and Q value of the inner planet to a higher precision than is possible for Jupiter \citep{batygin09,mardling10}."
 We are conducting a Doppler survey of interinediate-nass subeiant stars at the Lick aud heck Observatories with the goal of understanding the iufluence stellar uass on the plysical properties. orbital architectures and nmultiplicitv rates of planetary svstenis;," We are conducting a Doppler survey of intermediate-mass subgiant stars at the Lick and Keck Observatories with the goal of understanding the influence stellar mass on the physical properties, orbital architectures and multiplicity rates of planetary systems."
" Our survey ws resulted duo the discovery of Ll new singletou exoplauets (27777?οδν, "," Our survey has resulted in the discovery of 14 new singleton exoplanets \citep{johnson06, 
 johnson07,johnson08a, peek09,bowler10,johnson10b}."
In this contribution we annouuce he discovery of two pairs of Jovian plaucts orbiting the subeiauts 21 Sextanis (=D 990013) and 220096L., In this contribution we announce the discovery of two pairs of Jovian planets orbiting the subgiants 24 Sextanis $=$ 90043) and 200964.
 We began observations of aand aat Lick Observatory in 20012005 as part of our Doppler survey of mterimediate-niass subeiauts., We began observations of and at Lick Observatory in 2004–2005 as part of our Doppler survey of intermediate-mass subgiants.
" Details of the survey. including target selection aud observiug strategy are given in 7.. 7— and ον,"," Details of the survey, including target selection and observing strategy are given in \citet{johnson06b}, \citet{peek09} and \citet{bowler10}."
 Tn 2007 we expanded our survey of subeiants at Keck Observatory (7)— and we added aand tto our Weck target list for additional monitoring., In 2007 we expanded our survey of subgiants at Keck Observatory \citep{johnson10b} and we added and to our Keck target list for additional monitoring.
 At Lick Observatory. the Shane 3uuu aud ua Coude Ausiliary Telescopes (CAT) feed the IEunilton spectrometer (2).. and observations at Neck Observatory were obtained using the TIRES spectrometer (?)..," At Lick Observatory, the Shane m and m Coude Auxiliary Telescopes (CAT) feed the Hamilton spectrometer \citep{vogt87}, and observations at Keck Observatory were obtained using the HIRES spectrometer \citep{vogt94}."
 Doppler shifts ave measured frou cach observation using the jocine cell method described by 2 (seealso?)..," Doppler shifts are measured from each observation using the iodine cell method described by \citet{butler96} \citep[see
 also][]{marcy92b}."
 A temperativecontrolled Pyrex cell containing gaseous iodine is placed at the eutrauce slit of the spectrometer., A temperature–controlled Pyrex cell containing gaseous iodine is placed at the entrance slit of the spectrometer.
 The dense set of narrow molecular lines imprinted on cach stellar spectrum from 5000 to 6000. pprovides a robust waveleneth scale for cach observation. as well as information about the shape of the spectrometer’s instrumental response (?)..," The dense set of narrow molecular lines imprinted on each stellar spectrum from 5000 to 6000 provides a robust wavelength scale for each observation, as well as information about the shape of the spectrometer's instrumental response \citep{valenti95}."
 At Lick. typical exposure times of 60 minutes on the CAT and 5 minutes on the 3 1 vield a signal-to-noise ratio (SNR) of z120 at the ceuter of the iodine region (A=5500 Aj). providing a velocity precision of LO5.0 t.," At Lick, typical exposure times of 60 minutes on the CAT and 5 minutes on the 3 m yield a signal-to-noise ratio (SNR) of $\approx$ 120 at the center of the iodine region $\lambda = 5500$ ), providing a velocity precision of 4.0--5.0 ."
. At Keck. typical spectra lave SNR z180 at 9000A.. resulting in a velocity precision of 1.52.01405 .," At Keck, typical spectra have SNR $\approx 180$ at 5500, resulting in a velocity precision of 1.5--2.0 ."
 Tus addition to the internal. photou-limuted uncertainties. the RV measurements— inchide au additional noise term due to stellar “jitter”velocity noise iu excess of internal errors due to astrophysical sources such as pulsation aud rotational modulation of surface features (27)..," In addition to the internal, photon-limited uncertainties, the RV measurements include an additional noise term due to stellar “jitter”—velocity noise in excess of internal errors due to astrophysical sources such as pulsation and rotational modulation of surface features \citep[][]{saar98, wright05}."
 We therefore adopt a jitter value of ffor our subeiauts based ou the estimate of ?.., We therefore adopt a jitter value of 5 for our subgiants based on the estimate of \citet{johnson10b}.
 This jitter term is added iu quadrature to the iuterual errors before determining the EKepleranu orbital solutions., This jitter term is added in quadrature to the internal errors before determining the Keplerian orbital solutions.
 For the dynamical analysis in 6 we allow the jitter to vary asa free parameter in the fitting process., For the dynamical analysis in \ref{sec:dynamical} we allow the jitter to vary as a free parameter in the fitting process.
 Atinospheric parameters of the target stars are estimated from iodine-free. “template” spectra ung the LTE spectroscopic analysis packageEasy (SME:?2).. as described by 7? aud ?..," Atmospheric parameters of the target stars are estimated from iodine-free, “template” spectra using the LTE spectroscopic analysis package \citep[SME;][]{valenti96}, as described by \citet{valenti05} and \citet{fischer05b}."
" To coustrain he low surface eravities of the evolved stars we used he iterative scheme of ὃν, which ties the SMIE-derived value of logg to the eravity iutferred from the Yousci-Yale (Y?:2) stellar model exids."," To constrain the low surface gravities of the evolved stars we used the iterative scheme of \citet{valenti09}, which ties the SME-derived value of $\log{g}$ to the gravity inferred from the Yonsei-Yale \citep[Y$^2$;][]{y2} stellar model grids."
 The aualvsis vields a best-fitting estimate ofT...g..|Fe/TI].. aud 7.," The analysis yields a best-fitting estimate of, and ."
. The xoperties of our targets from Lick aud I&eck are listed iu he fourth edition of the Spectroscopic Properties of Cool Stars Catalog (SPOCS IV.:, The properties of our targets from Lick and Keck are listed in the fourth edition of the Spectroscopic Properties of Cool Stars Catalog (SPOCS IV.;
 Joluson et al., Johnson et al.
 2010. in prep).," 2010, in prep)."
 We adopt the SALE parameter uncertainties described iu he error analysis of ?.., We adopt the SME parameter uncertainties described in the error analysis of \citet{valenti05}.
 The bhuuinositv of cach star is estimated from the apparent V-band magnitude and the parallax frou (?).. together with the bolometric correction from ?..," The luminosity of each star is estimated from the apparent V-band magnitude and the parallax from \citep{hipp2}, together with the bolometric correction from \citet{vandenberg03}."
 Frou aan luminosity. we determine the stellar mass. racdius. and an age estimate by associating those observed properties with a model from the Y? stellar| interior calculations (7)..," From and luminosity, we determine the stellar mass, radius, and an age estimate by associating those observed properties with a model from the $^2$ stellar interior calculations \citep{y2}."
" We also measure the chromospleric cluission iu the KE line cores (7).. providing au ο value ou the Mt. Wilson system. which we couvert to aas per ὃν,"," We also measure the chromospheric emission in the K line cores \citep{wright04b}, providing an $S$ value on the Mt. Wilson system, which we convert to as per \cite{Noyes84}."
 The stellar properties of the host stars are sununarized in Table 1.., The stellar properties of the host stars are summarized in Table \ref{tab:stars}.
 Iu this section we present the RV time sexies for both stars aud the initial orbital analysis. which cousists of the stun of two I&epleriaus without eravitational interaction.," In this section we present the RV time series for both stars and the initial orbital analysis, which consists of the sum of two Keplerians without gravitational interaction."
 Iun& 6 we preseut the results of our Newtonian dynamical analysis for cach system. which properly accounts for," In \ref{sec:dynamical} we present the results of our Newtonian dynamical analysis for each system, which properly accounts for"
Thirty-six out of the 170 EROs present in these two fields have a IN. magnitude brighter than 18.5 aud are already under investigation bv au ongoing spectroscopic survey performed by our group (see Saracco et al. 2003.. 2001)).,"Thirty-six out of the 170 EROs present in these two fields have a K' magnitude brighter than 18.5 and are already under investigation by an ongoing spectroscopic survey performed by our group (see Saracco et al. \cite{Saracco1}, , \cite{Saracco2}) )."
 Tere we diseuss the XN-rav properties of 6 X-ray cutting EROs found iu the S2F1 field., Here we discuss the X-ray properties of 6 X-ray emitting EROs found in the S2F1 field.
 The data centered on the S2F5 field have not ve been made available by theAyency., The data centered on the S2F5 field have not yet been made available by the.
 A coumprehensive analysis of the whole sample of nemr-IBR selecte EROs including the stacked analysis aud the statistical N-rax properties performed ou both fields will be presented in a forthcoming paper., A comprehensive analysis of the whole sample of near-IR selected EROs including the stacked analysis and the statistical X-ray properties performed on both fields will be presented in a forthcoming paper.
" Throughout this paper we assume IIj270 xl E and 04,20.3.3 Q4—0.7."," Throughout this paper we assume $_0$ =70 km $^{-1}$ $^{-1}$ and $\Omega_M$ =0.3, $\Omega_{\Lambda}$ =0.7."
 All the magnitudes are in the Vega system., All the magnitudes are in the Vega system.
 While the large imajoritv of the Xrav cimitting EROs studied so far are Nrav selected. here we deal with a salple of uearinfrared selected EROs for which followup Xrav observations have Όσοι. obtained.," While the large majority of the X–ray emitting EROs studied so far are X–ray selected, here we deal with a sample of near–infrared selected EROs for which follow--up X–ray observations have been obtained."
 Using the photometric data available from the MUNICS catalog for he S2F1 field. we have selected ~70 EROs down to a uaeuitude of Kx 19.3.," Using the photometric data available from the MUNICS catalog for the S2F1 field, we have selected $\sim$ 70 EROs down to a magnitude of $\simeq$ 19.3."
 This corresponds to 110.05 EROs/arcuin?. iu agreement with the surface density ueasured in other surveys at ai comparable [|Kbaie nagnitude (e.g. Daddi et al. 2000)).," This corresponds to $\pm$ 0.05 $^{2}$, in agreement with the surface density measured in other surveys at a comparable K–band magnitude (e.g. Daddi et al. \cite{Daddi}) )."
 This field was observed by ou February 11. 2003 pointing: RA 03:06:11.56. Dec |00:01:00.D) in ful rane iode aud with the thin filter applied.," This field was observed by on February 11, 2003 pointing: RA 03:06:41.56, Dec +00:01:00.4) in full frame mode and with the thin filter applied."
" Iu order o investigate the Xrav properties of our ERO sample. we have considered the pipeline source lists provide: wothe SSCCenter, Watson ct al. 2001))"," In order to investigate the X–ray properties of our ERO sample, we have considered the pipeline source lists provided by the SSC, Watson et al. \cite{Watson01}) )"
 and created using the SAS System) version 5.1., and created using the SAS ) version 5.4.
 Using the SONrav brightest sources in the field. we found that both for EPICpu aud EPICMOS cameras the average displacement between X.ray aud optical (from the USNO catalog. Monet 1998)) positious is of 3741.57.," Using the 8 X–ray brightest sources in the field, we found that both for EPIC–pn and EPIC–MOS cameras the average displacement between X–ray and optical (from the USNO catalog, Monet \cite{Monet}) ) positions is of $\pm$."
 We have considered all the sources detected in at least one of the SSC cucrey aud we have cross- their astrometrically corrected positious with the MUNICS IKband catalog containing all the nearinfrared salaxies brighter than 19.3 (—620) iu the S2F1 field., We have considered all the sources detected in at least one of the SSC energy and we have cross-correlated their astrometrically corrected positions with the MUNICS K–band catalog containing all the near--infrared galaxies brighter than $\sim$ 19.3 $\sim$ 620) in the S2F1 field.
 To this eud. a conservative matching radius of has beeu used: this is the radius for which more than of the sources in the SSC catalog are associated with USNO A.2 sources.," To this end, a conservative matching radius of has been used: this is the radius for which more than of the sources in the SSC catalog are associated with USNO A.2 sources."
 We find that 6 EROs fall within of an Xravsource?.., We find that 6 EROs fall within of an X–ray.
 For all of these 6 sources the offset between the Xrav aud earmufrared positiou is smaller than[, For all of these 6 sources the offset between the X–ray and near–infrared position is smaller than.
νι Moreover. uo EROs have beeu found with an X.rav association between aud11”.. inuplviug that no NIR/Xταν associations ave been lost using he adopted matching radius.," Moreover, no EROs have been found with an X–ray association between and, implying that no NIR/X–ray associations have been lost using the adopted matching radius."
 Usine he probability of chancecoincidence!.. we estimate thet he expected nuniber of spurious EROs/Xrav source associations is «0.5.," Using the probability of chance, we estimate that the expected number of spurious EROs/X–ray source associations is $<$ 0.8."
 The same resul has been obtained στους correlating the nearinfrared positions with fake Xorav coordinates (obtained by shifting the πιο XNταν vositions by 1. 3 and 5 arcmin in different directions ou he sky).," The same result has been obtained by cross–correlating the near–infrared positions with fake X–ray coordinates (obtained by shifting the true X–ray positions by 1, 3 and 5 arcmin in different directions on the sky)."
 None of the 6 EROs discussed above has an optical spectruii in the MUNICS catalog., None of the 6 EROs discussed above has an optical spectrum in the MUNICS catalog.
 All of them appear clearly extended in the optical/ucarimfrared miages even if the quality of the data is not good enough to allow a detailer morphological analysis., All of them appear clearly extended in the optical/near–infrared images even if the quality of the data is not good enough to allow a detailed morphological analysis.
 Iun four Cases (S2PL771. S2F1.1103. S2PL_5507. no nearimfrared sources. in addition to the ERO. ‘all within of the Nταν centroids. thus vielclineC» unanbieuous matches.," In four cases 71, 493, 507, no near–infrared sources, in addition to the ERO, fall within of the X–ray centroids, thus yielding unambiguous matches."
 In two cases; more than oue nearinfrared source falls withLei the matching radius.," In two cases, more than one near--infrared source falls within the matching radius."
 Again. tone of these galaxies has au optical spectrum in the AIUNICS catalog.," Again, none of these galaxies has an optical spectrum in the MUNICS catalog."
 In particular. two field galaxics fall within of the Xrav source possibly associated with he ERO S2F1.1113.," In particular, two field galaxies fall within of the X–ray source possibly associated with the ERO 443."
 The first ealaxy (41135. I—18.1 nae) lies at from the Xταν centroid.," The first galaxy 435, K'=18.4 mag) lies at from the X–ray centroid."
 It appears extended in the optical/ucarinfrared images and the SED is well fitted by au cussion line ealaxy at z> 2., It appears extended in the optical/near–infrared images and the SED is well fitted by an emission line galaxy at $>$ 2.
 The secoud galaxy L137. IK—18.3 mae). which is also au SDSS ποιαος (SDSS J030632.1|QOOL09.3. SCC http:/ποsdss.ore/dr2/). lies away from the Nrav centroid.," The second galaxy 437, K'=18.3 mag), which is also an SDSS source (SDSS J030632.1+000109.3, see http://www.sdss.org/dr2/), lies away from the X–ray centroid."
 It appears exteuded with rather blue colors aud its SED is well &tted by au emission.line galaxy at z=0.5., It appears extended with rather blue colors and its SED is well fitted by an emission–line galaxy at z=0.5.
 Analogously. oue field galaxy (355552. I—18.9 imag) lies at a distance of from the X.ray source associated with the ERO S2F1.5551.," Analogously, one field galaxy 552, K'=18.9 mag) lies at a distance of from the X–ray source associated with the ERO 551."
 As reported iu the MUNICS catalog. the SED of the galaxy #25552 is well fitted by a z=0.6 elliptical galaxy.," As reported in the MUNICS catalog, the SED of the galaxy 552 is well fitted by a z=0.6 elliptical galaxy."
" In order to diseutaugle these ambienous matches, we used the chance coincidence probability aud. whenever available. the radio detection."," In order to disentangle these ambiguous matches, we used the chance coincidence probability and, whenever available, the radio detection."
" Tu particular. we have estimated from our data the cumulative surface density of field sources du WO band and we fud ,,5,(135)290.07.. Pri qu(137)50.09. (to. be compared with Pegotll3)29«10 7) aud P545(0552)20.02 (to be compared with Pere (551)=0.006)."," In particular, we have estimated from our data the cumulative surface density of field sources in K' band and we find $_{field}$ (435)=0.07, $_{field}$ (437)=0.09 (to be compared with $_{ERO}$ $\times10^{-5}$ ) and$_{field}$ (552)=0.02 (to be compared with $_{ERO}$ (551)=0.006)."
 The highly siguificaut, The highly significant
(AYA 2001-1646),(AYA 2001-1646).
 ~The work of AR is supported by the grant AYA 2002-00205., The work of AR is supported by the grant AYA 2002-00205.
As described in Johnston&Kulkarni(1991).. the factor ~ can be computed for surveys with and without coherent acceleration searches.,"As described in \citet{jk91}, the factor $\gamma$ can be computed for surveys with and without coherent acceleration searches."
 Most of the surveys considered. below had. relatively short. integration times and did not adopt acceleration searches., Most of the surveys considered below had relatively short integration times and did not adopt acceleration searches.
 However. the Doppler smearing effects can be significant for short orbital periods and this is taken into account in our simulations.," However, the Doppler smearing effects can be significant for short orbital periods and this is taken into account in our simulations."
 For the Parkes multibeam pulsar survey of the Galactic plane which had. 35-minute clwell times (Manchesteretal.2OOL).. acceleration. search techniques were applied (Faulkneretal.2004).," For the Parkes multibeam pulsar survey of the Galactic plane which had 35-minute dwell times \citep{mlc+01}, acceleration search techniques were applied \citep{fsk+04}."
. As discussed bv Faulkner et al.," As discussed by Faulkner et al.,"
" the ""stack search” method: used in this analvsis is typically less ellicient than a fully coherent acceleration search.", the “stack search” method used in this analysis is typically less efficient than a fully coherent acceleration search.
 We take this factor into account when computing * for this survey., We take this factor into account when computing $\gamma$ for this survey.
 The two other surveys with fully coherent acceleration searches we consider. are. the ongoing Pulsar Arecibo L-band Feed Array (PALPA) survey (Lorimeretal.2006). and the Green Bank 350-MllIz crit scan survey (GD'EDBRIET:Archibaleletal.2009)., The two other surveys with fully coherent acceleration searches we consider are the ongoing Pulsar Arecibo L-band Feed Array (PALFA) survey \citep{lsf+06} and the Green Bank 350-MHz drift scan survey \citep[GBTDRIFT;][]{asr+09}.
. With the above set of assumptions. we considered. two populations.," With the above set of assumptions, we considered two populations."
 For one population (model. DNS) we crew velocities from the distribution predicted for the DNS binary systems produced. in model X (see Fig., For one population (model DNS) we drew velocities from the distribution predicted for the DNS binary systems produced in model A (see Fig.
 2)., 2).
 The orbital period distribution we used for these systems was an analytic form of the predicted. distribution of DNS orbital periods from model A shown in Fig., The orbital period distribution we used for these systems was an analytic form of the predicted distribution of DNS orbital periods from model A shown in Fig.
 3., 3.
" For this model. we find that the cumulative number of svstems as a function of orbital period. is well approximated by the simple function NoD)=DOO)D. where D, is the orbital period in days."," For this model, we find that the cumulative number of systems as a function of orbital period is well approximated by the simple function $N(<P_b)=P_b/(1+P_b)$, where $P_b$ is the orbital period in days."
 For the second. population (model DID). we drew velocities from the distribution predicted for the DRPs from the same model.," For the second population (model DRP), we drew velocities from the distribution predicted for the DRPs from the same model."
 For both populations. we computed. the final position and expected Dux density of each model pulsar and used models of a variety of recent. pulsar surveys to calculate the number of detectable pulsars.," For both populations, we computed the final position and expected flux density of each model pulsar and used models of a variety of recent pulsar surveys to calculate the number of detectable pulsars."
 Our results are summarized in Table 3 where we calculate the number of each model pulsar population detected GNpxs and INpnp) and the ratio of the two populations fa=Npnxs/Nppi.," Our results are summarized in Table \ref{tab:simulations}
 where we calculate the number of each model pulsar population detected $N_{\rm DNS}$ and $N_{\rm
DRP}$ ) and the ratio of the two populations $f_{\rm obs} = N_{\rm DNS}/N_{\rm
DRP}$."
 Phe absolute values. of Nonxs and Nprp are. of course. arbitrarily high ancl chosen o be so to minimize statistical fluctuations.," The absolute values of $N_{\rm DNS}$ and $N_{\rm DRP}$ are, of course, arbitrarily high and chosen to be so to minimize statistical fluctuations."
 Civen our assertion of that the spindown ancl beaming of the two »opulations should be identical. it is their ratio that is of astrophysical significance.," Given our assertion of that the spindown and beaming of the two populations should be identical, it is their ratio that is of astrophysical significance."
 As can be seen. depencing on he survey parameters. there is a variation in the ratio in the range 0.91.7.," As can be seen, depending on the survey parameters, there is a variation in the ratio in the range 0.9–1.7."
 Surveys along the Calactic plane (i.c. PAISURY ancl PALEA) show the largest bias in favor of detecting DNS systems over DIS (i.e. the largest values of for.) while surveys away from the plane (e.g. PLISURY and Ντο) show much less of a bias.," Surveys along the Galactic plane (i.e. PMSURV and PALFA) show the largest bias in favor of detecting DNS systems over DRPs (i.e. the largest values of $f_{\rm obs}$ ), while surveys away from the plane (e.g. PHSURV and PKS70) show much less of a bias."
 Indeed. for the Swinburne ui¢h-latitucle survey Jacobyetal.(2007).. the bias is slightly ipped in favor of detecting DRPs.," Indeed, for the Swinburne high-latitude survey \cite{jbo+07}, the bias is slightly tipped in favor of detecting DRPs."
 Taken as a whole. the average value of fon.=1.25 in Table 3. suggests that we might expect to detect around more DNS binaries than DIPs due to selection cllects alone.," Taken as a whole, the average value of $f_{\rm obs}=1.25$ in Table \ref{tab:simulations}
 suggests that we might expect to detect around more DNS binaries than DRPs due to selection effects alone."
 Thus the observational ras is à relatively small perturbation on top of the intrinsic ratios found in the population svntheses listed in Table 2., Thus the observational bias is a relatively small perturbation on top of the intrinsic ratios found in the population syntheses listed in Table 2.
 Although we have only explicitly considered the velocity ancl orbital period distributions from model X in this study. similar results are found when the other model parameters are used as input.," Although we have only explicitly considered the velocity and orbital period distributions from model A in this study, similar results are found when the other model parameters are used as input."
 In summary. while we find that observational biases exist which favor the detection of DNSs over DARPs. their magnitude is not sullicient to significantly skew any underlying ratios of the two populations.," In summary, while we find that observational biases exist which favor the detection of DNSs over DRPs, their magnitude is not sufficient to significantly skew any underlying ratios of the two populations."
 This allows us to revisit the results from the population syntheses presented. in. Table. 2., This allows us to revisit the results from the population syntheses presented in Table 2.
 Xs. discussed. earlier. the observed ratio is ron.c1., As discussed earlier the observed ratio is $r_{\rm obs} \sim 1$.
 HE we fold this with observational jas factor (fan.= 1.25) the intrinsic ratio of DNS to DIPs is of the order ri~OS (DRPs slightly dominate over DNS)., If we fold this with observational bias factor $f_{\rm obs} = 1.25$ ) the intrinsic ratio of DNS to DRPs is of the order $r_{\rm int} \sim 0.8$ (DRPs slightly dominate over DNS).
 The comparison with Table 2. that shows the wecdieted ratios r. shows two things.," The comparison with Table 2, that shows the predicted ratios $r$, shows two things."
 First. the model with natal kicks adopted from. observations of single. pulsars (model A) does not reproduce the intrinsic ratio (r=0.3).," First, the model with natal kicks adopted from observations of single pulsars (model A) does not reproduce the intrinsic ratio $r=0.3$ )."
 Second. the models that are close to the intrinsic ratio (model Band €. r7=0.5.1.1 respectively) indicate that the 1lD dispersion of kick velocity distribution is of the order of aco~170 km © (approximately the mid. point between model B and €).," Second, the models that are close to the intrinsic ratio (model B and C, $r=0.5,\ 1.1$ respectively) indicate that the 1–D dispersion of kick velocity distribution is of the order of $\sigma_{\rm CC} \sim 170$ km $^{-1}$ (approximately the mid point between model B and C)."
 We have investigated the statistics of disrupted recycled pulsars (DRPs) and double neutron star (DNS) binaries where it ds observecl (see Section 2) that there are comparable numbers of DNS binary svstems anc Ον., We have investigated the statistics of disrupted recycled pulsars (DRPs) and double neutron star (DNS) binaries where it is observed (see Section 2) that there are comparable numbers of DNS binary systems and DRPs.
 From a population svnthesis of neutron star formation ancl evolution in binary systems (see Section 3). regardless of the assumed natal kick velocity. clistribution for neutron stars. we find that the velocity dispersion of DIUPs is significantly ügher than for DNS binaries.," From a population synthesis of neutron star formation and evolution in binary systems (see Section 3), regardless of the assumed natal kick velocity distribution for neutron stars, we find that the velocity dispersion of DRPs is significantly higher than for DNS binaries."
 Using the resulting orbital »eriod ancl velocity distributions in a mocel for radio pulsar selection clleets (see Section 4). we found that there is a small (~ 25%) observational bias in [avor of detecting DNS jnaries over DRPs.," Using the resulting orbital period and velocity distributions in a model for radio pulsar selection effects (see Section 4), we found that there is a small $\sim 25\%$ ) observational bias in favor of detecting DNS binaries over DRPs."
 The dilference in velocity. clispersions or the two populations lead. to a bias towards observing DNS binaries which are. on average. closer to the Earth than ος.," The difference in velocity dispersions for the two populations lead to a bias towards observing DNS binaries which are, on average, closer to the Earth than DRPs."
 This conclusion holds even after taking into account, This conclusion holds even after taking into account
A statistical model has been developed for the polarization of pulsar radio emission.,A statistical model has been developed for the polarization of pulsar radio emission.
 The model can explain a wide variely of polarization patterns observed in (he radio emission., The model can explain a wide variety of polarization patterns observed in the radio emission.
 The observations are (hus consistent with the models hypothesis Chat the polarization of the radiation is determined by (he simultaneous interaction of two. highly polarized. orthogonal modes.," The observations are thus consistent with the model's hypothesis that the polarization of the radiation is determined by the simultaneous interaction of two, highly polarized, orthogonal modes."
 The analvsis of the polarization data shows Chat polarization signatures ol physical processes can become apparent when (he Stokes parameters are analyzed together. instead of separately.," The analysis of the polarization data shows that polarization signatures of physical processes can become apparent when the Stokes parameters are analyzed together, instead of separately."
 An interpretation of the models assumptions and its application to the observations suggest that generalized Faraday. rotation mav be operative in pulsar maegnetospheres., An interpretation of the model's assumptions and its application to the observations suggest that generalized Faraday rotation may be operative in pulsar magnetospheres.
 The model shows. in a rigorous way. that polarization measurements follow (he statistics of direction.," The model shows, in a rigorous way, that polarization measurements follow the statistics of direction."
cloud conditions.,cloud conditions.
 Here we present a study of the cloud cover over SPM using an approach recently introduced by Carrascoetal.(2009)., Here we present a study of the cloud cover over SPM using an approach recently introduced by \citet{Carrasco09}.
. It consists of the computation of histograms of solar radiation values measured at the site and corrected for the zenital angle of the Sun., It consists of the computation of histograms of solar radiation values measured at the site and corrected for the zenital angle of the Sun.
" The data coverage is presented in section §22, the method is described in §33, the data obtained in SMP 844, the discussion of the results in §55, the statistics of cloud cover in §66 and the summary and conclusions in §77."," The data coverage is presented in section 2, the method is described in 3, the data obtained in SMP 4, the discussion of the results in 5, the statistics of cloud cover in 6 and the summary and conclusions in 7."
" The data presented here consist of records of solar radiation energy fluxes in units of Wm""? acquired with an Monitor automatic weather station (Schócketal.2009),, located 2m above the ground (Skidmoreetal.2009) at 31° 02' 43.84” N, 115? 28 10.45 W. It was in a tree free zone without visibility limitations."," The data presented here consist of records of solar radiation energy fluxes in units of $^{-2}$ acquired with an Monitor automatic weather station \citep{Schock09}, located 2m above the ground \citep{Skidmore09} at $^{\circ}$ $^{'}$ $^{""}$ N, $^{\circ}$ $^{'}$ $^{""}$ W. It was in a tree free zone without visibility limitations."
 The location of the weather station relative to the observatory headquarters is shown in Fig. 1.., The location of the weather station relative to the observatory headquarters is shown in Fig. \ref {location}.
 The Monitor sensors have a spectral response between 400 and 950 nm with an accuracy of 5 per cent according to the vendor., The Monitor sensors have a spectral response between 400 and 950 nm with an accuracy of 5 per cent according to the vendor.
" The data span between October 2, 2004 and August 8, 2008 with a sampling time of 2 minutes."," The data span between October 2, 2004 and August 8, 2008 with a sampling time of 2 minutes."
" 'The analysis does not include the data from 2004, when the radiation sensor was not working at the beginning of each day."," The analysis does not include the data from 2004, when the radiation sensor was not working at the beginning of each day."
" Table 1 summarises the temporal coverage of the data expressed in percentage, with due considerations of the diurnal cycle variation."," Table \ref{coverage_per_month} summarises the temporal coverage of the data expressed in percentage, with due considerations of the diurnal cycle variation."
" The data span from 2005 January 12 to 2008 August 8, with a 67 per cent effective coverage of the 3.6 year sample; data exist for 973 out of 1316 days."," The data span from 2005 January 12 to 2008 August 8, with a 67 per cent effective coverage of the 3.6 year sample; data exist for 973 out of 1316 days."
" The complete sample contains 596580 min out of 899520 possible; coverage was 59 per cent for 2005 and increased to 78 per cent towards the end of the campaign, in 2008."," The complete sample contains 596580 min out of 899520 possible; coverage was 59 per cent for 2005 and increased to 78 per cent towards the end of the campaign, in 2008."
 In Fig., In Fig.
 2 the solid line shows the total number of hours per month of solar radiation measured in situ while the red dotted line represents the corresponding expected radiation flux., \ref{coverage_plus} the solid line shows the total number of hours per month of solar radiation measured in situ while the red dotted line represents the corresponding expected radiation flux.
" The coverage per hour of day, shown in Table 2,, was obtained by counting the minutes of data and comparing with the total expected, given SPM coordinates."," The coverage per hour of day, shown in Table \ref{coverage_per_hour}, was obtained by counting the minutes of data and comparing with the total expected, given SPM coordinates."
" Hours with very low data coverage, less than 30 min, are excluded in this analysis."," Hours with very low data coverage, less than 30 min, are excluded in this analysis."
Iu order to check our scaling results of section refsecieni.. 2500 random bodies were coustructed in the manner described in refsecioni.,"In order to check our scaling results of section \\ref{sec:em}, 2500 random bodies were constructed in the manner described in \\ref{sec:em}."
 For each body we computed fy 2nd ας., For each body we computed $f_{Y}$ and $d_s$.
" Figure 3 shows fy for the randomly constructed bodies as a function. of spherical deviation. d,. along with the best fit foreq."," Figure \ref{fig:div} shows $f_Y$ for the randomly constructed bodies as a function of spherical deviation, $d_s$, along with the best fit for."
(20).. In addition. fy for 18 real asteroids (their shape was taken from ΕςΠΟ JPL) was computed using our aleorithin aud plotted together with the 2 measured. YORP for comparison.," In addition, $f_Y$ for 18 real asteroids (their shape was taken from ECHO JPL) was computed using our algorithm and plotted together with the 2 measured YORP for comparison."
 For most of the asteroids we can see a good correlation between our qualitative results and our precise calculations. although our random asteroids tend to have a higher fy.," For most of the asteroids we can see a good correlation between our qualitative results and our precise calculations, although our random asteroids tend to have a higher $f_Y$."
 The ratio between our calculated results aud the measured YORP for 1620 Ceoeraphos and 2000 PITS ave 2.18 and 5.22 respectively., The ratio between our calculated results and the measured YORP for 1620 Geographos and 2000 PH5 are $2.18$ and $5.22$ respectively.
 Taking the mean of the real asteroids. we find that fyz28-10%.," Taking the mean of the real asteroids, we find that $f_{Y}\approx 2.8\cdot10^{-3}$."
 Reexauinine the order of magnitude approach that was taken by CS. we cau see that their choice of fy6«10. is a bit low but is still within acceptable range.," Reexamining the order of magnitude approach that was taken by GS, we can see that their choice of $f_{Y}~6\times10^{-4}$ is a bit low but is still within acceptable range."
 Since under the mapping : to τν the obliquity changing component of the torque does uot change sign but the : component of the spin vector does. we have the autisviuuectrv: G(.e)=|G(0.x—e).," Since under the mapping $\hat{z}$ to $-\hat{z}$, the obliquity changing component of the torque does not change sign but the $z$ component of the spin vector does, we have the antisymmetry: $G(\theta,\epsilon)=-G(\theta,\pi-\epsilon)$."
 Snuibulv. since the spin changing coniponeut of the torque does chanec xeu: D(0.e)=D(0.xεἰ.," Similarly, since the spin changing component of the torque does change sign: $B(\theta,\epsilon)=B(\theta,\pi-\epsilon)$."
 It can be secu from that every asteroid. regardless of its shape. has at least two equilibrium points with regard to the change in the obliquity since for e=0 or 7/2. G is zero.," It can be seen from that every asteroid, regardless of its shape, has at least two equilibrium points with regard to the change in the obliquity since for $\epsilon=0$ or $\pi/2$, $G$ is zero."
 Whether they are stable or not depends ou the derivative of with respect to e. which depeuds on the asteroid’s geometry.," Whether they are stable or not depends on the derivative of with respect to $\epsilon$, which depends on the asteroid's geometry."
 Au asteroid will have an ideutical number of equilibrimu points in the rauge |0.7/2) aud the range (7/2. due to the svinmetry of G.," An asteroid will have an identical number of equilibrium points in the range $[0,\pi/2)$ and the range $(\pi/2,\pi]$ due to the symmetry of $G$."
 The stability of at εξ0 determines7| the stability of at all the other equilibriumé poiuts sincethe equilibrium €poiuts change stability alternatinelv., The stability of $\dot{\epsilon}$ at $\epsilon=0$ determines the stability of $\dot{\epsilon}$ at all the other equilibrium points sincethe equilibrium points change stability alternatingly.
 ? have classified the two most frequent spin aud obliquity behaviors of asteroids iuto Type I aud Type IT., \cite{VC02} have classified the two most frequent spin and obliquity behaviors of asteroids into Type I and Type II.
 Type Tis categorized by having é>0 for 0«e7/2 and a spin change rate that is positive for €=0 and negative for €=7/2., Type I is categorized by having $\dot{\epsilon}>0$ for $0<\epsilon<\pi/2$ and a spin change rate that is positive for $\epsilon=0$ and negative for $\epsilon=\pi/2$.
 Type IL is the opposite of Type 1. categorized by having é«0 for 0«€<7/2 aud a spin change rate that is negative for e=0 and positive for e=7/2.," Type II is the opposite of Type I, categorized by having $\dot{\epsilon}<0$ for $0<\epsilon<\pi/2$ and a spin change rate that is negative for $\epsilon=0$ and positive for $\epsilon=\pi/2$."
 Both Type I aud II are defined to have no nodes for ἑ iu the ranee (0.7/2).," Both Type I and II are defined to have no nodes for $\dot{\epsilon}$ in the range $(0,\pi/2)$."
 Our calculations show that 78% of our rvaudomly drawn asteroids are divided ito Type I aud IT with equal likelihood., Our calculations show that $78\%$ of our randomly drawn asteroids are divided into Type I and II with equal likelihood.
 Our calculations also show that 5 out of the Ls real asteroids ave not Type I or IL., Our calculations also show that 5 out of the 18 real asteroids are not Type I or II.
 Of the reaming 13 asteroids. 9 were Type Land Lwere Type IL which is consistent with our raudom asteroids.," Of the remaining 13 asteroids, 9 were Type I and 4 were Type II, which is consistent with our random asteroids."
 Ouc of the curious aspects of both types. is that their spin tends to slow down at their stable point with respect to obliquity.," One of the curious aspects of both types, is that their spin tends to slow down at their stable point with respect to obliquity."
 Au asteroid which starts with an obliquity in the range of (0.7/2). will tend to evolve toward €—0 if if is a Type II asteroid where its spin change rate is negative.," An asteroid which starts with an obliquity in the range of $(0,\pi/2$ ), will tend to evolve toward $\epsilon=0$ if it is a Type II asteroid where its spin change rate is negative."
 A Type EI asteroid will evolve toward €—7/2 where its spin change rate is also negative., A Type I asteroid will evolve toward $\epsilon=\pi/2$ where its spin change rate is also negative.
 Notice that once the spin rate reaches zero. the asteroid docs not simply change its obliquity from € to πε since that would also iuvolve inverting the z/ axis," Notice that once the spin rate reaches zero, the asteroid does not simply change its obliquity from $\epsilon$ to $\pi-\epsilon$ since that would also involve inverting the $z'$ axis."
 Rather the obliquity remains fixed while G changes its sien., Rather the obliquity remains fixed while $G$ changes its sign.
 This causes the equilibrium poiut to lose its stability aud results iu the asteroid evolving to its other equilibrium point where the spin will ounce again slow down., This causes the equilibrium point to lose its stability and results in the asteroid evolving to its other equilibrium point where the spin will once again slow down.
 A viable explanation for this phenomena can be found by inspecting the stability at e=0: The spin chanee rate with zero obliquity The correlation can be understood as follows., A viable explanation for this phenomena can be found by inspecting the stability at $\epsilon=0$ The spin change rate with zero obliquity The correlation can be understood as follows.
 Iu refsec:cln we saw that there is a strong auti-correlation between neighboring facets that causes a reduction in the YORP inaguitude., In \\ref{sec:em} we saw that there is a strong anti-correlation between neighboring facets that causes a reduction in the YORP magnitude.
 This auti-ccorrelation is represented by the expression in the parentheses dn audeq., This anti-correlation is represented by the expression in the parentheses in and.
"CI0)... To mimic this auti-correlation we take a set. {t,f. of N umunbers randomly drawn ήον] from -1 to 1 and represent the term in the pareutheses as the difference between any two consecutive nuubers."," To mimic this anti-correlation we take a set, $\{x_n\}$, of N numbers randomly drawn uniformly from -1 to 1 and represent the term in the parentheses as the difference between any two consecutive numbers."
 For exauple for the spin change rate we cau write: and for the obliquitystability: where 0 is a randonlv drawn vector of length Vl rangiue from 0 to π and sorted in an mereasing manner., For example for the spin change rate we can write: and for the obliquitystability: where $\theta'$ is a randomly drawn vector of length $N-1$ ranging from $0$ to $\pi$ and sorted in an increasing manner.
 Since in asteroids we lave we setaονp=potysinÜNa., Since in asteroids we have we set $x_{N}-x_{N-1}=\sum_{n=1}^{N-2}(x_{n+1}-x_{n})\sin\theta'_n/sin\theta_{N-1}$.
 The sign of défde|.y-ste30=pns0) for our simpleSOT fmodel las a likelihood of 85% heing positive. while the likelihood of défde|.y+Ste=0) for our randomly constructed asteroids being positive is NN (df is more than TN because it accounts for cases with amore than oulv 2 stable obliquity points).," The sign of $d\dot{\epsilon}/d\epsilon|_{\epsilon=0} \cdot\dot{s}(\epsilon=0)$ for our simple model has a likelihood of $85\%$ being positive, while the likelihood of ${d\dot{\epsilon}}/{d\epsilon}|_{\epsilon=0}\cdot \dot{s}(\epsilon=0)$ for our randomly constructed asteroids being positive is $88\%$ (it is more than $78\%$ because it accounts for cases with more than only 2 stable obliquity points)."
 The strong tendency of asteroids to spin-down is merely a result of the correlations between ucighboring facets., The strong tendency of asteroids to spin-down is merely a result of the correlations between neighboring facets.
 Asteroids with moderate thermal conductivity might exhibit differcut obliquity behavior which is bevoud the scope of this work (?).., Asteroids with moderate thermal conductivity might exhibit different obliquity behavior which is beyond the scope of this work \citep{CV04}.
 When the spin of the asteroid is sufficiently low. the asteroid nüeht fall iuto a chaotic tumbling rotation state and it is not clear if the asteroid can recover principal axes rotation (?)..," When the spin of the asteroid is sufficiently low, the asteroid might fall into a chaotic tumbling rotation state and it is not clear if the asteroid can recover principal axes rotation \citep{tumbling}. ."
 If the asteroid is a rubble pile. the spiu-up iuieht eventually break up the asteroid due to centrifieal force.," If the asteroid is a rubble pile, the spin-up might eventually break up the asteroid due to centrifugal force."
 However. rubble-pile asteroid deformations are not well understood (2??)..," However, rubble-pile asteroid deformations are not well understood \citep{deform, deform_scheeres, deform_walsh}. ."
 Tuspection of the shape of binary LODOILW LC?) sugeestsOO that break up is possible., Inspection of the shape of binary 1999KW4 \citep{1999kw4} suggests that break up is possible.
from being quiescent. the source is continuously active at a low level. aside from the pre-Dare periods of truly quenched emission.,"from being quiescent, the source is continuously active at a low level, aside from the pre-flare periods of truly quenched emission."
 Newell. Garrett Spencer (1998) observed some minor Haring episodes (peak Hluxes 300 mmJ.) with the Very Long Baseline Array (VLBA) and claimed. evidence [or superluminal expansion ancl contraction of the source.," Newell, Garrett Spencer (1998) observed some minor flaring episodes (peak fluxes $\sim300$ mJy) with the Very Long Baseline Array (VLBA) and claimed evidence for superluminal expansion and contraction of the source."
 No other high-resolution observations have addressed the nature of the source during the low-level. active state in which it spends the majority of its time.," No other high-resolution observations have addressed the nature of the source during the low-level, active state in which it spends the majority of its time."
 Phe resolved: nature of the source in the observations of Newelletal.(1998) demonstrated that the jets are still active even outside the major Haring events., The resolved nature of the source in the observations of \citet{New98} demonstrated that the jets are still active even outside the major flaring events.
 Direct evidence for jet activity outside Waring events is also seen in 11915|105. in which an AU-scale nuclear jet was resolved with the VLBA (Dhawan. Mirabel euez. 2000).," Direct evidence for jet activity outside flaring events is also seen in 1915+105, in which an AU-scale nuclear jet was resolved with the VLBA (Dhawan, Mirabel guez, 2000)."
 At the resolution of the images. the jet was observed to be continuous rather than knotty. with a length which varied with observing wavelength as 10A: AAU.," At the resolution of the images, the jet was observed to be continuous rather than knotty, with a length which varied with observing wavelength as $\sim10\lambda_{\rm cm}$ AU."
 The lighteurves of the observations confirmed that this was an optical depth ellect., The lightcurves of the observations confirmed that this was an optical depth effect.
 We sec emission from the 7=1 surface. which is further out at lower frequencies.," We see emission from the $\tau=1$ surface, which is further out at lower frequencies."
 This then results in a time delay between (lux variations at. dillerent frequencies. as any injection of relativistie plasma at the jet base takes time to propagate out to the point at which the jet ds optically thin at the observing frequency (asseeninCRS1915|105byMirabeletal. 1998).," This then results in a time delay between flux variations at different frequencies, as any injection of relativistic plasma at the jet base takes time to propagate out to the point at which the jet is optically thin at the observing frequency \citep[as seen in GRS\,1915+105
by][]{Mir98}."
. This also gives rise to the smoothing out of the variability at lower frequencies. since the observed. emission is à convolution over a larger region.," This also gives rise to the smoothing out of the variability at lower frequencies, since the observed emission is a convolution over a larger region."
 Measurements of the time delay between dilferent observing frequencies can thus help constrain the size scale of the jets., Measurements of the time delay between different observing frequencies can thus help constrain the size scale of the jets.
 Seine optically thick. such selt-absorbed. jets tend. to show very low levels of linear polarization.," Being optically thick, such self-absorbed jets tend to show very low levels of linear polarization."
 Corbelctal. detected linear. polarization at a level of ~2 per cent in the jets of 3339-4 while the source was in the owhard X-ray state (believed to be associated with steady. ow-Ievel jets).," \citet{Cor00} detected linear polarization at a level of $\sim2$ per cent in the jets of 339-4 while the source was in the low/hard X-ray state (believed to be associated with steady, low-level jets)."
 The position angle of the electric field vector remained constant over more than two vears. indicating a zwoured axis in the svstem. believed to be aligned. with he axis of the compact jets.," The position angle of the electric field vector remained constant over more than two years, indicating a favoured axis in the system, believed to be aligned with the axis of the compact jets."
 Transient jets. on the other iand. regularly show significantly higher levels of polarized emission. arising from optically thin ejecta (e.g.Fenderetal.1999:Llannikeinenetal.2000:Brocksopp 2007).. which may vary in amplitude ancl position angle with time. as dillerent components dominate the flux density at. llferent times. or if the source moves out from behind a screen of ionised electrons which rotate the position angle via Faraday rotation.," Transient jets, on the other hand, regularly show significantly higher levels of polarized emission, arising from optically thin ejecta \citep[e.g.][]{Fen99,Han00,Bro07}, which may vary in amplitude and position angle with time, as different components dominate the flux density at different times, or if the source moves out from behind a screen of ionised electrons which rotate the position angle via Faraday rotation."
 The relativistically-moving transient. ejecta observed during X-ray binary outbursts (e...Alirabel&Rodriguezpen1995) have previously been mocdelled either as discrete knots of adiabaticallv-expanding plasma (c.g.vanderLaan 1999).. or as internal shocks within a pre-existing steady How (e.g.. Fender. Belloni Gallo. 2004).," The relativistically-moving transient ejecta observed during X-ray binary outbursts \citep[e.g.][]{Mir94,Fen99,Tin95,Hje95} have previously been modelled either as discrete knots of adiabatically-expanding plasma \citep[e.g.][]{van66,Hje88,Ato99}, , or as internal shocks within a pre-existing steady flow (e.g., Fender, Belloni Gallo, 2004)."
 Atovan&Aharo-nian(1009). found that a discrete plasmon mocdel requires continuous replenishment of relativistic particles as well as radiative. aciabatic. ancl energyv-dependent escape. losses.," \citet{Ato99} found that a discrete plasmon model requires continuous replenishment of relativistic particles as well as radiative, adiabatic, and energy-dependent escape losses."
 kaiser. Sunvaey Spruit (2000) argued that such energy-dependent escape losses were inconsistent. with. continuous particle replenishment via shock acceleration. and adapted the internal shock model originally derived. for ΑΝ jets (Rees1978:Marscher&Gear1985) to X-ray binary systems.," Kaiser, Sunyaev Spruit (2000) argued that such energy-dependent escape losses were inconsistent with continuous particle replenishment via shock acceleration, and adapted the internal shock model originally derived for AGN jets \citep{Ree78,Mar85} to X-ray binary systems."
 Fenderetal.(2004) integrated the internal shock scenario into a model explaining the disc-jet coupling over the entire duty evele of an N-ray. binary system., \citet{Fen04} integrated the internal shock scenario into a model explaining the disc-jet coupling over the entire duty cycle of an X-ray binary system.
 1n this scenario. as a source moves [rom a hard to a soft. X-ray state. the bulk Lorentz factor of the pre-existing steady jet increases. giving rise to shocks where the highlv-relativistic plasma catches up with pre-existing slower-moving material downstream in the jets.," In this scenario, as a source moves from a hard to a soft X-ray state, the bulk Lorentz factor of the pre-existing steady jet increases, giving rise to shocks where the highly-relativistic plasma catches up with pre-existing slower-moving material downstream in the jets."
 In. this work. we focus on the shock-in-jet. model. since internal shocks form a natural explanation for the outbursts in the current disc-jet coupling xeture (Fenderctal.2004)... and since shocks provide a mechanism for the continuous replenishment of relativistic xwticles found to be required in a plasmon model (Atovan&Aharonian1999).," In this work, we focus on the shock-in-jet model, since internal shocks form a natural explanation for the outbursts in the current disc-jet coupling picture \citep{Fen04}, , and since shocks provide a mechanism for the continuous replenishment of relativistic particles found to be required in a plasmon model \citep{Ato99}."
. While detailed. model fitting for the dasmion scenario is deemed to be beyond the scope of this yaper. where relevant. we will provide brief. generic outlines of how the two classes of model dilfer.," While detailed model fitting for the plasmon scenario is deemed to be beyond the scope of this paper, where relevant, we will provide brief, generic outlines of how the two classes of model differ."
 In Section 2.. we present dual-frequeney racio ighteurves of Cygnus. X-3. taken when the source was in its normal low-level active state. in order to constrain he polarization of the source and. investigate the opacity ellects in the jet. (Section. 3)).," In Section \ref{sec:obs}, we present dual-frequency radio lightcurves of Cygnus X-3, taken when the source was in its normal low-level active state, in order to constrain the polarization of the source and investigate the opacity effects in the jet (Section \ref{sec:opacity}) )."
 In Section 4.. we fit the multifrequency lightcurves with a shock-in-jet model. in order to draw comparisons with the properties of the giant outbursts.," In Section \ref{sec:modelling}, we fit the multifrequency lightcurves with a shock-in-jet model, in order to draw comparisons with the properties of the giant outbursts."
 Cvenus N-3 was observed for hhours on 2002 January 25 552299) with the Very Large Array (VLA) in its most extended: X-configuration. under program. code. 4458.," Cygnus X-3 was observed for hours on 2002 January 25 52299) with the Very Large Array (VLA) in its most extended A-configuration, under program code 458."
 The VLA was split into two subarravs. and the source was observed. simultaneously. at. GiGlIIz in one subarray and at 43.340GCGLIz in the other.," The VLA was split into two subarrays, and the source was observed simultaneously at GHz in one subarray and at GHz in the other."
 Occasional snapshots ab 1.425. 4.860. 8460 and νά were also carried out in order to characterise the overall radio spectrum.," Occasional snapshots at 1.425, 4.860, 8.460 and GHz were also carried out in order to characterise the overall radio spectrum."
 Observations at cach frequeney. were mace in the standard VLA continuum moce (dual circular polarization in two 50-MllIz bancs. with full polarization products being recorded).," Observations at each frequency were made in the standard VLA continuum mode (dual circular polarization in two 50-MHz bands, with full polarization products being recorded)."
 The primary calibrator used. was 2286 11331|305). and the secondary calibrator was 22007|404.," The primary calibrator used was 286 1331+305), and the secondary calibrator was 2007+404."
 Phe absolute Hux density of 2286 was set using the cocllicients of Baarsetal.(LO77)., The absolute flux density of 286 was set using the coefficients of \citet{Baa77}.
. For the majority. of the observing run. calibrator observations of duration.  1mamin were interspersed with 1020-min scans on Cygnus X-3.," For the majority of the observing run, calibrator observations of duration $\sim 1$ min were interspersed with 10–20-min scans on Cygnus X-3."
 For 25mmin in the middle of the run however. fast-switching was used. slewing back and forth. between the target and he calibrator with a evele time of ss. spending I00ss on he target and. ss on the calibrator.," For min in the middle of the run however, fast-switching was used, slewing back and forth between the target and the calibrator with a cycle time of s, spending s on the target and s on the calibrator."
 This approach was designed to reduce tropospheric phase variation. allowing or dillraction-limited imaging. which on the long baselines at the high observing frequencies used might not otherwise jwe been possible.," This approach was designed to reduce tropospheric phase variation, allowing for diffraction-limited imaging, which on the long baselines at the high observing frequencies used might not otherwise have been possible."
 The data were reduced. using standard »ocedures within the data reduction package (Cireisen 2003)., The data were reduced using standard procedures within the data reduction package \citep{Gre03}.
. Primary referenced. pointing (pointing up on a calibrator at. à. lower frequeney to. derive. the relevant pointing olfsets for higher frequencies where the ollsets may »' à significant fraction of theprimary beam)was used at, Primary referenced pointing (pointing up on a calibrator at a lower frequency to derive the relevant pointing offsets for higher frequencies where the offsets may be a significant fraction of theprimary beam)was used at
cloud. then exits through the back surface of the shell to reside in the low density interior of the hot bubble driving the shell.,cloud then exits through the back surface of the shell to reside in the low density interior of the hot bubble driving the shell.
 The most interesting aspect of the interaction 1s the formation of a tail behind the cloud (forearliersimulationsTagle&Rozvezka 1984b).," The most interesting aspect of the interaction is the formation of a tail behind the cloud \citep[for earlier simulations which display
 similar but much thinner tails see][]{Tenorio-Tagle:1984b}."
. Phe tail is mainly composed of material [rom the shell. with only small amounts (less than a few percent concentration) of material ablated: or stripped. from the cloud.," The tail is mainly composed of material from the shell, with only small amounts (less than a few percent concentration) of material ablated or stripped from the cloud."
 The part of the shell adjacent to the cloud. moves in the lateral direction onto the axis clue to the pressure gradient which exists across its [ace as it sweeps over the cloud (see Fig. 3))., The part of the shell adjacent to the cloud moves in the lateral direction onto the axis due to the pressure gradient which exists across its face as it sweeps over the cloud (see Fig. \ref{fig:rzpre}) ).
 A Lage eddy formis which causes this material to lose speed relative to the, A large eddy forms which causes this material to lose speed relative to the
To exelude this possibility. we repeated our analysis with a nominal source cell size and did not find any difference in the list of supersoft sources.,"To exclude this possibility, we repeated our analysis with a nominal source cell size and did not find any difference in the list of supersoft sources."
 The results of our analysis are presented in Table 4.., The results of our analysis are presented in Table \ref{tab:xtok}.
 Listed in the table are the X-ray luminosity of unresolved emission Lxui. of resolved supersoft sources Ly... and of ionized gas Lxvay.," Listed in the table are the X-ray luminosity of unresolved emission $L_{\mathrm{X,unres}} $, of resolved supersoft sources $ L_{\mathrm{X,sss}} $, and of ionized gas $L_{\mathrm{X,gas}}$."
 From these quantities and from the K-band luminosity of the studied region (Table 1)). we computed the X-ray to K-band luminosity ratios —. Zx/Ly.," From these quantities and from the K-band luminosity of the studied region (Table \ref{tab:list2}) ), we computed the X-ray to K-band luminosity ratios – $L_{\mathrm{X}}/L_{\mathrm{K}}$."
" In the case of M31 and in NGC4278 we computed Ly/L, ratio in the outer regions. where no significant gas emission is detected."," In the case of M31 and in NGC4278 we computed $L_X/L_K$ ratio in the outer regions, where no significant gas emission is detected."
 The Milky Way value was obtained using the results of Sazonovetal.(2006).. who computed the luminosity of active binaries (ABs) and cataclysmic variables (CVs) in the solar neighborhood.," The Milky Way value was obtained using the results of \citet{sazonov}, who computed the luminosity of active binaries (ABs) and cataclysmic variables (CVs) in the solar neighborhood."
 The interstellar absorption is negligible in this case., The interstellar absorption is negligible in this case.
 We converted their X-ray-to-mass ratios from the 0.1—2.4 keV band to the 0.3—0.7 keV energy range. using typical spectra of ABs and CVs (see Fig. 3)).," We converted their X-ray-to-mass ratios from the $ 0.1-2.4 $ keV band to the $ 0.3-0.7 $ keV energy range, using typical spectra of ABs and CVs (see Fig. \ref{fig:softsrc}) ),"
" and assuming a mass-to-light ratio of M./Ly=1.0 (Kent.1992) The obtained ratios are in the range of Lx/Lg=(1.2—-107ergs""!Let. and show a large dispersion."," and assuming a mass-to-light ratio of $ M_{\star}/L_{K} =1.0 $ \citep{kent}
 The obtained ratios are in the range of $ L_{\mathrm{X}}/L_{\mathrm{K}} = (1.2-4.1) \cdot 10^{27} \ \mathrm{erg \ s^{-1} \ L_{K,\odot}^{-1}} $ and show a large dispersion."
 This dispersion is caused by the large difference in the point source detection sensitivity for the galaxies in our sample (Table 1)., This dispersion is caused by the large difference in the point source detection sensitivity for the galaxies in our sample (Table 1).
 To correct for this effect and to bring all galaxies to the same source detection sensitivity. we chose the threshold luminosity of 2-1009eres7!.," To correct for this effect and to bring all galaxies to the same source detection sensitivity, we chose the threshold luminosity of $ 2 \cdot 10^{36} \ \mathrm{erg \ s^{-1}} $."
" In those galaxies that had better source detection sensitivity (M31 bulge. M32. M105. Sagittarius). we did not remove any source fainter than 2-10°°eres! in computing the luminosity of ""unresolved"" emission."," In those galaxies that had better source detection sensitivity (M31 bulge, M32, M105, Sagittarius), we did not remove any source fainter than $ 2 \cdot 10^{36} \ \mathrm{erg \ s^{-1}} $ in computing the luminosity of “unresolved” emission."
 In the case of NGC3377 and NGC3585 having much worse detection sensitivity we subtracted the contribution of unresolved LMXBs in the luninosity range of 2-1079—2.107ergs! from the measured luminosity of unresolved emission., In the case of NGC3377 and NGC3585 having much worse detection sensitivity we subtracted the contribution of unresolved LMXBs in the luminosity range of $ 2 \cdot 10^{36} - 2 \cdot 10^{37} \ \mathrm{erg \ s^{-1}} $ from the measured luminosity of unresolved emission.
 To estimate the former we used two methods., To estimate the former we used two methods.
 In the first. We measured the combied X-ray emission from hard resolved sources in this lumiosity range in three galaxies. M31. MIOS. and NGC4278. which allowed us to compute the Zx/Lg ratio due to such sources for each of these three galaxies.," In the first, we measured the combined X-ray emission from hard resolved sources in this luminosity range in three galaxies, M31, M105, and NGC4278, which allowed us to compute the $L_{\mathrm{X}}/L_{\mathrm{K}}$ ratio due to such sources for each of these three galaxies."
 We obtained fairly uiform values with the average number of =(1.5£0.2)-107?ergsu!Ly. where the cited error is the rms of the calculated values.," We obtained fairly uniform values with the average number of $ \approx (1.5 \pm 0.2) \cdot 10^{27} \ \mathrm{erg \ s^{-1} \ L_{K,\odot}^{-1}} $, where the cited error is the rms of the calculated values."
 In the second method. the contribution ofunresolved hard sources was estimated from," In the second method, the contribution of unresolved hard sources was estimated from"
from the center of the core.,from the center of the core.
 The two digit numbers are the elapsed (ime in units of 40.000 vears after turning on sell-gravitv.," The two digit numbers are the elapsed time in units of 40,000 years after turning on self-gravity."
 We can clearly see from density profiles that the central density of the core is increasing as time goes on., We can clearly see from density profiles that the central density of the core is increasing as time goes on.
 The power index of density. profiles in the ouler region is increasing [rom shallower (han -2 al an earlier Gime to sleeper than -2 al a later time., The power index of density profiles in the outer region is increasing from shallower than -2 at an earlier time to steeper than -2 at a later time.
 At a given radial distance. the density ancl velocity dispersions are much smaller ian (he raclially averaged density. ancl velocity. respectively.," At a given radial distance, the density and velocity dispersions are much smaller than the radially averaged density and velocity, respectively."
 The racial velocity. profiles are quite interesting., The radial velocity profiles are quite interesting.
 In the central part of the core. most οἱ 1e profiles have negative bul very small velocity. which means that the central part of core is slowly collapsing.," In the central part of the core, most of the profiles have negative but very small velocity, which means that the central part of core is slowly collapsing."
 In the outer part of the core. the profiles have both positive ancl negative V.iens and their amplitudes are larger (han the thermal sound speed.," In the outer part of the core, the profiles have both positive and negative signs and their amplitudes are larger than the thermal sound speed."
 The large-amplitude velocily profiles are due to not only the large-scale turbulent flow nearby the core but also accretion shocks onto the core., The large-amplitude velocity profiles are due to not only the large-scale turbulent flow nearby the core but also accretion shocks onto the core.
 Even though we do not show radial clensitv ancl velocity profiles [rom a simulation with a weak initial field strength. 9]=1.0. the Iarge-amplitude velocily profiles in the outer part of a core are also found.," Even though we do not show radial density and velocity profiles from a simulation with a weak initial field strength, $\beta=1.0$, the large-amplitude velocity profiles in the outer part of a core are also found."
 However. infall velocities in the central part of the core have a bil larger (but still have a subsonic speed) (han ones of the case wilh 3=0.1.," However, infall velocities in the central part of the core have a bit larger (but still have a subsonic speed) than ones of the case with $\beta=0.1$."
 Figure 2 shows the comparison between dust and gas temperatures calculated. based on the cust continuum radiative transfer and the balance between heating ancl cooling of eas. respectively.," Figure 2 shows the comparison between dust and gas temperatures calculated based on the dust continuum radiative transfer and the balance between heating and cooling of gas, respectively."
 The eas temperature is decoupled [rom the dust temperature at densities X5x10! 7 where gas-grain collisions is not dominant. and has peaks at the surface of the model core due to the photoelectric heating.," The gas temperature is decoupled from the dust temperature at densities $\le 5\times 10^4$ $^{-3}$, where gas-grain collisions is not dominant, and has peaks at the surface of the model core due to the photoelectric heating."
 The evolution of the — radial abundance calculated. based on the density. and temperature evolution is presented in Figure 3., The evolution of the $^+$ radial abundance calculated based on the density and temperature evolution is presented in Figure 3.
 As expected. at small radii. is signilieantlv depleted [rom the gas phase as densitv grows because CO becomes Irozen-out. onto grain surfaces (Lee et al.," As expected, at small radii, $^+$ is significantly depleted from the gas phase as density grows because CO becomes frozen-out onto grain surfaces (Lee et al."
 2003. 2004 and references therein) in such dense and cold conditions.," 2003, 2004 and references therein) in such dense and cold conditions."
 The abundance drops at (hie core surface due to the dissociative recombination of — with electrons., The abundance drops at the core surface due to the dissociative recombination of $^+$ with electrons.
 As described in 32.2. the chemical evolution is caleulated at each grid point without following each gas parcel (Chat is. assuming the quasi-static evolution) due to the following reasons.," As described in 2.2, the chemical evolution is calculated at each grid point without following each gas parcel (that is, assuming the quasi-static evolution) due to the following reasons."
 In the inner region of the core. the static evolution is a good approximation since the velocity is much smaller than the sound speed.," In the inner region of the core, the static evolution is a good approximation since the velocity is much smaller than the sound speed."
 In the outer part of the core. however. densities are low. and thus the chemical time scale is (oo long (o be affected by the movement of gas parcels.," In the outer part of the core, however, densities are low, and thus the chemical time scale is too long to be affected by the movement of gas parcels."
 For example. an infalling gas parcel with the infall velocitv of 0.5 kms | at the surface moves inward only 20.02 pe for 40.000 vears. and (he densities of (wo positions are nol very different.," For example, an infalling gas parcel with the infall velocity of 0.5 km $^{-1}$ at the surface moves inward only $\sim$ 0.02 pc for 40,000 years, and the densities of two positions are not very different."
 This assumption is also well supported in Figure 3., This assumption is also well supported in Figure 3.
 The abundance of varies significantly at small radii. but at radii greater (han 0.1 pe. where velocities are possibly ereater than the sound speed. the abundance does not vary much with time.," The abundance of $^+$ varies significantly at small radii, but at radii greater than 0.1 pc, where velocities are possibly greater than the sound speed, the abundance does not vary much with time."
spectral lines from CO. IISO. and CLL). which likely increases (he scatter in (he line strength vs. velocily relationship.,"spectral lines from CO, $_2$ O, and $_4$, which likely increases the scatter in the line strength vs. velocity relationship."
" This is particularly. true for CO and CLL, because lines from these two molecules tend (o originate from different regions of the atmosphere CO [rom regions ol hotter gas. likely weighted towards the eastern terminator and CIL, from regions of colder eas on the western terminator."," This is particularly true for CO and $_4$ because lines from these two molecules tend to originate from different regions of the atmosphere – CO from regions of hotter gas, likely weighted towards the eastern terminator and $_4$ from regions of colder gas on the western terminator."
 Measuring the line strengths for only the 76 first-overtone lines of CO (not shown) results in a tighter linear relationship for line strength vs. velocity., Measuring the line strengths for only the 76 first-overtone lines of CO (not shown) results in a tighter linear relationship for line strength vs. velocity.
 llowever. (his particular set of lines samples a lar smaller range of altitude in the atmosphere. since all of the CO spectral lines are quite strong aud therefore originate [rom regions of hieh altitude and low pressure.," However, this particular set of lines samples a far smaller range of altitude in the atmosphere, since all of the CO spectral lines are quite strong and therefore originate from regions of high altitude and low pressure."
 Aleasuring Doppler shifts of individual spectra lines in (rausmiission is another effect (hat will almost certainly require next generation instrumentation to realize. due to the very hieh signal-to-noise requirements.," Measuring Doppler shifts of individual spectra lines in transmission is another effect that will almost certainly require next generation instrumentation to realize, due to the very high signal-to-noise requirements."
 The only measurements of Doppler shifts in Uransnission to date (2)| required the full spectrum from 2291 to 2349 nm to detect a Doppler shill ab km + precision., The only measurements of Doppler shifts in transmission to date \citep{sne10} required the full spectrum from 2291 to 2349 nm to detect a Doppler shift at km $^{-1}$ precision.
 Individual spectral lines were not. present in their spectra at close to sufficient signal-to-noise to measure RY shifts. even when integrating over a full transit.," Individual spectral lines were not present in their spectra at close to sufficient signal-to-noise to measure RV shifts, even when integrating over a full transit."
 We have coupled together an existing 3-D atmospheric dvinamics model with a transmission spectroscopy radiative transfer code to study (he effects of Doppler shilted winds (along with rotation and orbital motion) on the transmission spectra of hot Jupiter exoplanets., We have coupled together an existing 3-D atmospheric dynamics model with a transmission spectroscopy radiative transfer code to study the effects of Doppler shifted winds (along with rotation and orbital motion) on the transmission spectra of hot Jupiter exoplanets.
 We find that day-to-night winds at altitudes of < Ll mbar can produce significant bIueshifts in hot Jupiter transmission spectra at the level of 1-2 km +., We find that day-to-night winds at altitudes of $\lesssim$ 1 mbar can produce significant blueshifts in hot Jupiter transmission spectra at the level of 1-2 km $^{-1}$.
 Also. the combined effects of winds and the planets rotation lead to considerable Doppler broadening of the spectral lines bevond what is predicted if no Doppler shifts are included.," Also, the combined effects of winds and the planet's rotation lead to considerable Doppler broadening of the spectral lines beyond what is predicted if no Doppler shifts are included."
 These effects all become important [or transmission spectra taken al high spectral resolution of R>10., These effects all become important for transmission spectra taken at high spectral resolution of $R \gtrsim 10^5$.
 We have explored different. prescriptions for magnetic drag in the atmospheres of hot Jupiters. and we find that the models with the largest amount of magnetic drag produce the slowest wind speeds and therefore (he smallest Doppler (blue) shifts. while the models with no magnetic drag produce the largest velocity shilts.," We have explored different prescriptions for magnetic drag in the atmospheres of hot Jupiters, and we find that the models with the largest amount of magnetic drag produce the slowest wind speeds and therefore the smallest Doppler (blue) shifts, while the models with no magnetic drag produce the largest velocity shifts."
 In our modeling. the magnetic drag models produce net blueshifts of —1 km !. whereas the models with no drag produce blueshilts of ~2 kms !.," In our modeling, the magnetic drag models produce net blueshifts of $\sim$ 1 km $^{-1}$, whereas the models with no drag produce blueshifts of $\sim$ 2 km $^{-1}$."
 Ultimatelv differentiating between different drag prescriptions through observations of hot Jupiter (transmission spectra will therefore require RV precision of much higher (han 1 kms +., Ultimately differentiating between different drag prescriptions through observations of hot Jupiter transmission spectra will therefore require RV precision of much higher than 1 km $^{-1}$.
 In the meantime. the current measurement of a 241 km/s blueshift in LLD 209458bs óransmission spectrum by ? remains consistent will models both with and without magnetic drag.," In the meantime, the current measurement of a $2 \pm 1$ km/s blueshift in HD 209458b's transmission spectrum by \citet{sne10} remains consistent with models both with and without magnetic drag."
a foreground star refebsRV ).,a foreground star \\ref{c_absRV}) ).
Inconclusion. withnineteenstarslostorexcluded. theresultingsamplecomprisesSOEBT lund AE BT2stárs.outo f whichsixXEHI The measurements for the four spectra that were not the sum of two exposures. ie. the frames 3-2. 4-2. 5-]. and 6-3 (Table 1)). were in general less reliable. and they were oftei excluded for faint stars.," In conclusion, with nineteen stars lost or excluded, the resulting sample comprises 50 EBT1 and 14 EBT2 stars, out of which six EHB targets have $_\mathrm{eff}\geq$ 000 K. The measurements for the four spectra that were not the sum of two exposures, i.e. the frames 3-2, 4-2, 5-1, and 6-3 (Table \ref{t_obs}) ), were in general less reliable, and they were often excluded for faint stars."
 In the upper panel of Figure 8.. we plot the decrease in the binary detection efficiency. as a function of period. if these four frames are not considered.," In the upper panel of Figure \ref{f_detprob}, we plot the decrease in the binary detection efficiency, as a function of period, if these four frames are not considered."
 Their exclusior clearly does not affect the survey much. because the probability of detecting a true binary in general decreases by less thai366. except for two sensitive periodicities (1 day and ~ 18 days) where the loss is about155c.," Their exclusion clearly does not affect the survey much, because the probability of detecting a true binary in general decreases by less than, except for two sensitive periodicities (1 day and $\sim$ 18 days) where the loss is about."
. Therefore. we finally excludec them from the statistical analysis.," Therefore, we finally excluded them from the statistical analysis."
 The measurements for these lower-quality frames were indeed always more uncertain. anc were often excluded anyway. affecting the uniformity. of the measurements.," The measurements for these lower-quality frames were indeed always more uncertain, and were often excluded anyway, affecting the uniformity of the measurements."
 We then consider only the remaining ten epochs for each star., We then consider only the remaining ten epochs for each star.
 The identification of binary candidates requires criteria to define when the observed variations can be considered significant., The identification of binary candidates requires criteria to define when the observed variations can be considered significant.
 The criteria must satisfy two desiderata: the probability of a false detection (Pye) must be negligible. while the probability of detecting a true binary (P4) must be as high as possible. within the limitations imposed by the temporal sampling and the observational errors.," The criteria must satisfy two desiderata: the probability of a false detection $_\mathrm{false}$ ) must be negligible, while the probability of detecting a true binary $_\mathrm{det}$ ) must be as high as possible, within the limitations imposed by the temporal sampling and the observational errors."
 Usually the first point is satisfied if the statistical expectation is less than one false detection 1n the whole survey. which in our samples of 64 targets means Pry x0.014.," Usually the first point is satisfied if the statistical expectation is less than one false detection in the whole survey, which in our samples of 64 targets means $_\mathrm{false}\leq$ 0.014."
 A compromise between these requirements 1s often needed. because more stringent criteria reducing Pry. also reduce the efficiency of detecting genuine RV variables.," A compromise between these requirements is often needed, because more stringent criteria reducing $_\mathrm{false}$ also reduce the efficiency of detecting genuine RV variables."
 The parameter Py was estimated as a function of orbital period. generating 2500 synthetic binaries in circular orbits of period 9. comprising two stars of 0.5 M... uniformly distributed in the sin(/)-8 space. where / is the angle of inclination of the orbital plane and & is the orbital phase.," The parameter $_\mathrm{det}$ was estimated as a function of orbital period, generating 2500 synthetic binaries in circular orbits of period $\wp$, comprising two stars of 0.5 $_\odot$, uniformly distributed in the $i$ $\theta$ space, where $i$ is the angle of inclination of the orbital plane and $\theta$ is the orbital phase."
 These systems were then “observed” with the same temporal sampling of our survey. and each star satisfying the criteria under analysis represented a detection.," These systems were then ”observed"" with the same temporal sampling of our survey, and each star satisfying the criteria under analysis represented a detection."
 The fraction of detections over the whole sample thus indicated the efficiency of the survey for systems of period o., The fraction of detections over the whole sample thus indicated the efficiency of the survey for systems of period $\wp$.
 Pur was calculated by simulating 1000000 sets of N measurements drawn from a normal distribution centered on zero and of unity dispersion., $_\mathrm{false}$ was calculated by simulating 000 sets of $N$ measurements drawn from a normal distribution centered on zero and of unity dispersion.
 Each set represented the observations of a star with constant RV. affected by only random errors normalized to unity. and N=10 for our survey.," Each set represented the observations of a star with constant RV, affected by only random errors normalized to unity, and $N$ =10 for our survey."
 A false detection was claimed for each set of measurements satisfying the eriteria for binary detection. and Pry was estimated as the fraction of false detections over the whole sample of 0000 attempts.," A false detection was claimed for each set of measurements satisfying the criteria for binary detection, and $_\mathrm{false}$ was estimated as the fraction of false detections over the whole sample of 000 attempts."
 In previous investigations of HB stars in GCs. the eriteria adopted for the detection of a binary candidate was that the measured RV variation was larger than 3c. where c was either the error in the spectral shift among two epochs(??).. or the quadratic sum of the errors in RV measurements(2).," In previous investigations of HB stars in GCs, the criteria adopted for the detection of a binary candidate was that the measured RV variation was larger than $\sigma$, where $\sigma$ was either the error in the spectral shift among two epochs, or the quadratic sum of the errors in RV measurements."
. This strategy worked well for surveys based on 4-5 epochs. but is unsuitable for our work: the upper panel of Figure 7. shows that the probability of a false detection rapidly increases with the number of measurements. and in our 10-epochs survey we should expect of non-binary targets (~6 stars) to violate the threshold due to random errors only.," This strategy worked well for surveys based on 4-5 epochs, but is unsuitable for our work: the upper panel of Figure \ref{f_fdetprob} shows that the probability of a false detection rapidly increases with the number of measurements, and in our 10-epochs survey we should expect of non-binary targets $\sim$ 6 stars) to violate the threshold due to random errors only."
 The method could be applied even here. but to reduce the expected false detections to less than one star we should increase the threshold up to 3.80. as indicated by the lower panel of Figure 7.. i.e. ~25- km s! for the hotter stars.," The method could be applied even here, but to reduce the expected false detections to less than one star we should increase the threshold up to $\sigma$, as indicated by the lower panel of Figure \ref{f_fdetprob}, i.e. $\sim$ 25-30 km $^{-1}$ for the hotter stars."
" In the same Figure. we also show Py; for an alternative criteria. which we define as ""absolute"" (while the older one is called ""relative): a star is flagged"," In the same Figure, we also show $_\mathrm{false}$ for an alternative criteria, which we define as ”absolute"" (while the older one is called ”relative""): a star is flagged"
strong clear sinusoidal modulation at  Q.7d. The combined OGLE and NLACTIO data set for this object is presented in Figure 3..,strong clear sinusoidal modulation at $\sim0.7$ d. The combined OGLE and MACHO data set for this object is presented in Figure \ref{mo}.
 Though the precise modulation is not obvious [rom this figure. it clearly. shows the varying amplitude of the modulation over the data set.," Though the precise modulation is not obvious from this figure, it clearly shows the varying amplitude of the modulation over the data set."
 ΙΕ the total cata set is analyvsecl for periodic behaviour. then a period of 0.708572d is determined using a Lomb-Scargle analysis.," If the total data set is analysed for periodic behaviour, then a period of 0.70872d is determined using a Lomb-Scargle analysis."
 However. this »eriod is the average of the data. because if one splits up he data set into  150d samples a slightly dillerent period is found for each one.," However, this period is the average of the data, because if one splits up the data set into $\sim150$ d samples a slightly different period is found for each one."
 Figure 4 illustrates the Lomb-Scarele power spectrum. or one such subset ofdata., Figure \ref{pow} illustrates the Lomb-Scargle power spectrum for one such subset of data.
 To check on the aliasing with the vquist frequency and the effects of the window function. a simulated data set was created.," To check on the aliasing with the Nyquist frequency and the effects of the window function, a simulated data set was created."
 This data set consists of a single sinewave with period and amplitude determined from he original data sampled with exactly the same temporal structure as the original data., This data set consists of a single sinewave with period and amplitude determined from the original data sampled with exactly the same temporal structure as the original data.
 As can be seen by comparison between the two power spectra in Figure 4. there is no significant dillerence.," As can be seen by comparison between the two power spectra in Figure 4, there is no significant difference."
 Thus the conclusion is that there are no other frequencies present in the original clata set., Thus the conclusion is that there are no other frequencies present in the original data set.
 The shape of the modulation was determined by folding, The shape of the modulation was determined by folding
We consider MHD flows in a stationary and axisymmetric magnetosphere around a rotating black hole.,We consider MHD flows in a stationary and axisymmetric magnetosphere around a rotating black hole.
" The background metric g,, is written by the Boyer-Lindquist coordinate with c=G1.", The background metric $g_{\mu\nu}$ is written by the Boyer-Lindquist coordinate with $c=G=1$.
" The basic equations for MHD flows are the equation of the particle number conservation, the equation of motion and Maxwell equations."," The basic equations for MHD flows are the equation of the particle number conservation, the equation of motion and Maxwell equations."
 We also assume the ideal MHD condition and the polytropic relation for the plasma flows., We also assume the ideal MHD condition and the polytropic relation for the plasma flows.
" There are five field-aligned flow parameters on the flows; that is, the total energy E, the total angular momentum L, the angular velocity of the magnetic field line Qf and the number flux per flux-tube η and the entropy S (seeCamenzind1986a,b;Takahashietal.1990,forthedefinitionsoftheseflowparameters).."," There are five field-aligned flow parameters on the flows; that is, the total energy $E$, the total angular momentum $L$, the angular velocity of the magnetic field line $\Omega_F$ and the number flux per flux-tube $\eta$ and the entropy $S$ \citep[see][for the definitions of these flow
 parameters]{Camenzind86a,Camenzind86b,TNTT90}."
" 'The accreting flow onto a black hole must pass through the slow magnetosonic point, the point, and the fast magnetosonic point, in this order."," The accreting flow onto a black hole must pass through the slow magnetosonic point, the point, and the fast magnetosonic point, in this order."
" The critical conditions at the point and the magnetosonic points restrict the acceptable ranges of these parameters (seeTakahashi2002,forthedetails)..", The critical conditions at the point and the magnetosonic points restrict the acceptable ranges of these parameters \citep[see][for the details]{Takahashi02}.
" The poloidal magnetic field B, seen by a lab-frame observer is defined by B2=—[g'""(F4)?+ g*?(Fo4)?]/p2,, and the toroidal magnetic field is defined by By=(Δ/Σ)Εγο, where A=r?—2mr+a?, X=r?+a?cos?0, pl-Asin?0, and m and a are the hole's mass and spin, respectively."," The poloidal magnetic field $B_p$ seen by a lab-frame observer is defined by $B_p^2 \equiv -[ g^{rr}(F_{r\phi})^2 +
 g^{\theta\theta}(F_{\theta\phi})^2 ]/\rho_w^2$ and the toroidal magnetic field is defined by $B_\phi = (\Delta/\Sigma)F_{r\theta}$, where $\Delta=r^2-2mr+a^2$, $\Sigma=r^2+a^2\cos^2\theta$, $\rho_w^2=\Delta\sin^2\theta$, and $m$ and $a$ are the hole's mass and spin, respectively."
 The term Ἐν is the electromagnetic tensor., The term $F_{\mu\nu}$ is the electromagnetic tensor.
" In the following, we assume the cold inflows (S—0) except for the shock front."," In the following, we assume the cold inflows $(S=0)$ except for the shock front."
" Although, at the shock front, the plasma temperature can become so high, it falls off immediately by the radiation."," Although, at the shock front, the plasma temperature can become so high, it falls off immediately by the radiation."
" The relativistic Bernoulli equation for cold MHD flows, which determines the poloidal velocity (or the Mach number) along a magnetic tube, can be written as (Takahashi&Tomimatsu2008) where é=E—OpL with E=ΕἘ/με and L=L/{tc."," The relativistic Bernoulli equation for cold MHD flows, which determines the poloidal velocity (or the Mach number) along a magnetic tube, can be written as \citep{TT08}
 where $\ee\equiv \EE -\Omega_F \LL$ with ${\hat E}\equiv E/\mu_{c}$ and ${\hat L}\equiv L/\mu_{c}$."
 The enthalpy for cold flows is denoted by µε=Mpart; where Mpart is the particle’s mass.," The enthalpy for cold flows is denoted by $\mu_{c}=m_{\rm part}$, where $m_{\rm part}$ is the particle's mass."
" The terms B,=Β)/(Απµεη) and Bg=Βφ/(Απµεηρω) are introduced to non-dimensionalize,and the latter is given in terms of the relativistic Mach number and the flow parameters;"," The terms $\Bp \equiv B_p/(4\pi\mu_{c}\eta) $ and $\Bf \equiv B_\phi/(4\pi \mu_{c}\eta \rho_w) $ are introduced to non-dimensionalize,and the latter is given in terms of the relativistic Mach number and the flow parameters;"
by a Gaussian distribution with a standard deviation of 0.2 (no units).,by a Gaussian distribution with a standard deviation of 0.2 (no units).
" Accordingly, the initial ellipticity parameter values are adjusted using Equation so that ejy, matches the ellipticity determined from the simulated data image moments."," Accordingly, the initial ellipticity parameter values are adjusted using Equation \ref{eq:shearellip} so that $\epsilon_{\text{obs}}$ matches the ellipticity determined from the simulated data image moments."
 This ensures that the observed ellipticity of the initial model image matches that of the data image., This ensures that the observed ellipticity of the initial model image matches that of the data image.
" The AIM method converges to a minimum rapidly and consistently (>99% convergence, typically in less than 100 iterations)."," The AIM method converges to a minimum rapidly and consistently $>99\%$ convergence, typically in less than 100 iterations)."
 The final figure of merit χ per Degrees of Freedom (D.o., The final figure of merit $\chi^2$ per Degrees of Freedom (D.o.
F.) for converged fits have mean values of ~1.0-1.2.,F.) for converged fits have mean values of $\sim1.0$ $1.2$.
 A typical data image has 500-1000 D.o., A typical data image has 500–1000 D.o.
"F. Successful, converged fits are identified from the larger ensemble as those having x?/D.o0.F.«1.5 and o(V,,,,)>0.001 arcsec!.","F. Successful, converged fits are identified from the larger ensemble as those having $\chi^2/\text{D.o.F.}<1.5$ and $\sigma(\Psi_{mn})>0.001$ $^{-1}$."
" The latter condition is slightly couterintuitive, but it is useful for excluding fits which tightly constrain one or more flexion parameters to erroneous values in local minima of the X? surface."," The latter condition is slightly couterintuitive, but it is useful for excluding fits which tightly constrain one or more flexion parameters to erroneous values in local minima of the $\chi^2$ surface."
 We are able to identify this threshold because we know the true input flexion values., We are able to identify this threshold because we know the true input flexion values.
 Fits with one or more flexion parameter constrained this tightly by the minimization do not return accurate flexion estimates., Fits with one or more flexion parameter constrained this tightly by the minimization do not return accurate flexion estimates.
" The error between the true and fit normalization and size parameters (logSp and a) are small, with RMS values of 0.1 for logSg and 0704 for a."," The error between the true and fit normalization and size parameters $\log S_0$ and $\alpha$ ) are small, with RMS values of $0.1$ for $\log S_0$ and $0\farcs04$ for $\alpha$."
" These parameters are positively correlated, with typical correlation coefficients of Piogs,/4~0.7."," These parameters are positively correlated, with typical correlation coefficients of $\rho_{\log S_0/\alpha}\sim0.7$."
" For low surface brightness iinput profiles with indices significantly different from the Gaussian value of 0.5, the errors in logSp and a become exaggerated."," For low surface brightness input profiles with indices significantly different from the Gaussian value of 0.5, the errors in $\log S_0$ and $\alpha$ become exaggerated."
" This scatter from model mismatching is expected, and residual images show that the central region of the image is not well estimated."," This scatter from model mismatching is expected, and residual images show that the central region of the image is not well estimated."
" The flexion can still be accurately determined, as flexion primarily distorts the isophotes away from the image center."," The flexion can still be accurately determined, as flexion primarily distorts the isophotes away from the image center."
 T'his property is indicated by the absence of any significant correlations, This property is indicated by the absence of any significant correlations
the wavelength error margin of our chemical software.,the wavelength error margin of our chemical software.
" However, as noted earlier, the respective wavelength intervals occupied by the model FIR. bands comply with observations, and the wavelengths at half-1naximuia of the bare 21-/11 band (Fig."," However, as noted earlier, the respective wavelength intervals occupied by the model FIR bands comply with observations, and the wavelengths at half-maximum of the bare $\mu$ m band (Fig."
 7) nearly coincide with those of the normalized baud deterinined by Hrivnak et al. (2009).., 7) nearly coincide with those of the normalized band determined by Hrivnak et al. \cite{hri}.
" Rather than the wavelengths, one is therefore led to question the adopted relative structure abundances, or intensity errors (due to intrinsic inaccuracy of the software, and larger than wavenumber errors) which are more likely to affect the band profile and, hence, the peak position."," Rather than the wavelengths, one is therefore led to question the adopted relative structure abundances, or intensity errors (due to intrinsic inaccuracy of the software, and larger than wavenumber errors) which are more likely to affect the band profile and, hence, the peak position."
" Thus, the lines of thiourea and thiourea derivative (e) in Fig."," Thus, the lines of thiourea and thiourea derivative (e) in Fig."
" 3, fall at 20.3 and 20.1 µια, respectively; if their relative abundances or their intrinsic IR intensities were underestimated in the models, any increase in their values would shift the band peak in the right direction."," 3, fall at 20.3 and 20.1 $\mu$ m, respectively; if their relative abundances or their intrinsic IR intensities were underestimated in the models, any increase in their values would shift the band peak in the right direction."
" It should also be worth looking into the details of extracting the 21-jan band from the full spectra, and inquiring if these may affect the peak"," It should also be worth looking into the details of extracting the $\mu$ m band from the full spectra, and inquiring if these may affect the peak"
only measurement of 0/[z=0.1. so fax.,"only measurement of $\delta\!\Omega/4\pi = 0.1$, so far."
 This already rules out all classes of 110dels requiring uuplutsible laree amounts of beaming. 10. or even beyond.," This already rules out all classes of models requiring unplausibly large amounts of beaming, $10^{-8}$ or even beyond."
 Hopofulls. more such measurements will come iu the future. since this observationally heavy method is subject to many fewer wncertaiutics than the competing method of trving to locate breaks in the timedecay of aftereglows.," Hopefully, more such measurements will come in the future, since this observationally heavy method is subject to many fewer uncertainties than the competing method of trying to locate breaks in the time–decay of afterglows."
 Also. the radiative efficiency of the burst can be estimated: correcting the observed burst enerev release 10?erg for the sae beaming factor. the radiative efficiency is Eegipé/Ur/GEviEqlz)= 0.3. again a unique determination.," Also, the radiative efficiency of the burst can be estimated: correcting the observed burst energy release $E_{GRB} = 2\times 10^{51}\; erg$ for the same beaming factor, the radiative efficiency is $E_{GRB} 
\delta\!\Omega/4\pi /(E_{New}+E_{rel}\delta\!\Omega/4\pi) = 0.3$ , again a unique determination."
 Notice however that this figure is subject to a systematic uncertamtv: we do not know whether the beaming fraction is the same for the burst proper aud for the afterglow., Notice however that this figure is subject to a systematic uncertainty: we do not know whether the beaming fraction is the same for the burst proper and for the afterglow.
 Somethingc» is rotten in the fireball kingdomC» as well. namely. departures from pure powerlaw behaviours. aud the spectra of the bursts proper.," Something is rotten in the fireball kingdom as well, namely, departures from pure power–law behaviours, and the spectra of the bursts proper."
" Departures from powerlaws are expected when oue considers the extremely idealized character of the solutions discussed so far: perfect spherical svuuuetry. uuiforii sumrounding medina. smooth wind frou the explosion. εν, and ep coustaut iu space and tine."," Departures from power–laws are expected when one considers the extremely idealized character of the solutions discussed so far: perfect spherical symmetry, uniform surrounding medium, smooth wind from the explosion, $\epsilon_{eq}$ and $\epsilon_B$ constant in space and time."
 The tricky poiut here is to diseutanele these distinct factors., The tricky point here is to disentangle these distinct factors.
 Iu GRD 970508 aud GRB 970828 (Piro«L.. 1999. YoshidaaL... 1999) a major departure was observed in the Xrav enussion. within a couple of davs from the burst: they coustitute the single. hugest violations observed so fau. im terns of uuuber of photons.," In GRB 970508 and GRB 970828 (Piro, 1999, Yoshida, 1999) a major departure was observed in the X–ray emission, within a couple of days from the burst; they constitute the single, largest violations observed so far, in terms of number of photons."
 It is remarkable that spectral variations were siuultaueouslv observed. aud that both bursts showed traces (at the 2.70 sigulficance level) of au iron cussion line.," It is remarkable that spectral variations were simultaneously observed, and that both bursts showed traces (at the $2.7\sigma$ significance level) of an iron emission line."
 The similarity of the bursts’ behaviour argues in favor of the reality of these spectral features. which have been interpreted as thermal emission from a surrounding stellarsize leftover. preexpelled bv the burst’s progenitor (Lazzatial... 1999. Vietrial... 1999).," The similarity of the bursts' behaviour argues in favor of the reality of these spectral features, which have been interpreted as thermal emission from a surrounding stellar–size leftover, pre–expelled by the burst's progenitor (Lazzati, 1999, Vietri, 1999)."
 Clearly. these departures hold major pieces of information on the bursts surroundings. aud the nature of bursts’ progenitors.," Clearly, these departures hold major pieces of information on the bursts' surroundings, and the nature of bursts' progenitors."
 It has been argued (Rhoads 1997) that. whenever the afterglow shell decelerates ο below 5zzL/0. where 0 is the beam semiopening anele. emission should decrease jocause of the lack of euütting surface. compared to anu isotropic source.," It has been argued (Rhoads 1997) that, whenever the afterglow shell decelerates to below $\gamma \approx 1/\theta$, where $\theta$ is the beam semi–opening angle, emission should decrease because of the lack of emitting surface, compared to an isotropic source."
 But. iu view of the existence of clear enviromuental effects (CRB 970508 aud CRB 97085258). it appears premature to put much stock iu the interpretation of timepowerlaw weaks as due to beaming effects.," But, in view of the existence of clear environmental effects (GRB 970508 and GRB 970828), it appears premature to put much stock in the interpretation of time–power–law breaks as due to beaming effects."
 Aud equally. it appears to this reviewer that the sale conuueut applies to the interpretation of a resurgence of flux as due to the appearance of a SN remnant behind the shell.," And equally, it appears to this reviewer that the same comment applies to the interpretation of a resurgence of flux as due to the appearance of a SN remnant behind the shell."
 The major uucertaintv here is the ionunivoqueness of the iuterpretation: Wasximan aud Draine (2000) have shown hat effects due to dust can mimic the same plienomienuon., The major uncertainty here is the non–univoqueness of the interpretation: Waxman and Draine (2000) have shown that effects due to dust can mimic the same phenomenon.
" A clearprediction of the emission of optically thin svuchrotron is that the low spectra should scale like dN,/déx ov"". with a= 3/2. since the"," A clearprediction of the emission of optically thin synchrotron is that the low--photon--energy spectra should scale like $d\!N_\nu/d\!\nu \propto
\nu^{\alpha}$ , with $\alpha = -3/2$ , since the"
Alartiusetal.(2007) for a summary of the procedure used to build the models.,\citet{gc07} for a summary of the procedure used to build the models.
 To derive the parameters of interest. we lave rui imodels with: 19000 <ἕως 30000 IK. 3.0<logg« E75. 0.1 Πο <2.0aud10 “<AL< t..," To derive the parameters of interest, we have run models with: 19000 $< T_{\rm eff} <$ 30000 K, 3.0$< \log g <$ 4.75, 0.1 $<$ He/H $<$ 2.0 and $^{-8}$ $< \dot{\rm
M} <$ $^{-5.5}$."
 These models and svuthetie spectra iucluded. in addition to IT aud He. €. N. O. Si. Saud Fe.," These models and synthetic spectra included, in addition to H and He, C, N, O, Si, Sand Fe."
 We adopted the solar abundances of Crevesse&Sauval (1995)., We adopted the solar abundances of \citet{gs98}.
. The spectrum shown in retspec.2/stypicalofancarly Bstar(secalsoGhe, The spectrum shown in \\ref{spec_s2} is typical of an early B star \citep[see also][]{ghez03}.
tictal.-2003). Fusycetiomgft Gat eco] uq μα. lis expected.," Inspection of the atlases of \citet{wh97} and \citet{hanson05} shows that for late O stars, is expected."
 We do uot detect this line in spite of the eood enoush S/N ratio., We do not detect this line in spite of the good enough S/N ratio.
 For stars with spectral types later than B3. the He lines vanish.," For stars with spectral types later than B3, the He lines vanish."
 Since we detect several of them. we cau safely argue that S2 has a spectral type between DO aud D2.5.," Since we detect several of them, we can safely argue that S2 has a spectral type between B0 and B2.5."
 112 of Mansonetal.(2005). shows that in supereiauts and elauts. lis clearly separated from) Πο 2.161jan. while for dafs lis broad enough to merge with the We line.," 12 of \citet{hanson05} shows that in supergiants and giants, is clearly separated from He 2.161, while for dwarfs is broad enough to merge with the He line."
 This latter morphology is simular to what we observe for S2 (sec below for a quantitative comparison)., This latter morphology is similar to what we observe for S2 (see below for a quantitative comparison).
 Hence. iu addition to being spectroscopically ideuti&ed as an carly D star. we can conclude from these qualitative arguments thatsupergiant/qiant.," Hence, in addition to being spectroscopically identified as an early B star, we can conclude from these qualitative arguments that."
. The key question we want to answer here is the exact nature of S2., The key question we want to answer here is the exact nature of S2.
 Spectroscopicallv. S2 is unambiguously au early D clwart.," Spectroscopically, S2 is unambiguously an early B dwarf."
 However. this does not necessarily mica that S2 is a vounug. massive star.," However, this does not necessarilly mean that S2 is a young, massive star."
 It could be the core of an older. evolved star which would have lost its euvelope through tidal interaction with SerA* but would still spectroscopically look like a D star.," It could be the core of an older, evolved star which would have lost its envelope through tidal interaction with SgrA* but would still spectroscopically look like a B star."
 In that case. the star could have formed far away frou SerA* before being drageed to its proximity and expericucing an cuvelope stripping.," In that case, the star could have formed far away from SgrA* before being dragged to its proximity and experiencing an envelope stripping."
 There would be no paradox of vouth., There would be no paradox of youth.
 Recently. Davies&ine(2005) aud Drayetal.(2006) modeled this stripping process as well as the subsequent evolution of the remaining core iu the vicinity of SerA*.," Recently, \citet{kd05} and \citet{dray06} modeled this stripping process as well as the subsequent evolution of the remaining core in the vicinity of SgrA*."
 Thev showed that. wader certain coudition on the IME and the capture rate. the population of S stars could be explained by tidal stripping.," They showed that, under certain condition on the IMF and the capture rate, the population of S stars could be explained by tidal stripping."
 The arguueut is however sed on the nunber of stars predicted at the position of the S stars in the IIR. diagram., The argument is however based on the number of stars predicted at the position of the S stars in the HR diagram.
 Expressed differently. he conclusion comes from the fact that the modeled stripped stars can reach the huninositics aud effective euniperatures of D stars.," Expressed differently, the conclusion comes from the fact that the modeled stripped stars can reach the luminosities and effective temperatures of B stars."
 But strictly speaking. this docs rot exclude that the S stars are genuiue massive stars. which would lie at the same position iu the IIR diagram.," But strictly speaking, this does not exclude that the S stars are genuine massive stars, which would lie at the same position in the HR diagram."
 For that. the only parameter which cau uuiuubiguously )0 uxed is the stellar mass.," For that, the only parameter which can unambiguously be used is the stellar mass."
 The most massive stars able to expericuce envelope stripping are ACB stars., The most massive stars able to experience envelope stripping are AGB stars.
 According to stellar evolution. such objects are the evolved desceudents of jdn sequence stars Xwith A < M," According to stellar evolution, such objects are the evolved descendents of main sequence stars with M $<$ 8."
MMSE ult199 Πα massive: Table lof Forestiui&Charbonnel(1997). shows that their mass is lower than 1M., The core of such objects is actually much less massive: Table 4 of \citet{fc97} shows that their mass is lower than 1.
.. In the scenario explored by Drayetal.(2006).. onlv stars having lost at least of their envelope could explain the S stars.," In the scenario explored by \citet{dray06}, only stars having lost at least of their envelope could explain the S stars."
" ""Thus. their mass should be at most ~ 1AL..."," Thus, their mass should be at most $\sim$ 1."
 To estimate the mass of $2. we can rely ou gravity aud radius: AS=yR?/C where y is the eravity. P? the radius and G the eravitational coustaut.," To estimate the mass of S2, we can rely on gravity and radius: $M = g
R^{2}/G$ where $g$ is the gravity, $R$ the radius and $G$ the gravitational constant."
 Caavity eau be derived frou the shape ofDr;.. while radius is straightforwardly obtained from the knowledge of effective. temperature and luminosity.," Gravity can be derived from the shape of, while radius is straightforwardly obtained from the knowledge of effective temperature and luminosity."
 Below. we explain how we proceeded to constrain these parameters.," Below, we explain how we proceeded to constrain these parameters."
temperature. Hs usually derived from the ratio of lines from two consecutive ionization states: He / Πο lines for ο stars aud Sil / Si for carly D stars., is usually derived from the ratio of lines from two consecutive ionization states: He / He lines for O stars and Si / Si for early B stars.
 Unfortunately. 82 does not show Ie aud $i lines iu the KK baud.," Unfortunately, S2 does not show He and Si lines in the K band."
" Ποσο, we can only rely on seimi-quautitative areunments to estimateTig."," Hence, we can only rely on semi-quantitative arguments to estimate."
 We have shown above that S2 is a DOV to D2.5V star., We have shown above that S2 is a B0V to B2.5V star.
 According to the recent studies of Duftonctal.(2006) and Trundleetal. (2007).. such stars have 19000 «dug OOOOT ehacethusramnodelsforTiag -]9.22.25.2TnA30 Luninosity..," According to the recent studies of \citet{dufton06} and \citet{trundle07}, , such stars have 19000 $<$ $<$ 30000 K. We have thus run models for = 19, 22, 25, 27 and 30 kK. ."
 To estimatemd K.the stars Iniinuositv. for cach," To estimate the star's luminosity, for each"
 The existence of high. velocities 1000 Jan 1) (MeCarthy. 1996) iu. the extended eas (EELB) of high redshift (2 22) radio galaxies (IZRC) is in contrast with the more relaxed kinematics observed in the majority of low redshift radio galaxies (EWIINI« 100 kin 1) (Tadluuter 1989)., The existence of high velocities $>$ 1000 km $^{-1}$ ) (McCarthy 1996) in the extended gas (EELR) of high redshift $z>$ 2) radio galaxies (HZRG) is in contrast with the more relaxed kinematics observed in the majority of low redshift radio galaxies $<$ 400 km $^{-1}$ ) (Tadhunter 1989).
 The nature of such extreme kinematic motious is not well uuderstood., The nature of such extreme kinematic motions is not well understood.
 We investigate here this ise studving the kinematics of the exteuded eas ina small sample of E distant active galaxies (2 >2): MRC1558-003. NIBC2025-218 aud MRC2101-212. (radio ealaxies) aud SAIAL02399-0136 (livperhuiinous type 2 active galaxy with very weal: radio enission).," We investigate here this issue studying the kinematics of the extended gas in a small sample of 4 distant active galaxies $z>$ 2): MRC1558-003, MRC2025-218 and MRC2104-242 (radio galaxies) and SMM02399-0136 (hyperluminous type 2 active galaxy with very weak radio emission)."
 The spectroscopic observations were carried out ou the welts 1997 July 3-5 aud L998 July 25-27 usine the EMMI multi-purpose iustrmucut at the NTT (New Technology Telescope) in La Silla Observatory (ESO-Chile)., The spectroscopic observations were carried out on the nights 1997 July 3-5 and 1998 July 25-27 using the EMMI multi-purpose instrument at the NTT (New Technology Telescope) in La Silla Observatory (ESO-Chile).
 The detector was a Tektronix CCD with «2018. pixels of size 21 yan. resulting iu a spatial scale of 0.27 arcsec per pixel.," The detector was a Tektronix CCD with $\times$ 2048 pixels of size 24 $\mu$ m, resulting in a spatial scale of 0.27 arcsec per pixel."
 We used EMMI in RILD spectroscopic mode (Red Tnageieao aud Low Dispersou Spectroscopy)., We used EMMI in RILD spectroscopic mode (Red ging and Low Disperson Spectroscopy).
 We used the same eria (4633) for all objects., We used the same grism 3) for all objects.
 This has a blaze waveleneth of L600A.. dispersion 5.9 //pixel aud wavelength range 1000-5200A.," This has a blaze wavelength of 4600, dispersion 5.9 /pixel and wavelength range 4000-8300."
. The slit was aligued with the radio axis for the three radio galaxies., The slit was aligned with the radio axis for the three radio galaxies.
 We positioned the slit aloug the two iain optical compoucuts of SATAI02399-0136 (L1 aud L2. adopting the nomeuclature of Ivinson 1998 [IV98 hereafter]," We positioned the slit along the two main optical components of SMM02399-0136 (L1 and L2, adopting the nomenclature of Ivinson 1998 [IV98 hereafter])."
 A log of the spectroscopic observatious is shown im Table 1., A log of the spectroscopic observations is shown in Table 1.
 Staudard data reduction techniques were applied using IRAF software (sec 1n 1998 for a iore detailed description)., Standard data reduction techniques were applied using IRAF software (see n 1998 for a more detailed description).
 Tn order to study the kinematics of the gas. we fitted the emission lines with a Gaussiau profile at every spatial position (pixel).," 	In order to study the kinematics of the gas, we fitted the emission lines with a Gaussian profile at every spatial position (pixel)."
 Several spatial pixels were added where the enmuüssiou was too faint., Several spatial pixels were added where the emission was too faint.
 We used the Starliuk σος DIPSO for this purpose., We used the Starlink ge DIPSO for this purpose.
 The FWIIM. fiux and ceutral wavelength were measured from the Gaussian fitted to the line profile.," The FWHM, flux and central wavelength were measured from the Gaussian fitted to the line profile."
 The FWIIM was corrected in quadrature for iustrunenutal broadeniug (the iustruucenutal profiles in the observed frame are given in Table 1)., The FWHM was corrected in quadrature for instrumental broadening (the instrumental profiles in the observed frame are given in Table 1).
 Sinele Caussiaus did uot always provide a perfect fit and underlying broad wines were sometimes present., Single Gaussians did not always provide a perfect fit and underlying broad wings were sometimes present.
 This is probably duc to the presence of several kinematic components and/or absorption of Lya bw ueutral hydrogen., This is probably due to the presence of several kinematic components and/or absorption of $\alpha$ by neutral hydrogen.
 To climinnate uncertaintics due to the second niechanisni we also preseut the result of the fit for the second strongest enmisssion line CIVA1550 not susceptible of hydrogen absorption.," To nate uncertainties due to the second mechanism, we also present the result of the fit for the second strongest ssion line $\lambda$ 1550 not susceptible of hydrogen absorption."
 At the s/n of the data. we are confined to using single Gaussian fits to the lines. a procedure which is the same as that followed by Tadluuter (1989).," At the s/n of the data, we are confined to using single Gaussian fits to the lines, a procedure which is the same as that followed by Tadhunter (1989)."
 À sinele Gaussian fit will à) lose auv information about multiple components b) neglect any possible weak bro ]liug wines (as is observed in AIRC2101-212. see Fie.," A single Gaussian fit will a) lose any information about multiple components b) neglect any possible weak broad lying wings (as is observed in MRC2104-242, see Fig."
 1 left cloud). sinec the fit will be optimized for the domiuaut part of the line.," 1 left cloud), since the fit will be optimized for the dominant part of the line."
 However. the main goal of this paper docs not require such a precise analysis.," However, the main goal of this paper does not require such a precise analysis."
 The broad wing on AIRC2101-212 will have little influence on the fit. which will be dominated by the stroug. narrower component.," The broad wing on MRC2104-242 will have little influence on the fit, which will be dominated by the strong, narrower component."
"agreement for small gravity, while for strong gravity only method 1 is able to quantify the shift.","agreement for small gravity, while for strong gravity only method 1 is able to quantify the shift."
" For cool prominences, the results show that by increasing the gravity, the location of the maximum pressure shifts in the downwards direction."," For cool prominences, the results show that by increasing the gravity, the location of the maximum pressure shifts in the downwards direction."
 This downward shift is largest when the temperature is a flux function., This downward shift is largest when the temperature is a flux function.
" Furthermore, in a strong gravitational potential the three choices of the chosen flux function show large deviations foi each other in, for example, the pressure and density."," Furthermore, in a strong gravitational potential the three choices of the chosen flux function show large deviations from each other in, for example, the pressure and density."
forma when it is derived from heavily spatially filtered observations.,form when it is derived from heavily spatially filtered observations.
 Following other authors (Larson19723:Ziunecker1981:Adams&Fatuzzo 1996).. we have suggested hat the clump mass function has a lognormal form. due to the cumulative action of mam independent Xxocesses In determining the mass of any given clump.," 	Following other authors \citep{larson73,z84,af96}, we have suggested that the clump mass function has a lognormal form due to the cumulative action of many independent processes in determining the mass of any given clump."
 We have extended the set of such possible processes to cheolpass hot only plivsical processes occurring in star-ornüue regions. but the processes of data acquisition and analysis.," We have extended the set of such possible processes to encompass not only physical processes occurring in star-forming regions, but the processes of data acquisition and analysis."
" The cumulative action of factors such as turbulence. temperature variations. radiative effects. munierous uncertainties in our conversion of flux to nass, our clunip-fBiucdius algorithiis. image noise. source lending. and spatial Blteiug iav that cbhuup nass functions abwavs appear lognormal."," The cumulative action of factors such as turbulence, temperature variations, radiative effects, numerous uncertainties in our conversion of flux to mass, our clump-finding algorithms, image noise, source blending, and spatial filtering may that clump mass functions always appear lognormal."
 The Salpeter-ike appearance of them liel-anass euds may simply reflect this loguormal form., The Salpeter-like appearance of their high-mass ends may simply reflect this lognormal form.
 Collectively. these results sugeest that we ought to adopt a skeptical approach when interpreting the chump lass function.," 	Collectively, these results suggest that we ought to adopt a skeptical approach when interpreting the clump mass function."
 We caunot conclude that. because the lass function of a sot of clumps has a Salpeter-like fori. those clips represcut the precursors of individual stars.," We cannot conclude that, because the mass function of a set of clumps has a Salpeter-like form, those clumps represent the precursors of individual stars."
 We be able to draw this conclusion iu the very limited set of cases in which our observations have very little noise aud sufücieut resolution to distinguish individual pre-stellar cores., We be able to draw this conclusion in the very limited set of cases in which our observations have very little noise and sufficient resolution to distinguish individual pre-stellar cores.
 Dust continua maps mace with IHerschels PACS iustriment have a lot of promise in this regard because they have unparalleled scusitivity and resolution., Dust continuum maps made with Herschel's PACS instrument have a lot of promise in this regard because they have unparalleled sensitivity and resolution.
 Ilowever. we will demoustrate iu a forthcoming paper that even clump mass functions derived from PACS iaps can show a convincing Salpeter-like forma in cases where we do not believe the coustitueut clamps to be pre-stellar cores.," However, we will demonstrate in a forthcoming paper that even clump mass functions derived from PACS maps can show a convincing Salpeter-like form in cases where we do not believe the constituent clumps to be pre-stellar cores."
 The study of the origin of the stellay IAIF is nuportaut to nuuiv areas of astronomy., 	The study of the origin of the stellar IMF is important to many areas of astronomy.
 It is worth verv careful scrutiny., It is worth very careful scrutiny.
 We suggest that the best measurements of the chunp mass fiction with the current generation of instruments will come from a combination of PACS and SCUDA?2 data., We suggest that the best measurements of the clump mass function with the current generation of instruments will come from a combination of PACS and SCUBA2 data.
 High-sensitivity. multinwaveleneth observations at hieh spatial resolution will allow us te reduce the effects of many of the uncertaiutics discussed in this paper.," High-sensitivity, multi-wavelength observations at high spatial resolution will allow us to reduce the effects of many of the uncertainties discussed in this paper."
 Using the multiowaveleugth data. we will be able to better constrain the temperatures and dust opacitics of the chips. iniproviung our estimates of their masses.," Using the multi-wavelength data, we will be able to better constrain the temperatures and dust opacities of the clumps, improving our estimates of their masses."
 Usine Spitzer and PAC'S data. we will be able to do a better job of filtering out cores which are already forming stars.," Using Spitzer and PACS data, we will be able to do a better job of filtering out cores which are already forming stars."
 Follow-up observations to obtain high-resolutiou molecular Lue data will further allow for the exclusion of chumps which are not eravitationally bound. as well as limited deconvolutiou of the emission along the line of sieht.," Follow-up observations to obtain high-resolution molecular line data will further allow for the exclusion of clumps which are not gravitationally bound, as well as limited deconvolution of the emission along the line of sight."
 The comparison of Herschel and SCUBA? chunp catalogs for matching regious will be highly instructive., 	The comparison of Herschel and SCUBA2 clump catalogs for matching regions will be highly instructive.
 Such a comparison would allow us to assess. du a quantitative aud statistically sieuificant wav. whether our nieasurements of the masses of individual clumps are robust.," Such a comparison would allow us to assess, in a quantitative and statistically significant way, whether our measurements of the masses of individual clumps are robust."
 If for example. both SCUBA2 and Uerschel generate Salpeter-like mass fuuctions. but with very differcut masses for cach individual clamp. this will be eood evidence for our argunmieut that the shape of the ΟΠΗ mass function can be set by nou-plivsical meus.," If, for example, both SCUBA2 and Herschel generate Salpeter-like mass functions, but with very different masses for each individual clump, this will be good evidence for our argument that the shape of the clump mass function can be set by non-physical means."
 We will be very reassured if the two clump catalogs contain similar objects with similar masses (or fluxes)., We will be very reassured if the two clump catalogs contain similar objects with similar masses (or fluxes).
 Iu the more distant future. the Cornell Caltech Atacama Telescope (CCAT. Sebringetal. 2006)) promises to be a powerful tool for measuring the clump mass function.," 	In the more distant future, the Cornell Caltech Atacama Telescope (CCAT, \citealt{ccat}) ) promises to be a powerful tool for measuring the clump mass function."
 As a sinele-dish telescope. it will not suffer the spatial filtering effects that may make its contemporary. the Atacama Large Millimeter Array. loss useful for imeasumiug the clump mass function.," As a single-dish telescope, it will not suffer the spatial filtering effects that may make its contemporary, the Atacama Large Millimeter Array, less useful for measuring the clump mass function."
 With an expected dish diameter of 25 m. CCAT's aneular resolution of aat 200 wwill male it a powerful chuup-fuding tool.," With an expected dish diameter of 25 m, CCAT's angular resolution of at 200 will make it a powerful clump-finding tool."
completed.,completed.
 The time to calculate the photometric redshift and error is simply the computational time to query each SOM to find the BMU - less than a few hundredths of a second per galaxy on a typical modern desktopmachine., The time to calculate the photometric redshift and error is simply the computational time to query each SOM to find the BMU – less than a few hundredths of a second per galaxy on a typical modern desktop.
".. Hildebrandt et (2010) present a system for the consistent esting of different codes: ""PHAT: AccuracyT", Hildebrandt et (2010) present a system for the consistent testing of different codes: `PHAT: Accuracy.
"esting PHAT provides a standard mock catalogue containing galaxies ""..represented by the empirical spectral energy distribution emplates of WWu (61980) and. Kinney et ((1996). together covering the full range of galaxy spectral ypes from passive ellipticals to starburst systems."," PHAT provides a standard mock catalogue containing galaxies represented by the empirical spectral energy distribution templates of Wu (1980) and Kinney et (1996), together covering the full range of galaxy spectral types from passive ellipticals to starburst systems."
 Synthetic colour information for each galaxy is calculated for each template ‘or photometric bands spanning the ultraviolet to mid-infrared. specitically: the Canada-France-Hawaii Telescope MEGACAM ugriz-bands. the United Kingdom Infrared Telescope Y/HA-bands and the 3.67/m and 5j/m IRAC bands.," Synthetic colour information for each galaxy is calculated for each template for photometric bands spanning the ultraviolet to mid-infrared, specifically: the Canada-France-Hawaii Telescope MEGACAM -bands, the United Kingdom Infrared Telescope -bands and the $\mu$ m and $\mu$ m IRAC bands."
 As ours is an empirical method and requires a training set where the redshift is known. we use the ‘large’ PHAT catalogue of 0000 objects with noise included (where a parametrie model for the signal-to-noise ratio as a function of source flux is used. and photometry perturbed accordingly according to a gaussian distribution).," As ours is an empirical method and requires a training set where the redshift is known, we use the `large' PHAT catalogue of 000 objects with noise included (where a parametric model for the signal-to-noise ratio as a function of source flux is used, and photometry perturbed accordingly according to a gaussian distribution)."
 We create a training sub-set by randomly sampling of the full catalogue., We create a training sub-set by randomly sampling of the full catalogue.
 In this example. we initialise a 200...200 SOM and set the number of iterations to oversample the training set by a factor of 5.," In this example, we initialise a $200\times200$ SOM and set the number of iterations to oversample the training set by a factor of 5."
 Hildebrandt et ((2010) define the accuracy figure of merit as the mean and scatter (rms) in Al=suedeως and the outlier rate as the fraction of objects with |Nz|o>0.1.," Hildebrandt et (2010) define the accuracy figure of merit as the mean and scatter (rms) in $\Delta z = z_{\rm model} - z_{\rm phot}$, and the outlier rate as the fraction of objects with $|\Delta z|>0.1$."
 For comparison with the results presented in Hildebrandt et (2010) for PHAT-testing of 16 recent codes (several of which are in widespread use). we calculate the same statistics on the predicted redshifts retrieved for the galaxies that did not participate in the training of our SOM.," For comparison with the results presented in Hildebrandt et (2010) for PHAT-testing of 16 recent codes (several of which are in widespread use), we calculate the same statistics on the predicted redshifts retrieved for the galaxies that did not participate in the training of our SOM."
 The best codes tested by Hildebrandt et (2010) typically have £[4A|0.005. scatters of a(Az)—0.01— 0.02 and small outlier rates of <0.14c.," The best codes tested by Hildebrandt et (2010) typically have $\left<|\Delta z|\right >\leq 0.005$, scatters of $\sigma(\Delta z)
\sim$ 0.01--0.02 and small outlier rates of $<0.1$."
. Testing the trained SOM on a sub-sample of 0000 galaxies from the large catalogue that did not participate in training we find an average (Ac)=το103. m(;iNz)=0.016 and outlier rate of0.," Testing the trained SOM on a sub-sample of 000 galaxies from the large catalogue that did not participate in training we find an average $\left<\Delta z\right >
=-7\times10^{-4}$, $\sigma(\Delta z) = 0.016$ and outlier rate of."
1366... The relatively large outlier rate (compared to some of the codes tested in Hildebrandt et 22010) is driven by the poorer accuracy at the tails of the redshift distribution. which is a natural bias in this method.," The relatively large outlier rate (compared to some of the codes tested in Hildebrandt et 2010) is driven by the poorer accuracy at the tails of the redshift distribution, which is a natural bias in this method."
 When considering only galaxies in the range 0.1<20.5. although the rms accuracy is the same. the outlier rate drops toc.," When considering only galaxies in the range $0.1<z<0.5$, although the rms accuracy is the same, the outlier rate drops to."
. Thus. the empirical SOM method for prediction is competitive with established codes.," Thus, the empirical SOM method for prediction is competitive with established codes."
 It is likely that the accuracy could be improved further by using an even larger training sample with a longer learning period. at the expense of computational time.," It is likely that the accuracy could be improved further by using an even larger training sample with a longer learning period, at the expense of computational time."
 Aside from the limitations discussed above regarding the choice training set. and the natural biases that are encoded into the SOM. there are several other important issues to consider. and we briefly review these here.," Aside from the limitations discussed above regarding the choice training set, and the natural biases that are encoded into the SOM, there are several other important issues to consider, and we briefly review these here."
 The rate of learning. or how quickly the SOM adapts during training. is set by (a) two learning coefficients (equation | and 4) which vary as a function of node distance and learning time: (b) the rate of decay of these coefficients: (c) the shape of and rate of decay of the region of influence around the BMU where neighbouring nodes are allowed to change: (d) the size. or resolution of the SOM. and (e) the total learning time.," The rate of learning, or how quickly the SOM adapts during training, is set by (a) two learning coefficients (equation 1 and 4) which vary as a function of node distance and learning time; (b) the rate of decay of these coefficients; (c) the shape of and rate of decay of the region of influence around the BMU where neighbouring nodes are allowed to change; (d) the size, or resolution of the SOM, and (e) the total learning time."
 It is not clear what the optimum combination of these factors is that would produce the best mapping is. and it would take a long time to do so.," It is not clear what the optimum combination of these factors is that would produce the best mapping is, and it would take a long time to do so."
 So. the exact choice of training parameters might be the main limiting factor in the SOM technique.," So, the exact choice of training parameters might be the main limiting factor in the SOM technique."
 However. during the course of this investigation. we have found some simple configurations tha appear to produce robust results.," However, during the course of this investigation, we have found some simple configurations that appear to produce robust results."
 First. the number of nodes in the SOM should be initialized such that the total number scales roughly with the number of raining parameters. 2?. and a good minimum is ~400 nodes arranged in a 20grid”...," First, the number of nodes in the SOM should be initialized such that the total number scales roughly with the number of training parameters, $\sim$$2^N$, and a good minimum is $\sim$ 400 nodes arranged in a $20\times20$."
" This is to allow the mapping o ""resolve"" possible correlations and clustering between severa xrameters.", This is to allow the mapping to `resolve' possible correlations and clustering between several parameters.
 Clearly. when making predictions for new test data. he size of the SOM sets a fundamental limit on the accuracy. as he total input parameter space is diseretised into a finite number of bins.," Clearly, when making predictions for new test data, the size of the SOM sets a fundamental limit on the accuracy, as the total input parameter space is discretised into a finite number of bins."
 In the case of this photometric redshift example. we set he total number of nodes to be 107. and this seems adequate to make accurate predictions whilst keeping down training time.," In the case of this photometric redshift example, we set the total number of nodes to be $10^4$, and this seems adequate to make accurate predictions whilst keeping down training time."
 In he example of object selection however. we were more interested in training the SOM to make selections of objects in rather broad swathes of the parameter space. and so in this ease a SOM with ewer nodes was successful (and is also beneficial for visualisation »urposes).," In the example of object selection however, we were more interested in training the SOM to make selections of objects in rather broad swathes of the parameter space, and so in this case a SOM with fewer nodes was successful (and is also beneficial for visualisation purposes)."
 Note that there are variant SOM algorithms that allow he number of nodes in the map to be dynamic. growing according o the need of the training sample (Alahakoon 11998) The total number of iterations was set to ten times the number of elements in the training set.," Note that there are variant SOM algorithms that allow the number of nodes in the map to be dynamic, growing according to the need of the training sample (Alahakoon 1998) The total number of iterations was set to ten times the number of elements in the training set."
 This was to allow the SOM to see each training vector about ten times. and participate in the refining of the self-organisation at different stages in the learning process.," This was to allow the SOM to see each training vector about ten times, and participate in the refining of the self-organisation at different stages in the learning process."
 We could envision even better results if we allowed more sampling of the training set. but this comes at the cost of longer training times.," We could envision even better results if we allowed more over-sampling of the training set, but this comes at the cost of longer training times."
 Finally. we initialised the learning co-efficients to unity. and set the size of the neighbourhood function to be approximately half the linear size of the SOM.," Finally, we initialised the learning co-efficients to unity, and set the size of the neighbourhood function to be approximately half the linear size of the SOM."
 This initial size allows test vectors selected at the start of the learning to influence large. unretined sectors of the map.," This initial size allows test vectors selected at the start of the learning to influence large, unrefined sectors of the map."
 As iterations cumulate. new training vectors simply refine the map. contributing less drastic changes due to the decreasing size of the neighbourhood function and declining learning coefficients.," As iterations cumulate, new training vectors simply refine the map, contributing less drastic changes due to the decreasing size of the neighbourhood function and declining learning coefficients."
 We found that the shape of the neighbourhood function (a gaussian). the rate of its decay (the size decreases linearly with time). and the decay of the learning coefticients produced excellent results in multiple SOM realisations involving different types ofdata.," We found that the shape of the neighbourhood function (a gaussian), the rate of its decay (the size decreases linearly with time), and the decay of the learning coefficients produced excellent results in multiple SOM realisations involving different types of data."
 Again. a future study could investigate what the optimal learning parameters are. with the best results perhaps coming from a more extended committee of hundreds or thousands of SOMs (that could be trained in parallel). each with different styles and learning capabilities.," Again, a future study could investigate what the optimal learning parameters are, with the best results perhaps coming from a more extended committee of hundreds or thousands of SOMs (that could be trained in parallel), each with different self-organisation styles and learning capabilities."
covering the spatial interval |-2.+2]x[-2. with 4000 grid cells inboth the x and v direction.,"covering the spatial interval $[-2,+2]\times[-2,+2]$ with $4000$ grid cells inboth the $x$ and $y$ direction."
 10 particles are placed randomly in a ring of full width 0.08 centred at the radial distance r= 1., $10^4$ particles are placed randomly in a ring of full width $0.08$ centred at the radial distance $r=1$ .
 A central gravity source. of strength GM=I. is placed in the centre of the coordinate frame.," A central gravity source, of strength $G
M=1$, is placed in the centre of the coordinate frame."
 We integrate the particle orbits. including collisions. for 107 revolutions of the ring centre.," We integrate the particle orbits, including collisions, for $10^4$ revolutions of the ring centre."
 In order to compare directly with Lithwick&Chiang(2007) we use their 2-D approximation.," In order to compare directly with \cite{LithwickChiang2007}
 we use their 2-D approximation."
 The particle number density can be approximated as 2~Y/H. where © is the column (number) density and H ts the scale height of the particle disc.," The particle number density can be approximated as $n \sim \varSigma/H$, where $\varSigma$ is the column (number) density and $H$ is the scale height of the particle disc."
 The random particle motion « can be written as 4Πω., The random particle motion $u$ can be written as $u \sim H \varOmega$.
 This yields a collision time where nou7=So XSoQis the verticalrT optical. depth of. the dise. and Tow=27/0 1s the orbital time-scale., This yields a collision time where $\tau=\varSigma \sigma$ is the vertical optical depth of the disc and $T_{\rm orb}=2\pi/\varOmega$ is the orbital time-scale.
 While the collision time-scale in general depends on the random particle motion. this dependence vanishes in the 2-D Keplerian dise approximation — faster random motion cancels with increased particle height in the collision time expression.," While the collision time-scale in general depends on the random particle motion, this dependence vanishes in the 2-D Keplerian disc approximation – faster random motion cancels with increased particle scale-height in the collision time expression."
" Requiring that orbits are maintained for 107 orbital scales. we set the time-step of the Pencil Code to or= 0.0107!, covering each orbit Ty,=22/2 by around 600 time-steps."," Requiring that orbits are maintained for $10^4$ orbital time-scales, we set the time-step of the Pencil Code to $\delta t=0.01 \varOmega^{-1}$ , covering each orbit $T_{\rm orb}=2\pi/\varOmega$ by around 600 time-steps."
 This proved necessary because the third order time integration scheme of the Pencil Code is not constructed to conserve orbital angular momentum and energy., This proved necessary because the third order time integration scheme of the Pencil Code is not constructed to conserve orbital angular momentum and energy.
 Using the highly optimized orbital dynamics code SWIFT. Lithwick& solve the same problem with slightly less than five time-steps per orbit.," Using the highly optimized orbital dynamics code SWIFT, \cite{LithwickChiang2007} solve the same problem with slightly less than five time-steps per orbit."
 In we show the eccentricity evolution of the particle ring., In we show the eccentricity evolution of the particle ring.
" For a coefhicient of restitution of €=0.3 the particles relax to an equilibrium eccentricity of around ej,=0.001. comparable to ὃν."," For a coefficient of restitution of $\epsilon=0.3$ the particles relax to an equilibrium eccentricity of around $e_{\rm rms}=0.001$, comparable to $\delta
x/r$."
 A higher coetficient of restitution of 0.6 leads instead to catastrophic heating of the disc (Goldreich&Tremaine. 1978)... with an eccentricity that evolves linearly with time.," A higher coefficient of restitution of $\epsilon=0.6$ leads instead to catastrophic heating of the disc \citep{GoldreichTremaine1978}, with an eccentricity that evolves linearly with time."
 The results presented in show that the superparticle collision algorithm is in excellent agreement with Lithwick&Chiang(2007) in the limit of inflated particles., The results presented in show that the superparticle collision algorithm is in excellent agreement with \cite{LithwickChiang2007} in the limit of inflated particles.
 The width of a particle ring increases due to collisional viscosity., The width of a particle ring increases due to collisional viscosity.
 Since the collision time-scale scales inversely with particle density. the collisional evolution slows down with time.," Since the collision time-scale scales inversely with particle density, the collisional evolution slows down with time."
 An analytical solution to the diffusion problem was found by Petit&Henon(1987)., An analytical solution to the diffusion problem was found by \cite{PetitHenon1987}.
". In the notation of Lithwick&Chi-ang(2007) the width c, of an initially narrow ring increases according to Here 4, is a dimensionless factor that depends on the coefficient of restitution e. ὃν is the grid spacing. r Is the mean radial coordinate of the particles. M, is the particle number and t the time."," In the notation of \cite{LithwickChiang2007} the width $\sigma_r$ of an initially narrow ring increases according to Here $k_\nu$ is a dimensionless factor that depends on the coefficient of restitution $\epsilon$, $\delta x$ is the grid spacing, $\overline{r}$ is the mean radial coordinate of the particles, $N_{\rm tp}$ is the particle number and $t$ the time."
 We follow Lithwick&Chiang(2007) and define an initially very narrow ring of radial extent 2A=107., We follow \cite{LithwickChiang2007} and define an initially very narrow ring of radial extent $2 \Delta=10^{-3}$.
 The units follow from our choice of GM=|., The units follow from our choice of $G M=1$.
 The evolution of the radial width is shown in over 101 orbits., The evolution of the radial width is shown in over $10^4$ orbits.
" We overplot the analytical solution for &,=0.016. similar to the fit in (2007).. and find excellent agreement."," We overplot the analytical solution for $k_\nu=0.016$, similar to the fit in \cite{LithwickChiang2007}, , and find excellent agreement."
 Hill'sequations describe motion relative to a frame that corotates with the Keplerian frequency © at an arbitrary distanee from the central gravity source., Hill'sequations describe motion relative to a frame that corotates with the Keplerian frequency $\varOmega$ at an arbitrary distance from the central gravity source.
 The coordinate axes are defined such that x points radially outwards and v points along the flow of the disc., The coordinate axes are defined such that $x$ points radially outwards and $y$ points along the flow of the disc.
 The 2-D equations of motion of, The 2-D equations of motion of
(ένο Is longer). again proportional to source fiux.,"$\thalf$ is longer), again proportional to source flux."
" Thus the rate is proportional to F?, viclding the surface brightucss fluctuation flux F when inteerated over the luninosity fiction."," Thus the rate is proportional to $F^2$, yielding the surface brightness fluctuation flux $\overline{F}$ when integrated over the luminosity function."
 This relation is of course affected by finite source size effects; as the maximi magnification will depend ou stellar radii.," This relation is of course affected by finite source size effects, as the maximum magnification will depend on stellar radii."
 These rates assume a imaxwelliau velocity distribution of lenses with uniforiulv moving sources., These rates assume a maxwellian velocity distribution of lenses with uniformly moving sources.
 If the source velocitics are also masxwellian (as should be approximately the case for an elliptical galaxy). the extra velocity integrals can be separated out.," If the source velocities are also maxwellian (as should be approximately the case for an elliptical galaxy), the extra velocity integrals can be separated out."
 The final outcome is the same if the ideutification e?(leus)>47e(sonree) is nado., The final outcome is the same if the identification $v_c^2({\rm lens})\rightarrow v_c^2({\rm lens})+x^2v_c^2({\rm source})$ is made.
 The surface xiehtuess profile of AIST has been well studied bv numerous authors., The surface brightness profile of M87 has been well studied by numerous authors.
" We will construct a conrposite profiο from several studies that extend from 0.02"" to more tlvan 150"".", We will construct a composite profile from several studies that extend from $0.02\arcsec$ to more than $150\arcsec$.
 Within 20”of the center of M87. we use the f-haud surface brightuess profile of Lauer ct al. (," Within of the center of M87, we use the $I$ -band surface brightness profile of Lauer et al. ("
1992).,1992).
 We 1se the profile from Young ot al. (, We use the profile from Young et al. (
"1978) to exteud toNUO"".",1978) to extend to.
", At the largest radii. out toπο, we use the R-baud results of Peletier et al. ("," At the largest radii, out to, we use the $R$ -band results of Peletier et al. ("
1990).,1990).
" These three measurements are spliced together. aud fi with a smoothlybroken power law whose error is less thaw 4 0.liuas↜ 2 in the range 0.1""«kr<150"", given by in. nag arcsecD. where A=0.58* «mmerus the speed of the power law break. a;=0.6/1n1)-2026.a,5.5/lun10=2.39 ave the immer iid outer )ower law slopes. and +;=15.3.+,8.9 ave normalizatio1 constants;"," These three measurements are spliced together, and fit with a smoothlybroken power law whose error is less than $0.1$ mag $^{-2}$ in the range $0.1\arcsec<r<150\arcsec$, given by in mag $^{-2}$, where $\lambda=0.58$ governs the speed of the power law break, $\alpha_i=0.6/\ln 10=0.26,\;\alpha_o=5.5/\ln10=2.39$ are the inner and outer power law slopes, and $\gamma_i=15.3,\;\gamma_o=8.9$ are normalization constants."
" Note that A>x gives a standard broken powy law. with break at lurτσs;M(n;654)=01 (rzs20"")."," Note that $\lambda\rightarrow\infty$ gives a standard broken power law, with break at $\ln r=(\gamma_o-\gamma_i)/(\alpha_i-\alpha_o)=3.01$ $(r\approx 20\arcsec)$."
 At very sanall aud very large radii. this reduces o a single power law: pgστανωd555," At very small and very large radii, this reduces to a single power law: $\mu_I\approx\alpha_{i,o}\ln r+\gamma_{i,o}$."
 The fit to the surface brghtuess profile is siuooth. and thus we can perform an Abel inversion under the asstuuption that the svstei is spherically sviunetric.," The fit to the surface brightness profile is smooth, and thus we can perform an Abel inversion under the assumption that the system is spherically symmetric."
" For convenience. we define the 2-d luminosity density 6;=10 9-5, "," For convenience, we define the 2-d luminosity density $\sigma_I=10^{-0.4\mu_I}$ ."
Takine its derivative. we cau write down the 3-d hinunosity deusitv. This vields a huninositv density for AIST. in ae 7. which we can apply to microlensing simulations.," Taking its derivative, we can write down the 3-d luminosity density, This yields a luminosity density for M87, in mag $^{-3}$, which we can apply to microlensing simulations."
 The Abel inversion is done umuerically. vielding a table of deusity values;," The Abel inversion is done numerically, yielding a table of density values."
 This table is again fit to a smoothly woken power law., This table is again fit to a smoothly broken power law.
" The fit coustauts are A=0.975. a;=2.6/lnl0.a,τοαι 1ο. +;=17.5.5,10.9."," The fit constants are $\lambda=0.975$, $\alpha_i=2.6/\ln
10,\;\alpha_o=7.5/\ln10$ , $\gamma_i=17.5,\;\gamma_o=10.9$."
" This Bt las errors less than 0.075 mag > in the range 1""«r150"".", This fit has errors less than $0.075$ mag $^{-3}$ in the range $1\arcsec<r<150\arcsec$.
 To ive at a liass density. we assuue hat the Z-baud mass to liebt ratio is [0 A./L..," To arrive at a mass density, we assume that the $I$ -band mass to light ratio is 4.0 $M_\odot/L_\odot$."
" We asstune that the velocity distribution of M87 stars is παπαμα, with 1-d velocity dispersion o=360 kins |."," We assume that the velocity distribution of M87 stars is maxwellian, with 1-d velocity dispersion $\sigma=360$ km $^{-1}$."
 Furthermore we assunue that it is isotropic. so radial aud aueential dispersions are the sanie.," Furthermore we assume that it is isotropic, so radial and tangential dispersions are the same."
 We will use simple models for the dark halos of cach relevant object., We will use simple models for the dark halos of each relevant object.
 The isothermal sphere with core has au asvinptotic 1/r? deusity profile. giviug a flat rotation curve.," The isothermal sphere with core has an asymptotic $1/r^2$ density profile, giving a flat rotation curve."
 The lack of observed ceutral density cusps inclicates that a core is appropriate., The lack of observed central density cusps indicates that a core is appropriate.
 The density of leuses making up a fraction fiiy of the dark halo is giveu by where ¢.220 kins + is the asviuptotic rotation speed of the Milkv. Way., The density of lenses making up a fraction $f_{\rm MW}$ of the dark halo is given by where $v_c=220$ km $^{-1}$ is the asymptotic rotation speed of the Milky Way.
 We will take a core radius r.=5 Ispe. though the value doesu't much matter as the line of sight to ALS7 is nearly perpendicular to the Milky. Way disk.," We will take a core radius $r_c=5$ kpc, though the value doesn't much matter as the line of sight to M87 is nearly perpendicular to the Milky Way disk."
 The velocity distribution of the halo is taken to be maxwellian. with a circular velocity equal to 0. making στ155 lan s+.," The velocity distribution of the halo is taken to be maxwellian, with a circular velocity equal to $v_c$, making $\sigma=155$ km $^{-1}$."
 We impose a cutoff at a distance of 200 Epe from tle center., We impose a cutoff at a distance of 200 kpc from the center.
 For ALS7 we will also use an isothermal sphere with a core., For M87 we will also use an isothermal sphere with a core.
" We will vary the core radius. taking r,.=5 kpe as the fiducial value."," We will vary the core radius, taking $r_c=5$ kpc as the fiducial value."
" We assume a l-d velocity dispersion στοὐ Ίαν +. giving e,=510 lans. 1. Based simply ou dispersion velocity. M87 is roughly five times as massive as the Milkv Wav."," We assume a 1-d velocity dispersion $\sigma=360$ km $^{-1}$, giving $v_c=510$ km $^{-1}$ Based simply on dispersion velocity, M87 is roughly five times as massive as the Milky Way."
 We allow the halo leus fraction fipsz to be indepeudent of fii., We allow the halo lens fraction $f_{\rm M87}$ to be independent of $f_{\rm MW}$.
 The halo of the Virgo cluster is more problematic., The halo of the Virgo cluster is more problematic.
 Again. we will assune an isothermal sphere with a core. with —10001140 1 (6.=1100 kms 23.," Again, we will assume an isothermal sphere with a core, with $\sigma=1000$ km $^{-1}$ $v_c=1400$ km $^{-1}$ )."
 We will assume that AIST is centered in the Virgo halo., We will assume that M87 is centered in the Virgo halo.
 This approach requires that we assign a very large core radius to the Vireo halo: for ras small as LOO kpc. Virgo dominates at a radius of 10 kpe from the center of M87.," This approach requires that we assign a very large core radius to the Virgo halo: for $r_c$ as small as 100 kpc, Virgo dominates at a radius of 40 kpc from the center of M87."
 Again. we allow an indepeudent halo leus fraction fy.," Again, we allow an independent halo lens fraction $f_{\rm
Vir}$."
 Armed with the model for \IS7 and the Virgo cluster. we can now proceed to compute the expected rate of detectable mücroleusiug eveuts," Armed with the model for M87 and the Virgo cluster, we can now proceed to compute the expected rate of detectable microlensing events."
 Some experiucutal parameters are required., Some experimental parameters are required.
 Furthermore. we must make assuniptious about the luminosity function of AIST stars. and about the mass function of the lenses.," Furthermore, we must make assumptions about the luminosity function of M87 stars, and about the mass function of the lenses."
 The capabilities of the WFPC2 can be suinniarized for our purposes as follows., The capabilities of the WFPC2 can be summarized for our purposes as follows.
" We assume that the zero poiut iu FatiW is mee=23.86 mag in the 7-band (this flux gives oue plhoto-clectron per second). and that ouly the FelAW frames are used to detect events: niuuclv au exposure of fon,=Lx260 8 = LOL0 s per orbit."," We assume that the zero point in F814W is $m_I^{\rm ZP}=23.86$ mag in the $I$ -band (this flux gives one photo-electron per second), and that only the F814W frames are used to detect events: namely an exposure of $t_{\rm
obs}=4\times 260$ s = 1040 s per orbit."
 The zero point for this exposure time is m=mee|2.5logLolo31.10 mae. eiving one ploto-clectron over the exposure.," The zero point for this exposure time is $m_I^0=m_I^{\rm ZP}+2.5\,\log 1040=31.40$ mag, giving one photo-electron over the exposure."
 The resolution can be characterized bv one umber per chip. Opag=1/8202. where co; is the normalized PSF (Could 1996).," The resolution can be characterized by one number per chip, $\Omega_{\rm PSF} = 1/\sum \psi_i^2$, where $\psi_i$ is the normalized PSF (Gould 1996)."
" Measured in pixels (talking (0.0155 arcsec)? for PCL and (0.1 aresec)? for ΝΕΟΣ, WFEC3. WEC1). the PSF sizes are 20.0. 7.31. 9.05. 7.89 for the PCL. WEC2. WEC3. and WFCL. respectively."," Measured in pixels (taking (0.0455 $^2$ for PC1 and (0.1 $^2$ for WFC2, WFC3, WFC4), the PSF sizes are 20.0, 7.31, 9.05, 7.89 for the PC1, WFC2, WFC3, and WFC4, respectively."
 These are somewhat less than O.1 aresec?., These are somewhat less than 0.1 $^2$ .
 Lastly. we assunie that the read noise is 5 photoclectrous. aud that the dark noise is negligible.," Lastly, we assume that the read noise is 5 photoelectrons, and that the dark noise is negligible."
 We asstune that the source population is circularly sviunietric. with surface brightuess taken from refsec:SB.," We assume that the source population is circularly symmetric, with surface brightness taken from \\ref{sec:SB}."
.We take the background sky. brghtuess to be a uniform figg=2105 mag 7 in the L-band., .We take the background sky brightness to be a uniform $\mu_{\rm sky}=21.5$ mag $^{-2}$ in the $I$ -band.
 We will compute the microlensing rate at radial positions spaced, We will compute the microlensing rate at radial positions spaced
aancd A used in order to reproduce the stellar mass and scale ength of the MW. are smaller than those used. in. other studies (Dalcanton. Spergel Summers LOOT: Mo. Mao White 199s; FAOO. AEO0).,"and $\lambda$ used in order to reproduce the stellar mass and scale length of the MW, are smaller than those used in other studies (Dalcanton, Spergel Summers 1997; Mo, Mao White 1998; FA00, AF00)."
" The cise mass fraction in haloes.ae used in these works was e0.05. only «σι smaller han the barvon to total mass fraction. Q,/£(,,. for the conservative value of Q,7=0.010 (Logan 1998) and Q,,,= 3."," The disc mass fraction in haloes, used in these works was $\approx 0.05$, only slightly smaller than the baryon to total mass fraction, $\Omega_{b} /\Omega_{m}$, for the conservative value of $\Omega_b h^2\approx 0.010$ (Hogan 1998) and $\Omega_{m}=0.3$ ."
" Ehis disc mass fraction increases to f,e0.15 taking into account the higher estimate of Q,57. (20.019) inferred from he deuterium absorption in quasars (Burles et al.", This disc mass fraction increases to $\fb\approx 0.15$ taking into account the higher estimate of $\Omega_b h^2$ $\approx $ 0.019) inferred from the deuterium absorption in quasars (Burles et al.
 1998)., 1998).
 Thus. for the MW the barvon fraction (Ma.|Adsteuseiue.Αμμος|WJ fAL) seems to be smaller than the universal xwvon fraction.," Thus, for the MW the baryon fraction $\md+M_{\rm stellar \ halo}+M_{\rm satellites}+...)/\mvir$ ) seems to be smaller than the universal baryon fraction."
 Cosmological numerical simulations indeed show that most ofthe barvons in the past and in the present are not within eravitationally bound systems. but in forni of dilfuse and warm-hot intergalactic gas (Cen Ostriker 1999: Davétt al.," Cosmological numerical simulations indeed show that most of the baryons in the past and in the present are not within gravitationally bound systems, but in form of diffuse and warm-hot intergalactic gas (Cen Ostriker 1999; Davétt al."
 2000)., 2000).
" Smaller values of aallow for smaller values of A (given a fixed r,)) that otherwise could lead the cise to destructive. gravitational instabilities (see Mo et al.", Smaller values of allow for smaller values of $\lambda$ (given a fixed ) that otherwise could lead the disc to destructive gravitational instabilities (see Mo et al.
 1998: FAOO)., 1998; FA00).
 Lf the distribution of X is mainlv responsible for the ealaxy distribution in surface brightness. then. that high-surface brightness MW-tvpe galaxies should have Àzz0.02 agrees with a distribution where low surface brightness (LSB) galaxies (A 0.05) are equally abundant (c.g. AleGaugh 1996).," If the distribution of $\lambda$ is mainly responsible for the galaxy distribution in surface brightness, then, that high-surface brightness MW-type galaxies should have $\lambda\approx 0.02$ agrees with a distribution where low surface brightness (LSB) galaxies $\lambda \grtsim 0.05$ ) are equally abundant (e.g. McGaugh 1996)."
 To conclude. the values for fy ancl A inferred for the average NALE seem to be consistent with several observational and theoretical pieces ol evidence.," To conclude, the values for $\fd$ and $\lambda$ inferred for the average MAH seem to be consistent with several observational and theoretical pieces of evidence."
 In Fig., In Fig.
 2a the rotation curve decomposition of the ficlucial AIW mocel is shown by the thick lines. with the continuous curve eivine the total rotation curve. the dashed one the halo component. and the dotted one the dise contribution. at the present epoch.," 2a the rotation curve decomposition of the fiducial MW model is shown by the thick lines, with the continuous curve giving the total rotation curve, the dashed one the halo component, and the dotted one the disc contribution, at the present epoch."
 The maximum of the final rotation curve occurs at al zz2.2 wwith a value of 235, The maximum of the final rotation curve occurs at at $\approx 2.2$ with a value of 235.
 The model rotation curve is somewhat more. peaked than the observed one (Fieh Tremaine 1991) and the halo component dominates over the disc component at almost all raclil., The model rotation curve is somewhat more peaked than the observed one (Fich Tremaine 1991) and the halo component dominates over the disc component at almost all radii.
 “This is a direct consequence of the high central mass concentration ofthe CDM halo., This is a direct consequence of the high central mass concentration of the CDM halo.
 There is no way of obtaining a flat rotation curve for the parameters of the MW. when a ΝΤ halo is used., There is no way of obtaining a flat rotation curve for the parameters of the MW when a CDM halo is used.
 Ehe density profile of our “virgin” CDM halo (without the gravitational drag cue to disc formation) is well described by the NEW profile., The density profile of our “virgin” CDM halo (without the gravitational drag due to disc formation) is well described by the NFW profile.
 toecent very high-resolution simulations show that the inner density. profile of CDAL haloes is even steeper than the r+ slope of NEW profiles (Moore e al., Recent very high-resolution simulations show that the inner density profile of CDM haloes is even steeper than the $r^{-1}$ slope of NFW profiles (Moore et al.
 999b: see also Fukushige Makino 1997)., 1999b; see also Fukushige Makino 1997).
 The rotation curve of a MW. mode in this case would be even more peaked than that shown in Eig., The rotation curve of a MW model in this case would be even more peaked than that shown in Fig.
 2. which should be taken as a lower limi in terms of the central overshooting.," 2, which should be taken as a lower limit in terms of the central overshooting."
 The intrinsic scatter in the density. profies of CDM haloes does not help to alleviate this problem. as can be seen in Fig.," The intrinsic scatter in the density profiles of CDM haloes does not help to alleviate this problem, as can be seen in Fig."
 2b. where the total final rotation curves corresponding to the five particular MAIS of Fig.," 2b, where the total final rotation curves corresponding to the five particular MAHs of Fig."
 Lh are shown., 1b are shown.
" Several pieces of evidence point out that clark matter haloes at all scales indeed have constant clensity cores (Moore 1994. Flores Primack 1994 and. Burkert 1995 in chvarl galaxies. de Blok MeGaugh LOOT in LSB galaxies. llernandez Cilmore 1998 anc Salucci 2001 for normal spirals. Έντο, Ixochanski DellAntonio 1998 for galaxy clusters)."," Several pieces of evidence point out that dark matter haloes at all scales indeed have constant density cores (Moore 1994, Flores Primack 1994 and Burkert 1995 in dwarf galaxies, de Blok McGaugh 1997 in LSB galaxies, Hernandez Gilmore 1998 and Salucci 2001 for normal spirals, Tyson, Kochanski Dell'Antonio 1998 for galaxy clusters)."
 According to the analvsis of rotation curves of chvarl and LSB galaxies carried out in Firmani et al. (, According to the analysis of rotation curves of dwarf and LSB galaxies carried out in Firmani et al. (
2001). the core radius of the “virgin” halo of a galaxy of the size of the MW. should be z10 kpe with a central density of,"2001), the core radius of the “virgin” halo of a galaxy of the size of the MW should be $\approx 10$ kpc with a central density of"
the energy [Iux aud Mheelectriefield.,the energy flux and the electric field.
D| heconservationofmasso[componentll is expressed by wilh pthemassfractionandmalhhf ihe material current densitv., The conservation of mass of component is expressed by with the mass fraction and the material current density.
 The classical entropy of the svstem is defined wilh (he usual Gibbs equation By diflferentating this equation wilh respect to lime. and substituting (4)) and (5)) in the subsequent equation we obtain Arranging terms. we obtain four fluxes and [our generalized forces appearing in the entropy. production. namely. the last four terms in the right hand side οἱ As it ds known. a generalized force can produce not only its associated flux. but also other [Iuxes. like in thermoelectricity or (hermocliffision (deGroot& (2001))).," The classical entropy of the system is defined with the usual Gibbs equation By differentiating this equation with respect to time, and substituting \ref{ener}) ) and \ref{consma}) ) in the subsequent equation we obtain Arranging terms, we obtain four fluxes and four generalized forces appearing in the entropy production, namely, the last four terms in the right hand side of As it is known, a generalized force can produce not only its associated flux, but also other fluxes, like in thermoelectricity or thermodiffusion \cite{GROOT, EIT1}) )."
 In our example. we analvse the coupling between electric field ancl (he gradient of chemical potential.," In our example, we analyse the coupling between electric field and the gradient of chemical potential."
 The constitutive equations of the corresponding fluxes are, The constitutive equations of the corresponding fluxes are
density of the extra bins is reset to zero.,density of the extra bins is reset to zero.
 We have found that for the binning scheme that we have usecl (eq. 3)), We have found that for the binning scheme that we have used (eq. \ref{eq:sizebins}) )
 one extra bin is enough to ensure mass couservation but more bius are needed when a finer distribution is used., one extra bin is enough to ensure mass conservation but more bins are needed when a finer distribution is used.
" The time rate of change of the number deusity of grains of mass 74 due to coagulation is given by the Smoluchowski equation To this we add a trausport teri to account for secimeutation: aud a source teri. (μη,z./). to take into account auy grains that are introduced either by the breakup of captured plauetesimals. or by the accretion of gas containing graius in the outermost atmospheric layer."," The time rate of change of the number density of grains of mass $m$ due to coagulation is given by the Smoluchowski equation To this we add a transport term to account for sedimentation: and a source term, $Q(m,z,t)$, to take into account any grains that are introduced either by the breakup of captured planetesimals, or by the accretion of gas containing grains in the outermost atmospheric layer."
 The total time rate of chanee in the nunber density of grains of mass i is elven by The rate of plauetesimal mass deposition as a fuuction of height iu the envelope was kindly provided by Dr. O. Hubickyj. and. correspouds to the rate of planetesunal accretiou used iu ?..," The total time rate of change in the number density of grains of mass $m$ is given by The rate of planetesimal mass deposition as a function of height in the envelope was kindly provided by Dr. O. Hubickyj, and corresponds to the rate of planetesimal accretion used in \citet{hubickyj}."
 We have converted these rates into a source terms by assumiug that all of the mass Is deposited in the form of graius of size ay (monomers)., We have converted these rates into a source term by assuming that all of the mass is deposited in the form of grains of size $a_1$ (monomers).
 In addition. we assume that the gas accreted outo the planet provides an additional source of erains whose mass was usually taken to be of the acereted eas mass.," In addition, we assume that the gas accreted onto the planet provides an additional source of grains whose mass was usually taken to be of the accreted gas mass."
 For simplicity. we assumed that these accreted grains were initially of the saine size as the eraius from plauetestinal breakup.," For simplicity, we assumed that these accreted grains were initially of the same size as the grains from planetesimal breakup."
 Ouce the rate of cliauge due to the combined ellects of coagulation. sedimentation. aud the source term is calculated. a time step is chosen. stuall enough to ensure that the total change in number cleusity at the eud of the time step for every size bin and in every layer will uot exceed one per ceut of the number deusity at the beginning of the time step.," Once the rate of change due to the combined effects of coagulation, sedimentation, and the source term is calculated, a time step is chosen, small enough to ensure that the total change in number density at the end of the time step for every size bin and in every layer will not exceed one per cent of the number density at the beginning of the time step."
 We have tested the coagulation algorithiu by applying it to some special cases that have analytic solutions. such as the case of a constant kernel. fy;=a.," We have tested the coagulation algorithm by applying it to some special cases that have analytic solutions, such as the case of a constant kernel, $K_{ij}=\alpha$."
 With all grains initially in the stnallest size bin. the total number of grains in the distribution that are left alter / secoucls is foul to be (?) ," With all grains initially in the smallest size bin, the total number of grains in the distribution that are left after $t$ seconds is found to be \citep{wetherill90}
 "
2000).,.
. By contrast. technetium-poor S stars are known as “extrinsic” S stars.," By contrast, technetium-poor S stars are known as ""extrinsic"" S stars."
 These stars are likely to be part of binary systems and their unusual chemical abundances probably originated in a past mass-transfer episode (VanEck&Joris-sen2000).., These stars are likely to be part of binary systems and their unusual chemical abundances probably originated in a past mass-transfer episode \citep{2000A&A...360..196V}.
 The present extrinsic S star likely once accreted s-process rich material from its companion. a TP-AGB star at the time that has since evolved into a white dwarf.," The present extrinsic S star likely once accreted $s$ -process rich material from its companion, a TP-AGB star at the time that has since evolved into a white dwarf."
 Extrinsic S stars therefore display enriched s-process elements. despite having never produced these elements themselves.," Extrinsic S stars therefore display enriched $s$ -process elements, despite having never produced these elements themselves."
 Most known extrinsic S stars are assumed to be members of the red giant branch (RGB)., Most known extrinsic S stars are assumed to be members of the red giant branch (RGB).
 They can sometimes be distinguished from intrinsic S stars on the basis of color. because they do not necessarily show the red excess characteristic of stars on the AGB.," They can sometimes be distinguished from intrinsic S stars on the basis of color, because they do not necessarily show the red excess characteristic of stars on the AGB."
 While all currently known extrinsic S stars are thought to be giants. these definitions open up the possibility of extrinsic S stars on the main sequence (hereafter referred to as dwarf S stars) that have previously accreted s-process material and carbon from à companion but whose Te has since decayed.," While all currently known extrinsic S stars are thought to be giants, these definitions open up the possibility of extrinsic S stars on the main sequence (hereafter referred to as dwarf S stars) that have previously accreted $s$ -process material and carbon from a companion but whose Tc has since decayed."
 Analogous to the dwarf C stars (Greenetal.1991). à funt S star could be shown to be a dwarf if it has a sufficiently large parallax or proper motion: a large proper motion predicts a tangential velocity greater than the Galactic escape speed unless the object is faint and nearby.," Analogous to the dwarf C stars \citep{Green91}, a faint S star could be shown to be a dwarf if it has a sufficiently large parallax or proper motion; a large proper motion predicts a tangential velocity greater than the Galactic escape speed unless the object is faint and nearby."
 S stars are very similar to C stars. with the major difference being a slightly lower C/O ratio.," S stars are very similar to C stars, with the major difference being a slightly lower C/O ratio."
 Faint high galactic latitude carbon (FHLC) stars were once assumed be giant stars at large distances., Faint high galactic latitude carbon (FHLC) stars were once assumed be giant stars at large distances.
 In 1977. however. G77-61 was discovered to have high proper motion and an upper limit absolute magnitude of +9.6. therefore making it the first known carbon dwarf star (Dahnetal.1977)..," In 1977, however, G77-61 was discovered to have high proper motion and an upper limit absolute magnitude of +9.6, therefore making it the first known carbon dwarf star \citep{1977ApJ...216..757D}."
 In this case. the term dwarf refers to a star on the main sequence.," In this case, the term dwarf refers to a star on the main sequence."
 Greenetal.(1991) discovered four other dwarf carbon (dC) stars using techniques that selected known carbon stars for high proper motion.," \citet{Green91}
 discovered four other dwarf carbon (dC) stars using techniques that selected known carbon stars for high proper motion."
 Now. well over 100 dwarf carbon stars are known (Downesetal.2004)..," Now, well over 100 dwarf carbon stars are known \citep{2004AJ....127.2838D}."
 The local space density of dCs 1s far higher than all types of C giants combined (Greenetal.1992).., The local space density of dCs is far higher than all types of C giants combined \citep{1992ApJ...400..659G}.
 Therefore. contrary to previous assumptions. dwarf C stars are the numerically dominant type of carbon star in the Galaxy.," Therefore, contrary to previous assumptions, dwarf C stars are the numerically dominant type of carbon star in the Galaxy."
 Since dC stars are now known to be so common. we have begun a search for dwarf S stars.," Since dC stars are now known to be so common, we have begun a search for dwarf S stars."
 There is little reason to believe that dwarfS stars should not exist., There is little reason to believe that dwarf S stars should not exist.
 In fact. they may be more abundant than dC stars. since less carbon enhancement is required to produce an S dwarf as compared to a C dwarf.," In fact, they may be more abundant than dC stars, since less carbon enhancement is required to produce an S dwarf as compared to a C dwarf."
 On the other hand. if the range of abundance ratios that produces the characteristic features of S stars 1s narrow. they may be quite rare.," On the other hand, if the range of abundance ratios that produces the characteristic features of S stars is narrow, they may be quite rare."
 Furthermore. the range of C/O ratios that produces S star spectral features may be different for giants and dwarfs. given the higher gravities and larger temperature ranges in dwarfs.," Furthermore, the range of C/O ratios that produces S star spectral features may be different for giants and dwarfs, given the higher gravities and larger temperature ranges in dwarfs."
 We use medium-resolution digital spectra of known S stars (which are probably giants) to generate corresponding Sloan Digital Sky Survey (SDSS) colors. to see whether their colors might be sufficiently distinctive to search for additional S stars in the SDSS with reasonable efficiency.," We use medium-resolution digital spectra of known S stars (which are probably giants) to generate corresponding Sloan Digital Sky Survey (SDSS) colors, to see whether their colors might be sufficiently distinctive to search for additional S stars in the SDSS with reasonable efficiency."
 We also use the FAST spectra to investigate molecular band spectral indices for classification., We also use the FAST spectra to investigate molecular band spectral indices for classification.
 Our paper is organized as follows: in refsec:obs we briefly review the observations and our data reduction and processing procedures., Our paper is organized as follows: in \\ref{sec:obs} we briefly review the observations and our data reduction and processing procedures.
 In section refsec:spatlas we describe the production of a spectral atlas of S stars. and derive spectral indices from the molecular band strengths in refsec:specind..," In section \\ref{sec:spatlas}
 we describe the production of a spectral atlas of S stars, and derive spectral indices from the molecular band strengths in \\ref{sec:specind}."
 In refsec:colors we describe the generation of SDSS colors and analyze the overall colors of the FAST sample in order to determine whether an efficient color selection for S stars exist., In \\ref{sec:colors} we describe the generation of SDSS colors and analyze the overall colors of the FAST sample in order to determine whether an efficient color selection for S stars exist.
 Ins refsec:intext we discuss techniques for distinguishing intrinsic and extrinsic S stars and apply them to the FAST sample., In \\ref{sec:intext} we discuss techniques for distinguishing intrinsic and extrinsic S stars and apply them to the FAST sample.
 In refsec:motion. we analyze the parallaxes and proper motions of S stars in the sample to characterize upper and lower limit magnitudes and distances., In \\ref{sec:motion} we analyze the parallaxes and proper motions of S stars in the sample to characterize upper and lower limit magnitudes and distances.
 We use colors to generate approximate temperature indices for S stars in refsec:temp.., We use colors to generate approximate temperature indices for S stars in \\ref{sec:temp}.
 In refsecisum— we summarize our results and present our conclusions.," In \\ref{sec:sum}
 we summarize our results and present our conclusions."
 The largest spectral catalog of S stars is Stephenson's second edition (1984). which includes 1347 objects with poorly known positions.," The largest spectral catalog of S stars is Stephenson's second edition (1984), which includes 1347 objects with poorly known positions."
 The stars in this catalog were originally identified from blue. red. and infrared objective prism plates.," The stars in this catalog were originally identified from blue, red, and infrared objective prism plates."
 The majority of the S stars were discovered on the basis of the red system of ZrO absorption bands. with a bandhead aroundA.," The majority of the S stars were discovered on the basis of the red system of ZrO absorption bands, with a bandhead around."
. Since the Stephenson catalog has a limiting V. magnitude of approximately 11.5. most of the objects are highly saturated in the SDSS and reliable u. g. r. i. and z magnitudes have not been found for any known S stars.," Since the Stephenson catalog has a limiting V magnitude of approximately 11.5, most of the objects are highly saturated in the SDSS and reliable u, g, r, i, and z magnitudes have not been found for any known S stars."
 We assembled a sample of known S giants in order to generate likely & and r colors for S giants and dwarfs., We assembled a sample of known S giants in order to generate likely g and r colors for S giants and dwarfs.
" These constraints on colors of S giants and dwarfs could allow us to search the SDSS and 2MASS catalogs for potential dwarf S star candidates,", These constraints on colors of S giants and dwarfs could allow us to search the SDSS and 2MASS catalogs for potential dwarf S star candidates.
 To choose the stars making up the sample. we selected high Galactic latitude (|5]>20 deg). northern (67—05 deg) S stars from Stephenson's catalog.," To choose the stars making up the sample, we selected high Galactic latitude $|b| > 20$ deg), northern $\delta > -05 $ deg) S stars from Stephenson's catalog."
 This ensures that our sample is accessible from Mt. Hopkins. and also decreases problems of object confusion or reddening.," This ensures that our sample is accessible from Mt. Hopkins, and also decreases problems of object confusion or reddening."
" We then correlated the sample from Stephenson's catalog with 2MASS to find improved positions for most objects: accuracy of the original positions is typically ~4"". but commonly as poor as20”."," We then correlated the sample from Stephenson's catalog with 2MASS to find improved positions for most objects; accuracy of the original positions is typically $\sim 4\arcsec$, but commonly as poor as."
. The final sample list. which includes 57 objects. can be found in reftab:stars..," The final sample list, which includes 57 objects, can be found in \\ref{tab:stars}."
 Each object is accompanied by its identification in both the Stephenson and 2MASS catalogs. as well as its position.," Each object is accompanied by its identification in both the Stephenson and 2MASS catalogs, as well as its position."
 Since many of these stars are known to be variable. we include the date of observation.," Since many of these stars are known to be variable, we include the date of observation."
 We include other common identifiers for each target and à published spectral type. if available.," We include other common identifiers for each target and a published spectral type, if available."
 We include our calculated temperature index for the star. which is discussed further in refsec:temp..," We include our calculated temperature index for the star, which is discussed further in \\ref{sec:temp}."
 Spectral types and temperature indices of the S stars in the sample may vary as a function of time. because the stars themselves do.," Spectral types and temperature indices of the S stars in the sample may vary as a function of time, because the stars themselves do."
 When spectral types for different epochs were available. we match the V magnitudes of the epochs to those listed in reftab:mags to find the spectral type.," When spectral types for different epochs were available, we match the $V$ magnitudes of the epochs to those listed in \\ref{tab:mags} to find the spectral type."
 Finally. we include identifications of some stars as intrinsic or extrinsic (denoted respectively by r and ο) from Yangetal.(2006). or from our own calculations based on AKARI magnitudes.," Finally, we include identifications of some stars as intrinsic or extrinsic (denoted respectively by 'i' and 'e') from \citet{2006AJ....132.1468Y} or from our own calculations based on AKARI magnitudes."
 For more information regarding the intrinsic/extrinsic identifications. see refsec:intext..," For more information regarding the intrinsic/extrinsic identifications, see \\ref{sec:intext}. ."
 Spectra were obtained using the FAST instrument on the 1.5 m Tillinghast reflector on Mt. Hopkins., Spectra were obtained using the FAST instrument on the 1.5 m Tillinghast reflector on Mt. Hopkins.
 FAST produces, FAST produces
expect lower eracdieuts as well.,expect lower gradients as well.
 These lower eradieuts would eive canals that shift position with frequency sienificauth. which we do not observe.," These lower gradients would give canals that shift position with frequency significantly, which we do not observe."
 The shape of the decline in P across a canal or the “steepness” of a canal gives a lower limit fo the abruptuess of the change in polarization augle across a canal. as can be seeu in Fig. 9..," The shape of the decline in $P$ across a canal, or the “steepness” of a canal, gives a lower limit to the abruptness of the change in polarization angle across a canal, as can be seen in Fig. \ref{f3:can_the}."
 Tere a ouc-dimenusional exinuple is given of a change in polarization angle Ao=907 (left) and the corresponding change in 7 after convolution with the telescope beam (right)., Here a one-dimensional example is given of a change in polarization angle $\Delta\phi=90\dg$ (left) and the corresponding change in $P$ after convolution with the telescope beam (right).
 The narrowest P profile is achieved when the changeC» in anele, The narrowest $P$ profile is achieved when the change in angle
 The narrowest P profile is achieved when the changeC» in aneleC, The narrowest $P$ profile is achieved when the change in angle
 The narrowest P profile is achieved when the changeC» in aneleC», The narrowest $P$ profile is achieved when the change in angle
objects. (11) large-area detectors with high time resolution capability (effective area: 2000 cui: telemetry: LO kbps. with 128 kbps available for short periods: 2 ps time resolution). (ii) good low euergv response (down to l keV). aud (iv) a high flexibility in data handling.,"objects, (ii) large-area detectors with high time resolution capability (effective area: 2000 $^2$; telemetry: 40 kbps, with 128 kbps available for short periods; 2 $\mu$ s time resolution), (iii) good low energy response (down to 1 keV), and (iv) a high flexibility in data handling."
 Other special features include absolute timc-tageiue (to 2 ps) using a GPS receiver., Other special features include absolute time-tagging (to 2 $\mu$ s) using a GPS receiver.
 The principal tareets for USA are N-ray binaries whose N-vay cmitting members are neutron stars. black holes. or white dwarfs.," The principal targets for USA are X-ray binaries whose X-ray emitting members are neutron stars, black holes, or white dwarfs."
 Study of physical processes im these svstenis have been among the main thrusts of N-rav astronomy since the founding of the field., Study of physical processes in these systems have been among the main thrusts of X-ray astronomy since the founding of the field.
 Today it remains true that many of the most importaut results on these systems are found by studving their X-ray variability. aud the push to shorter (millisecond) timescales is proving highly fruitful.," Today it remains true that many of the most important results on these systems are found by studying their X-ray variability, and the push to shorter (millisecond) timescales is proving highly fruitful."
 If the source is bright (2 ΙΙτας}. such short timescales are more readilv reached with non-mniasius instruments having large collecting apertures thanwith imagine istruucuts., If the source is bright $>$ milliCrabs) such short timescales are more readily reached with non-imaging instruments having large collecting apertures than with imaging instruments.
", Physics issues studied in these sources are ecucrally related to the fact that parameters such as nagnetic field strength. mass aud energy deusitics. and eravitational fields reach extreme values. heuce providing the preferred testing erouuds for physical theories."," Physics issues studied in these sources are generally related to the fact that parameters such as magnetic field strength, mass and energy densities, and gravitational fields reach extreme values, hence providing the preferred testing grounds for physical theories."
 N-rav fuuug is a cornerstone of relativistic astroplivsics., X-ray timing is a cornerstone of relativistic astrophysics.
 USA. in turn. is oue of the two main resources at the present epoch for N-rax imine experiments. the other being the Proportional Counter Array (PCA) ou RATE.," USA, in turn, is one of the two main resources at the present epoch for X-ray timing experiments, the other being the Proportional Counter Array (PCA) on RXTE."
 USA has its own special areas of eimipliasis. oue of which is its observing au.," USA has its own special areas of emphasis, one of which is its observing plan."
 Preseut plans call for the observation of about 30 primary targets. with cach being observed for about 1 month over a nominal mission life of 3 wears: selected targets will be observed for shorter periods of tine.," Present plans call for the observation of about 30 primary targets, with each being observed for about 1 month over a nominal mission life of 3 years; selected targets will be observed for shorter periods of time."
 Sources observed o date (through 31 August. 1999) include Cre N-1 (700 ks on target). Δά (100. ks). Con N-3 (65 kx). X1630-172 (60 kx). Cre N-2 (50 ks). N1636-536 C15 kx). GN L1 LCIO ks). 1E2259|586 (CIO ks}. N1820-30 (10 x). N1630-172 (35 kx). 1E1018.1-5957 (30 ks). and CRS 1915|105 (25 ks).," Sources observed to date (through 31 August 1999) include Cyg X-1 (700 ks on target), Aql X-1 (100 ks), Cen X-3 (65 ks), X1630-472 (60 ks), Cyg X-2 (50 ks), X1636-536 (45 ks), GX 1+4 (40 ks), 1E2259+586 (40 ks), X1820-30 (40 ks), X1630-472 (35 ks), 1E1048.1-5937 (30 ks), and GRS 1915+105 (25 ks)."
 The total time on each source is typically scheduled as à umber of ~1 ks observations distributed over weeks or uouths., The total time on each source is typically scheduled as a number of $\sim$ 1 ks observations distributed over weeks or months.
 Simultancous observation with other observatories. such as the Compton Canuna Rav Observatory aud Rossi X-ray Timing Explorer. aud with erouud based clescopes are also beime uudoertaken.," Simultaneous observation with other observatories, such as the Compton Gamma Ray Observatory and Rossi X-ray Timing Explorer, and with ground based telescopes are also being undertaken."
 Figure Ll shows two sample light curves taken with USA., Figure 1 shows two sample light curves taken with USA.
 The first is an N-rax must from the burster N1735-L11. and the second is an observation of a faring state of the Galactic microquasar GBS1915|105.," The first is an X-ray burst from the burster X1735-444, and the second is an observation of a flaring state of the Galactic microquasar GRS1915+105."
 Tn 1735-11 the instrument is on he source throughout the interval displaved while in GRS 1915|105 the steep rise at the beginning of the plot is the iustruneut slewing outo the source: the earliest seconds represeut the background for this observation., In 1735-44 the instrument is on the source throughout the interval displayed while in GRS 1915+105 the steep rise at the beginning of the plot is the instrument slewing onto the source; the earliest seconds represent the background for this observation.
 The special importance of the low mass X-ray binaries (LMXNDs) arises from their conrparativelv weak maguetic felds which allows the disk to penetrate very. close to the star., The special importance of the low mass X-ray binaries (LMXBs) arises from their comparatively weak magnetic fields which allows the disk to penetrate very close to the star.
 This eives rise to fast timune effects that can be used to probe the, This gives rise to fast timing effects that can be used to probe the
Low mass X-ray binaries (LMXBs) are interacting binaries where a low mass donor is transferring material onto a neutron star or a black hole.,Low mass X-ray binaries (LMXBs) are interacting binaries where a low mass donor is transferring material onto a neutron star or a black hole.
 In order to transport the excess of angular momentum outwards. an accretion dise is formed.," In order to transport the excess of angular momentum outwards, an accretion disc is formed."
 In the disc. the gravitational potential energy is transformed into mainly X-ray radiation and kinetic energy. and temperatures approach ~10° K. The mass transfer rate supplied by the donor star. M». is driven by the binary/donor evolution and mass transfer rates Mz;Moy~007MΚαyr! Gvhere Ma is the mass of the Sun in kg) result in persistently bright X-ray sources (Kingetal. 1996).," In the disc, the gravitational potential energy is transformed into mainly X-ray radiation and kinetic energy, and temperatures approach $\sim 10^8$ K. The mass transfer rate supplied by the donor star, $\dot{M}_2$, is driven by the binary/donor evolution and mass transfer rates $\dot{M}_2>\dot{M}_{\rm crit}\sim 10^{-9}M_{\odot} ~ \mathrm{kg} ~ \mathrm{yr}^{-1}$ (where $M_{\odot}$ is the mass of the Sun in kg) result in persistently bright X-ray sources \citep{kinget96}."
. There are ~200 such bright (Lx~10°°—10°Serg s!) LMXBs in the Galaxy and most of them harbour neutron stars as implied by the detection of pulsations and X-ray bursts resulting from nuclear burning caused by the accumulation of Hydrogen and Helium on their surfaces., There are $\sim 200$ such bright $L_{\rm X} \simeq 10^{36} - 10^{38} \mathrm{erg} ~ \mathrm{s}^{-1}$ ) LMXBs in the Galaxy and most of them harbour neutron stars as implied by the detection of pulsations and X-ray bursts resulting from nuclear burning caused by the accumulation of Hydrogen and Helium on their surfaces.
 They show energy spectra dominated by emission from their irradiated accretion dises which also dominate at optical wavelengths (e.g..vanParadijs&MeClintock 1905).," They show energy spectra dominated by emission from their irradiated accretion discs which also dominate at optical wavelengths \citep[e.g.,][]{vanpet95}."
 Even in the near-infrared (NIR). where the companion star could have an important contribution. the disc emission seems dominant in bright systems.," Even in the near-infrared (NIR), where the companion star could have an important contribution, the disc emission seems dominant in bright systems."
 For instance. in the prototypical persistent neutron star. Sco X-1. which given its relatively long orbital period (~19 h) should have a large. evolved companion star. 10 spectral feature from the donor has been detected in the NIR (Bandyopadhyayetal.1997).," For instance, in the prototypical persistent neutron star, Sco X–1, which given its relatively long orbital period $\sim 19$ h) should have a large, evolved companion star, no spectral feature from the donor has been detected in the NIR \citep{bandet97}."
. In most persistent neutron star X-ray binaries. spectral and temporal studies have favoured an X-ray heated accretion dise as the origin of the NIR emission (e.g..4U1705-440:Homanetal.2009).," In most persistent neutron star X-ray binaries, spectral and temporal studies have favoured an X-ray heated accretion disc as the origin of the NIR emission \citep[e.g., 4U 1705--440;][]{homaet09}."
. Compact Jets producing synchrotron emission typically dominate the radio emission (Mighari&Fender2006) and their spectra can extend to higher frequencies., Compact jets producing synchrotron emission typically dominate the radio emission \citep{miglfe06} and their spectra can extend to higher frequencies.
 In the NIR. high amplitude flares from GX 17+2 (Callananetal.2002).. a synchrotron spectrum in 4U 0614+09 (Migharietal.2010) and variable linear polarization in Sco X-1 (Russell&Fender2008) have suggested a strong infrared jet contribution in these persistent neutron star X-ray binaries.," In the NIR, high amplitude flares from GX 17+2 \citep{callet02}, a synchrotron spectrum in 4U 0614+09 \citep{miglet10} and variable linear polarization in Sco X–1 \citep{russfe08} have suggested a strong infrared jet contribution in these persistent neutron star X-ray binaries."
 One of the classical neutron star systems ts 4U. 1636—53 (= 4U 1636-536 = V801] Ara)., One of the classical neutron star systems is 4U 1636–53 (= 4U 1636–536 = V801 Ara).
 It is an X-ray burster. which has been extensively studied in X-ray and optical regimes for more than three decades (e.g..Pedersenetal.1982).," It is an X-ray burster, which has been extensively studied in X-ray and optical regimes for more than three decades \citep[e.g.,][]{pedeet82}."
. It has à 3.8 h orbital period (vanParadijsetal.1990:Giles2002) pointing to a relatively faint. late type companion star.," It has a 3.8 h orbital period \citep{vanpet90,gileet02} pointing to a relatively faint, late type companion star."
 The spectrum of the system from X-ray to optical wavelengths seems to be dominated by the emission of its bright accretion disc. the companion star only being detected by using emission lines arising from reprocessing of the strong X-ray emission (Ly~10°erg so!) in its inner hemisphere (Casares 2000).," The spectrum of the system from X-ray to optical wavelengths seems to be dominated by the emission of its bright accretion disc, the companion star only being detected by using emission lines arising from reprocessing of the strong X-ray emission $L_X \sim 10^{37 - 38} \mathrm{erg} ~ \mathrm{s}^{-1}$ ) in its inner hemisphere \citep{casaet06}."
. To date. no detections of 4U 1636-53 have been reported at wavelengths longer than the optical regime.," To date, no detections of 4U 1636–53 have been reported at wavelengths longer than the optical regime."
 At radio frequencies. upper limits of both the persistent and burst fluxes were presented in Thomasetal. (1979)).," At radio frequencies, upper limits of both the persistent and burst fluxes were presented in \citeauthor{thomet79} \citeyear{thomet79}) )."
 Here we present the first detection of the near-infrared counterpart of 4U 1636-53., Here we present the first detection of the near-infrared counterpart of 4U 1636–53.
 Together with available optical and UV data. we construct the intrinsic 0.2—2.2 gm spectral energy distribution (SED).," Together with available optical and UV data, we construct the intrinsic 0.2–2.2 $\mu \mathrm{m}$ spectral energy distribution (SED)."
 The data were acquired with the Infrared Spectrometer And Array Camera (ISAAC) on the European Southern Observatory (ESO) 8-melass Very Large Telescope UT3 (Melipal) on 2010- 02:23 - 03:17 UT (MJD 55337.118x 0.019) under ESO, The data were acquired with the Infrared Spectrometer And Array Camera (ISAAC) on the European Southern Observatory (ESO) 8-m class Very Large Telescope UT3 (Melipal) on 2010-05-21 02:23 – 03:17 UT (MJD $55337.118 \pm 0.019$ ) under ESO
high redshifts. while the faintest are at low redshifts. mace it dillieult to study how QSO properties depend on luminosity.,"high redshifts, while the faintest are at low redshifts, made it difficult to study how QSO properties depend on luminosity."
 Now. surveys such as 25LAQ (Cannon et al.," Now, surveys such as 2SLAQ (Cannon et al."
 2006) that span a wide range of QSO luminosities. have broken that redshift-Iuminosity degeneracy and revealed. little QSO clustering dependence on luminosity. at fixed redshilt. (da Angela οἱ al.," 2006) that span a wide range of QSO luminosities, have broken that redshift-luminosity degeneracy and revealed little QSO clustering dependence on luminosity, at fixed redshift (da $\hat{A}$ ngela et al."
 2006)., 2006).
 Moreover. the amplitude of the QSO clustering is correlated with the average mass of the halos associated with the QSOs. providing indications of QSO lifetimes and making it possible to constrain QSO evolutionary models (Croom et al.," Moreover, the amplitude of the QSO clustering is correlated with the average mass of the halos associated with the QSOs, providing indications of QSO lifetimes and making it possible to constrain QSO evolutionary models (Croom et al."
 2005. cla Angela et al.," 2005, da $\hat{A}$ ngela et al."
 2008)., 2008).
 ltedshift space distortions of the clustering pattern also contain dynamical information on the QSO bias that are independent of any assumption about underlving mass clustering., Redshift space distortions of the clustering pattern also contain dynamical information on the QSO bias that are independent of any assumption about underlying mass clustering.
 The clustering is allectec at. small scales. by the rms velocity dispersion of QSOs along the line-of-sight (Fingers of &od) and by clynamical infall of matter into higher density regions. which causes a Uattening of the clustering pattern in the redshift’ direction.," The clustering is affected at small scales by the rms velocity dispersion of QSOs along the line-of-sight (Fingers of god) and by dynamical infall of matter into higher density regions, which causes a flattening of the clustering pattern in the redshift direction."
 In. addition to these cdvnanmical distortions. geometrical distortions are introduced. if an incorrect. cosmological model is used. in order to convert the observed redshifts into comoving distances.," In addition to these dynamical distortions, geometrical distortions are introduced if an incorrect cosmological model is used in order to convert the observed redshifts into comoving distances."
" Phev therefore also constrain. more weakly. the value of the cosmological density parameter. ©,,,."," They therefore also constrain, more weakly, the value of the cosmological density parameter, $\Omega_m$."
 1n the lincar regime of clustering. dynamical infall is governed bv the parameter. 3OP?fb. (," In the linear regime of clustering, dynamical infall is governed by the parameter $\beta =\Omega_m^{0.6}/b$. ("
Peebles. 1980. Ixaiser 1987. Loveclay ct al.,"Peebles, 1980, Kaiser 1987, Loveday et al."
 1996. Matsubara Suto 1996. Alatsubara Szalav 2001. Peacock et al.," 1996, Matsubara Suto 1996, Matsubara Szalay 2001, Peacock et al."
 2001. Llovle οἱ al.," 2001, Hoyle et al."
 2002. Coil et al.," 2002, Coil et al."
 2005. Myers ct al.," 2005, Myers et al."
 2006. 2007. Porciani Norberg 2006. da .Angela et al.," 2006, 2007, Porciani Norberg 2006, da $\hat{A}$ ngela et al."
 2008. Ross et al.," 2008, Ross et al."
 2007)., 2007).
 La recent vears. measurements of QSO clustering (da Angela e al.," In recent years, measurements of QSO clustering (da $\hat{A}$ ngela et al."
 2008) vielded a Joso(2=L4)20.60.0H and bosols=14)=L5Xx0.2 for a combined sample of QSOs from the 201 QSO Redshift Survey (2094. Croom et al.," 2008) yielded a $\beta_{QSO}(z=1.4)=0.60_{-0.11}^{+0.14}$ and $b_{QSO}(z=1.4)=1.5\pm0.2$ for a combined sample of QSOs from the 2dF QSO Redshift Survey (2QZ, Croom et al."
 2004) anc the 2dE-SDSS LRG and QSO Survey (2SLAQ. Cannon ct al.," 2004) and the 2dF-SDSS LRG and QSO Survey (2SLAQ, Cannon et al."
 2006)., 2006).
 Ross et al. (, Ross et al. (
"2007) performed similar measurements on the 25LAQ Luminous Red Galaxies (LAGS) clustering anc founc trneds=0.55)0.45tz and 6,po(s1.66+ 0.35.",2007) performed similar measurements on the 2SLAQ Luminous Red Galaxies (LRGs) clustering and found $\beta_{LRG}(z=0.55)=0.45_{-0.05}^{+0.05}$ and $b_{LRG}(z=0.55)=1.66\pm0.35$ .
 In this paper we use QSOs from the 20Z. 28LAC arn SDSS (York et al.," In this paper we use QSOs from the 2QZ, 2SLAQ and SDSS (York et al."
 2000) Data Release 5 (015: Adclman-AleCarthy 2007) surveys anc LRGs from 25LAQ anc AAOmega first to study the dependence. of QSO-LRG clustering amplitude on QSO luminosity., 2000) Data Release 5 (DR5; Adelman-McCarthy 2007) surveys and LRGs from 2SLAQ and AAOmega first to study the dependence of QSO-LRG clustering amplitude on QSO luminosity.
 We also measure QSO-LRG redshift distortions to estimate the dynamica infall parameter. 3.," We also measure QSO-LRG redshift distortions to estimate the dynamical infall parameter, $\beta$."
 Phese surveys. provide large numbers of QSOs anc LRGs with a range of luminosities at. fixe redshifts., These surveys provide large numbers of QSOs and LRGs with a range of luminosities at fixed redshifts.
 So our results. for example on QSO bias. should be statistically improved over those from QSO-QSO clustering.," So our results, for example on QSO bias, should be statistically improved over those from QSO-QSO clustering."
 Moreover. we use photometric LRG samples. which are significantIy larger than the spectroscopic ones and measure QSO 2-D correlation function amplitudes. using Limber's formula to convert to 32D real-space measurements.," Moreover, we use photometric LRG samples, which are significantly larger than the spectroscopic ones and measure QSO 2-D correlation function amplitudes, using Limber's formula to convert to 3-D real-space measurements."
 In section 2 we deseribe the QSO anc LAGsamples we use in our measurements., In section 2 we describe the QSO and LRGsamples we use in our measurements.
" In section 3 we present results from the 2-point. cross-correlation function (6). in Sections 4 and 5 we show our results for the redshift-space Cross-correlation function. £,. and the semi-projected. cross- function. wi(m)/o. respectively."," In section 3 we present results from the 2-point cross-correlation function $\omega (\theta)$, in Sections 4 and 5 we show our results for the redshift-space cross-correlation function, $\xi
_s$, and the semi-projected cross-correlation function, $w_p(\sigma)/\sigma$ , respectively."
 Section 6 has our results for the real-space cross-correlation function and in Section 7 we present our (a.x) results. model the redshift-space distortions and estimate the QSO infall mass and bias.," Section 6 has our results for the real-space cross-correlation function and in Section 7 we present our $\xi (\sigma, \pi )$ results, model the redshift-space distortions and estimate the QSO infall mass and bias."
 We also study. in Section S. the dependence of the redshift-space cross-correlation function. the QSO bias and the mass of the QSO-LRG Dark Matter Haloes (Alois) on QSO luminosities at fixed redshifts.," We also study, in Section 8, the dependence of the redshift-space cross-correlation function, the QSO bias and the mass of the QSO-LRG Dark Matter Haloes $M_{DMH}$ ) on QSO luminosities at fixed redshifts."
 Finally. in Section 9 we present our conclusions.," Finally, in Section 9 we present our conclusions."
 Our spectroscopic LAC sample is taken [rom the 2SLAQ and consists of 8.656 LRGs within 0.35<2.=0.75 (that is the “Gold Sample’ of Ross et al. (," Our spectroscopic LRG sample is taken from the 2SLAQ and consists of 8,656 LRGs within $0.35\leq z\leq 0.75$ (that is the $`$ Gold Sample' of Ross et al. ("
2007). sce their Fig.,"2007), see their Fig."
 1 for the LRG distribution)., 1 for the LRG distribution).
 5.995 LRGs are in the Northern strip (sectors a. b. c. d. e. from Fig.," 5,995 LRGs are in the Northern strip (sectors a, b, c, d, e, from Fig."
 1 of Ross et al., 1 of Ross et al.
 2007) and 2.661 LRGs in the Southern strip (sector s).," 2007) and 2,661 LRGs in the Southern strip (sector s)."
 Our QSOs are taken from three spectroscopic samples: the NGC of 20Z. the NGC|SCC of 28LAOQ and the Data Release 5 (DR5) of SDSS.," Our QSOs are taken from three spectroscopic samples; the NGC of 2QZ, the NGC+SGC of 2SLAQ and the Data Release 5 (DR5) of SDSS."
 Phe QSO redshift range mainly used in our analysis is the same one as for the 25LAQ LRGs (0.35x2 0.75)., The QSO redshift range mainly used in our analysis is the same one as for the 2SLAQ LRGs $0.35\leq z\leq 0.75$ ).
 The 25LAQ QSOs have the same distribution on the skv as the spectroscopic 28LAC) LRGs (see Fig., The 2SLAQ QSOs have the same distribution on the sky as the spectroscopic 2SLAQ LRGs (see Fig.
 2 of da ctngelaet al., 2 of da $\hat{A}$ ngelaet al.
 2008)., 2008).
 The 20% and SDSS QSOs cover only the NGC of the 25LAO LRGs., The 2QZ and SDSS QSOs cover only the NGC of the 2SLAQ LRGs.
 The brightest of our QSO samples is from SDSS. which consists ol QSOs with higos19.1.," The brightest of our QSO samples is from SDSS, which consists of QSOs with $i_{AB}< 19.1$."
 Our 2QZ sample consists of QSOs with 18.25xby:20.85 and the 25LAQ sample of QSOs with 18.0xg21.85., Our 2QZ sample consists of QSOs with $18.25\leq b_J\leq 20.85$ and the 2SLAQ sample of QSOs with $18.0\leq g\leq 21.85$.
 After matching the QSO and spectroscopic 25LAQ LRG areas we get the numbers shown in ‘Table 1.., After matching the QSO and spectroscopic 2SLAQ LRG areas we get the numbers shown in Table \ref{Table:spec_qso}. .
 For measuring the 2-point angular eross-correlation function. (0). we can also use larger. photometric— LIt€: samples from the 28LAOand the ANOmeea surveys.," For measuring the 2-point angular cross-correlation function, $w(\theta)$ , we can also use larger, photometric LRG samples from the 2SLAQand the AAOmega surveys."
 For, For
continue to accrete until they reach the “isolation” mass. MyxALPTALay. Such à super-miassive star would presumably grow via accretion [rom a gas disc around it.,"continue to accrete until they reach the “isolation” mass, $M_{\rm i}\simeq M_d^{3/2} M_{\rm BH}^{-1/2}$, Such a super-massive star would presumably grow via accretion from a gas disc around it."
 Phe linear sizes of the disc would. be of the order of the Hill radius of the star. Hg=RGOdH/3Mpgga)7.," The linear sizes of the disc would be of the order of the Hill radius of the star, $R_{\rm H} = R (M_{\rm i}/3 M_{\rm
BH})^{1/3}$."
 The dise may become cuite massive. and fragment further.," The disc may become quite massive, and fragment further."
 In this way systems more complicated than a single massive star can be formed., In this way systems more complicated than a single massive star can be formed.
 I is not impossible that the compact star cluster 11215. which orbits uuncomfortably close. was formed in this way (MilosaylIjevié&Loeb.2004:NavakshinCuacdra.2005:Levin. 2006).," It is not impossible that the compact star cluster IRS13E, which orbits uncomfortably close, was formed in this way \citep{Milosavljevic04,NC05,Levin06}."
. We searched for such massive bound systems containing many stars in the results of our simulations., We searched for such massive bound systems containing many stars in the results of our simulations.
 While we clic find many binaries of massive stars. nothing on the scale of the isolation mass was present.," While we did find many binaries of massive stars, nothing on the scale of the isolation mass was present."
 La terms of physical ellects that could limit the growth of such groups. a too rapid disc fragmentation is the most likely one.," In terms of physical effects that could limit the growth of such groups, a too rapid disc fragmentation is the most likely one."
 Namely. for the smaller value of the cooling parameter 2. the disc fragments quickly into too many stars that then compete for the gas.," Namely, for the smaller value of the cooling parameter $\beta$, the disc fragments quickly into too many stars that then compete for the gas."
" No clear ""winners"" emerge. as can be seen from the shape of the IME. which rolls over very quickly at the higher mass end (sce Fie. 1))."," No clear “winners” emerge, as can be seen from the shape of the IMF, which rolls over very quickly at the higher mass end (see Fig. \ref{fig:imf23}) )."
 For longer cooling times. i.e... 21. disc fragmentation is less vigorous. creating fewer stars. and leading to à more op-heavy LME.," For longer cooling times, i.e., $\beta \simgt 1$, disc fragmentation is less vigorous, creating fewer stars, and leading to a more top-heavy IMF."
 In this case. while the gaseous mass is still comparable to the stellar mass in the simulations. we cid ind many binaries ancl multiple svstemis. some containing up to 6 stars.," In this case, while the gaseous mass is still comparable to the stellar mass in the simulations, we did find many binaries and multiple systems, some containing up to 6 stars."
 However. closer to the end of these simulations. when the gas supply was exhausted. only tightly bound nares remained.," However, closer to the end of these simulations, when the gas supply was exhausted, only tightly bound binaries remained."
 There seem to be two reasons for this., There seem to be two reasons for this.
" Firstly. while the svstem is still gas-rich. collisions between ""mini star clusters” take place."," Firstly, while the system is still gas-rich, collisions between “mini star clusters” take place."
 Phe collisions tend to unbind the svstems (since d1)., The collisions tend to unbind the systems (since $\beta > 1 $ ).
 A few examples of this could be seen directly in videos of the time evolution of the simulations produced from the snapshots., A few examples of this could be seen directly in videos of the time evolution of the simulations produced from the snapshots.
 Secondly. when most of the gas is exhausted. individual multiple svstems are likely to evaporate the less massive components in [favour of Πο the most massive binary.," Secondly, when most of the gas is exhausted, individual multiple systems are likely to evaporate the less massive components in favour of tightening the most massive binary."
 These results could in principle simply mean that we do not have a sullicient. time resolution to integrate small scale dynamics of stars in these mini star clusters., These results could in principle simply mean that we do not have a sufficient time resolution to integrate small scale dynamics of stars in these mini star clusters.
 To check this. we have ran an additional simulation. identical to the run $2. but in which the time step criterium was 2 times more stringent.," To check this, we have ran an additional simulation, identical to the run S2, but in which the time step criterium was 2 times more stringent."
 In this simulation. not presented in the Table l. individual particle time steps were on average half of what they were in S2.," In this simulation, not presented in the Table 1, individual particle time steps were on average half of what they were in S2."
 The result was very similar in terms of the ΙΔΗΣ (Le. the average stellar mass and the average stellar mass squared were dilferent by ~3% and. 1054 only)., The result was very similar in terms of the IMF (i.e. the average stellar mass and the average stellar mass squared were different by $\sim 3$ and $10$ only).
 However. we did [ind a ~50% increase in the number of stars with several close neighboors.," However, we did find a $\sim 50\%$ increase in the number of stars with several close neighboors."
 However. again. no group was even remotely close to the isolation mass scale.," However, again, no group was even remotely close to the isolation mass scale."
 The largest group contained. four neighboors., The largest group contained four neighboors.
 While this issue requires further numerical work. we believe that the absense of massive densely. packed stellar groups is not a numerical artelact.," While this issue requires further numerical work, we believe that the absense of massive densely packed stellar groups is not a numerical artefact."
 Nevertheless. independently of the precision with which the numerical integration is performed. the results might also strongly depend. on the gas cooling physics.," Nevertheless, independently of the precision with which the numerical integration is performed, the results might also strongly depend on the gas cooling physics."
 A more careful treatment of gas cooling physics is needed in order to test the model of in situ. formation of LRSIZSE more thoroughly., A more careful treatment of gas cooling physics is needed in order to test the model of in situ formation of IRS13E more thoroughly.
 In this paper. we presented. some of our first attempts to simulate star formation in an accretion disc around A*in the low disc mass case.," In this paper, we presented some of our first attempts to simulate star formation in an accretion disc around in the low disc mass case."
 Since the relevant. physics is only weakly dependent. on the mass of the SALBLE (Goodman. 2003).. we expect that the results are relevant to more massive SMDIIS as well.," Since the relevant physics is only weakly dependent on the mass of the SMBH \citep{Goodman03}, we expect that the results are relevant to more massive SMBHs as well."
 On the technical side. in our numerical method we used a locally constant cooling time prescription. and we allowed for a finite collapse time of stellar “List cores” and their mergers (Sections 2 and ??)).," On the technical side, in our numerical method we used a locally constant cooling time prescription, and we allowed for a finite collapse time of stellar “first cores” and their mergers (Sections \ref{sec:methods} and \ref{sec:starformation}) )."
 We limited the accretion rate of stars to a fraction of the Ededington limit., We limited the accretion rate of stars to a fraction of the Eddington limit.
 Our simulations verified that the code reproduces disc fragmentation in agreement with previous analytical and numerical work (Section ??))., Our simulations verified that the code reproduces disc fragmentation in agreement with previous analytical and numerical work (Section \ref{sec:fragm}) ).
 We also tested the dependence of the results on some of the plausible parameter choices (Section 77. and Table 1)., We also tested the dependence of the results on some of the plausible parameter choices (Section \ref{sec:sens} and Table 1).
 The scientific results of our work can be summarized as follows:, The scientific results of our work can be summarized as follows:
 (e.g.Pageetal.etal.2005).," \citep[e.g.][]{Page97,Miyaji00,Miyaji01,LaFranca02,Cowie03,
Ueda03,Fiore03,Hunt04,Cirasuolo05,HMS05}."
. ssignificant and rapid evolution in the of the distribution of host galaxy masses. which cannot be accounted for in either semi-analytical models or numerical simulations and is not consistent with a wide range of galaxy observations.," significant and rapid evolution in the of the distribution of host galaxy masses, which cannot be accounted for in either semi-analytical models or numerical simulations and is not consistent with a wide range of galaxy observations."
 Although models which adopt these simplified prescriptions for quasar evolution have had success predicting the evolution of thebright end of the QLF (e.g.Kauffmann&Haehnelt2000:Wyithe&Loeb 2003).. they do not predict the faint- slope or its evolution. and as such cannot be reliably extrapolated to low luminosities or to redshifts where the slope is undetermined.," Although models which adopt these simplified prescriptions for quasar evolution have had success predicting the evolution of the end of the QLF \citep[e.g.][]{KH00,WL03}, they do not predict the faint-end slope or its evolution, and as such cannot be reliably extrapolated to low luminosities or to redshifts where the slope is undetermined."
 Observations of the high-redshift. faint end quasar luminosity function slope are highly uncertain. d no large. uniformly selected samples yet exist which measure the faint-end slope at both low (zX 1) and high (zz 3) redshifts. and therefore theoretical models of the faint-end slope are especially important.," Observations of the high-redshift, faint end quasar luminosity function slope are highly uncertain, and no large, uniformly selected samples yet exist which measure the faint-end slope at both low $z\lesssim1$ ) and high $z\gtrsim3$ ) redshifts, and therefore theoretical models of the faint-end slope are especially important."
 This high-z. faint-end slope is a critical quantity in determining the early formation history of black holes and. especially. their contribution. to reionization. as well as possible connections between quasars and tthe low-luminosity Seyferts seen at z~0.," This $z$, faint-end slope is a critical quantity in determining the early formation history of black holes and, especially, their contribution to reionization, as well as possible connections between quasars and the low-luminosity Seyferts seen at $z\sim0$."
 Without a more sophisticated model of quasar evolution. models which have attempted to reconcile observations of evolution in the faint-end QLF slope and BH populations (e.g..Merloni2004) have been forced to fit to the entire QLF and BH mass distribution to essentially arbitrary distributions of lifetimes/duty cycles and aceretion rates as a function. of redshift.," Without a more sophisticated model of quasar evolution, models which have attempted to reconcile observations of evolution in the faint-end QLF slope and BH populations \citep[e.g.,][]{Merloni04} have been forced to fit to the entire QLF and BH mass distribution to essentially arbitrary distributions of lifetimes/duty cycles and accretion rates as a function of redshift."
 Still. this phenomenological modeling has elucidated the anti-hierarchical. nature of BH growth. with smaller-mass BHs formed at lower redshift as an implication of this evolution in the QLF.," Still, this phenomenological modeling has elucidated the anti-hierarchical nature of BH growth, with smaller-mass BHs formed at lower redshift as an implication of this evolution in the QLF."
 But an actual prediction of the faint-end slope requires a more detailed model for both quasar lifetimes, But an actual prediction of the faint-end slope requires a more detailed model for both quasar lifetimes
"At rotation rates ~5 times faster than required for saturation it appears that coronal activity turns down again — a phenomenon dubbed ""super-saturation"" (Prosser et al.",At rotation rates $\sim 5$ times faster than required for saturation it appears that coronal activity turns down again – a phenomenon dubbed “super-saturation” (Prosser et al.
 1996)., 1996).
" Examples of super-saturated G- and K-stars. with L,/Liac10.77. have been found in a number of young open clusters (Stauffer et al."," Examples of super-saturated G- and K-stars, with $L_x/L_{\rm bol} \simeq 10^{-3.5}$, have been found in a number of young open clusters (Stauffer et al."
 1994. 1997: Patten Simon 1996: Randich 1998: Jeffries et al.," 1994, 1997; Patten Simon 1996; Randich 1998; Jeffries et al."
 2006). among the fast rotating components of contact W UMa binaries (Cruddace Dupree 1984: Steppien.. Schmitt Voges 2001) and has been suggested as the reason for lower X-ray activity in the fastest rotating. very young pre main-sequence stars (Stassun et al.," 2006), among the fast rotating components of contact W UMa binaries (Cruddace Dupree 1984; Stȩppień,, Schmitt Voges 2001) and has been suggested as the reason for lower X-ray activity in the fastest rotating, very young pre main-sequence stars (Stassun et al."
 2004: Preibisch et al., 2004; Preibisch et al.
 2005: Dahm et al., 2005; Dahm et al.
 2007)., 2007).
 Possible explanations for coronal super-saturation include negative feedback in the dynamo (Kitchatinov. Rüddiger Kükker 1994). decreasing coverage by active regions (Steppien et al.," Possible explanations for coronal super-saturation include negative feedback in the dynamo (Kitchatinov, Rüddiger Kükker 1994), decreasing coverage by active regions (Stȩppień et al."
 2001). reorganisation of the coronal magnetic field (Solanki et al.," 2001), reorganisation of the coronal magnetic field (Solanki et al."
 1997) or centrifugal stripping of the corona (Jardine 2004)., 1997) or centrifugal stripping of the corona (Jardine 2004).
 An important test of these ideas is to look at the coronal properties of fast rotators across a wide range of masses., An important test of these ideas is to look at the coronal properties of fast rotators across a wide range of masses.
 In particular. if is vital to gauge whether saturation and super-saturation occur at fixed values of rotation period or Rossby number.," In particular, it is vital to gauge whether saturation and super-saturation occur at fixed values of rotation period or Rossby number."
 This would illuminate which physical mechanisms are responsible., This would illuminate which physical mechanisms are responsible.
 One of the principal gaps in our knowledge is the behaviour of coronal emission for ultra-fast rotating M-dwarfs., One of the principal gaps in our knowledge is the behaviour of coronal emission for ultra-fast rotating M-dwarfs.
 These have larger convection zones (as a fraction of the star). longer convective turnover times and hence smaller Rossby numbers at a given rotation period than G- and K-dwarfs.," These have larger convection zones (as a fraction of the star), longer convective turnover times and hence smaller Rossby numbers at a given rotation period than G- and K-dwarfs."
 Of course M-dwarfs also have much lower bolometric luminosities than G- or K-dwarfs and so. at a given magnetic activity level. they are harder to observe in the young open clusters where the majority of ultra-fast rotators are found.," Of course M-dwarfs also have much lower bolometric luminosities than G- or K-dwarfs and so, at a given magnetic activity level, they are harder to observe in the young open clusters where the majority of ultra-fast rotators are found."
 The most comprehensive work so far was by James et al. (, The most comprehensive work so far was by James et al. (
2000) using X-ray observations for a small. inhomogeneous sample of fast rotating low-mass stars from the field and open clusters.,"2000) using X-ray observations for a small, inhomogeneous sample of fast rotating low-mass stars from the field and open clusters."
 They found that. like G- and K-type stars. M-dwarfs with periods below ~6 days and Rossby numbers below 0.1 showed saturated levels of X-ray emission with Lyπωc10.7.," They found that, like G- and K-type stars, M-dwarfs with periods below $\sim 6$ days and Rossby numbers below 0.1 showed saturated levels of X-ray emission with $L_x/L_{\rm bol} \simeq
10^{-3}$."
 They also claimed tentative evidence for super-saturation in the fastest rotating M-dwarfs. with periods of 0.2-0.3 days.," They also claimed tentative evidence for super-saturation in the fastest rotating M-dwarfs, with periods of 0.2–0.3 days."
 In this paper we re-visit the question of saturation. and super-saturation of coronal emission in fast-rotating. M-dwarfs., In this paper we re-visit the question of saturation and super-saturation of coronal emission in fast-rotating M-dwarfs.
 We analyse new. deep observations of a. large. homogeneous sample of rapidly rotating M-dwarfs identified in the open cluster NGC 2547 by Irwin et al. (," We analyse new, deep observations of a large, homogeneous sample of rapidly rotating M-dwarfs identified in the open cluster NGC 2547 by Irwin et al. ("
2008).,2008).
 NGC 2547 has an age of MMyr (Jeffries Oliveira 2005: Naylor Jeffries 2006) and a rich population of low-mass stars (Jeffries et al., NGC 2547 has an age of Myr (Jeffries Oliveira 2005; Naylor Jeffries 2006) and a rich population of low-mass stars (Jeffries et al.
 2004)., 2004).
 However. the cluster is at at 400 ppe. and while previous observations withROSAT (Jeffries Tolley 1998) andNewton (Jeffries et al.," However, the cluster is at at $\sim 400$ pc, and while previous X-ray observations with (Jeffries Tolley 1998) and (Jeffries et al."
 2006) demonstrated an X-ray active low- population. they were insufficiently sensitive to probe the coronal activity of its M-dwarfs in any detail.," 2006) demonstrated an X-ray active low-mass population, they were insufficiently sensitive to probe the coronal activity of its M-dwarfs in any detail."
 In section 2 we describe the new observations of NGC 2547 and the identification of X-ray sources with rapidly rotating M-dwarts from the Irwin et al. (, In section 2 we describe the new observations of NGC 2547 and the identification of X-ray sources with rapidly rotating M-dwarfs from the Irwin et al. (
2008) catalogue.,2008) catalogue.
 In section 3 we combine X-ray and optical data. estimate coronal activity levels and examine the evidence for coronal saturation and super-saturation using a homogeneous sample of fast rotating M-dwarfs several times larger than considered by James et al. (," In section 3 we combine X-ray and optical data, estimate coronal activity levels and examine the evidence for coronal saturation and super-saturation using a homogeneous sample of fast rotating M-dwarfs several times larger than considered by James et al. ("
2000).,2000).
 In section + we compare our results to those compiled in the literature for G- and K-stars and for other samples of M-dwarfs., In section 4 we compare our results to those compiled in the literature for G- and K-stars and for other samples of M-dwarfs.
 In section 5 we discuss our results in the context of competing models for saturation/super-saturation and our conclusions are summarised in section 6., In section 5 we discuss our results in the context of competing models for saturation/super-saturation and our conclusions are summarised in section 6.
 NGC 2547 was observed with between UT 22:30:03 on 12 November 2007 and UT 09:30:03 on 14 November 2007 using the European Photon Imaging Counter (EPIC) instrument. for a nominal exposure time of Kks (Observation. ID 0501790101).," NGC 2547 was observed with between UT 22:30:03 on 12 November 2007 and UT 09:30:03 on 14 November 2007 using the European Photon Imaging Counter (EPIC) instrument, for a nominal exposure time of ks (Observation ID 0501790101)."
 The two EPIC-MOS cameras and the EPIC-PN camera were operated in full frame mode (Turner et al., The two EPIC-MOS cameras and the EPIC-PN camera were operated in full frame mode (Turner et al.
 2001: Strüdder et al., 2001; Strüdder et al.
 2001). using the medium filter to reject optical light.," 2001), using the medium filter to reject optical light."
 The nominal pointing position of the observation was δή 006.15. Dec—49d 442.98 (J2000.03.," The nominal pointing position of the observation was $=08$ 06.1s, $=-49$ 42.9s (J2000.0)."
 Version 7.1 of the Science Analysis System was used for the initial data reduction and source detection., Version 7.1 of the Science Analysis System was used for the initial data reduction and source detection.
 Data from the three cameras were individually screened for high background periods and these time intervals were excluded from all subsequent analysis., Data from the three cameras were individually screened for high background periods and these time intervals were excluded from all subsequent analysis.
 Observation intervals were excluded where the total count rate for events with energies >LOkkeV. exceeded + and ! for the MOS and PN detectors respectively.," Observation intervals were excluded where the total count rate for events with energies $>10$ keV, exceeded $^{-1}$ and $^{-1}$ for the MOS and PN detectors respectively."
 The remaining useful exposure times were kks. ΚΚς and Kkks for the MOSI. MOS? and PN cameras respectively. which can be compared with the equivalent exposure times of KKs. kks and KKs in the less sensitive observation analysed by Jeffries et al. (," The remaining useful exposure times were ks, ks and ks for the MOS1, MOS2 and PN cameras respectively, which can be compared with the equivalent exposure times of ks, ks and ks in the less sensitive observation analysed by Jeffries et al. ("
2006).,2006).
 Images were created using theEVSELECT task and a spatial sampling of 2 areseconds per pixel., Images were created using the task and a spatial sampling of 2 arcseconds per pixel.
" The event lists were filtered to exclude anomalous pixel patterns and edge effects by including only those events with ""pattern""x:12 for the MOS detectors and 4 for the PN detectors.", The event lists were filtered to exclude anomalous pixel patterns and edge effects by including only those events with $\leq 12$ for the MOS detectors and $\leq 4$ for the PN detectors.
" The contrast between background and source events was also increased by retaining only those events in channels corresponding to energies of kkeV. The task was used to find sources with a combined maximum log likelihood value greater than 10 (approximately equivalent to lop. where p is the probability hat the ""source"" is due to a background fluctuation). in all three instruments combined. over the 0.3-3kkeV energy range."," The contrast between background and source events was also increased by retaining only those events in channels corresponding to energies of keV. The task was used to find sources with a combined maximum log likelihood value greater than 10 (approximately equivalent to $-\ln p$, where $p$ is the probability that the “source” is due to a background fluctuation), in all three instruments combined, over the keV energy range."
 We expect 1-2 spurious X-ray detections at this level of significance. hough they would be highly unlikely to correlate with NGC 2547 members. so will not hamper any analysis in this paper.," We expect 1-2 spurious X-ray detections at this level of significance, though they would be highly unlikely to correlate with NGC 2547 members, so will not hamper any analysis in this paper."
 The individual images from each instrument were source-searched first o confirm there were no systematic differences in the astrometry of he brightest sources., The individual images from each instrument were source-searched first to confirm there were no systematic differences in the astrometry of the brightest sources.
 Count rates in each detector were determined using vignetting-corrected exposure maps created within the same ask., Count rates in each detector were determined using vignetting-corrected exposure maps created within the same task.
 In addition. count rates were determined for each source in the KkeV and kkeV bands separately. in order to form a yardness ratio.," In addition, count rates were determined for each source in the keV and keV bands separately, in order to form a hardness ratio."
 A total of 323 significant X-ray sources were found., A total of 323 significant X-ray sources were found.
 Some of these only have count rates measured in a subset of the hree instruments because they fell in gaps between detectors. on wt pixels or lay outside the field of view.," Some of these only have count rates measured in a subset of the three instruments because they fell in gaps between detectors, on hot pixels or lay outside the field of view."
 In addition we decided only to retain count rates for analysis if they had a signal-to-noise ratio greater than 3. which resulted in the removal of three sources Tom our list.," In addition we decided only to retain count rates for analysis if they had a signal-to-noise ratio greater than 3, which resulted in the removal of three sources from our list."
 To check the EPIC astrometric solution. we cross-correlated all the brightest X-rays sources (those detected with a maximum og likelihood greater than 100) against a list of photometrically selected NGC 2547 members compiled by Naylor et al. (," To check the EPIC astrometric solution, we cross-correlated all the brightest X-rays sources (those detected with a maximum log likelihood greater than 100) against a list of photometrically selected NGC 2547 members compiled by Naylor et al. ("
2002 — their Table 6). which is based on D'Antona Mazzitelli (1997) isochrones and 1{ photometry. and which incorporates bright cluster members from Clariá (1982).,"2002 -- their Table 6), which is based on D'Antona Mazzitelli (1997) isochrones and $BVI$ photometry, and which incorporates bright cluster members from Clariá (1982)."
 Therewere 98 correlations found within 6 arcseconds of the nominal X-ray position and, Therewere 98 correlations found within 6 arcseconds of the nominal X-ray position and
«λαο than what is expected from strong cascading.,smaller than what is expected from strong cascading.
 As to PBOO prediction. it is inconsistent with data for all degrees of iubalauce including those with small nubalauce and normal viscosity. ie. TL aud 10.," As to PB09 prediction, it is inconsistent with data for all degrees of imbalance including those with small imbalance and normal viscosity, i.e. I1 and I3."
" Most of the attention of the theory has been directed. towards the sclfsimilay (or approximately selfsimular) reguue between dissipation aud driving which is colloquially known as “inertial range"" (IAolhnnuogorov. 1911)."," Most of the attention of the theory has been directed towards the self-similar (or approximately self-similar) regime between dissipation and driving which is colloquially known as “inertial range” (Kolmogorov, 1941)."
 Although attempts to study this regime started long time ago. it it uot ΠΠ 2roceuthy when sinuulatious with resolution higher than256° ion µαςbecome conuuonplace.," Although attempts to study this regime started long time ago, it it not until recently when simulations with resolution higher than $256^3$ has become commonplace."
 At this point the juterpretat of uunerical simulations of AIIID turbulence has been strongly affected by experieuce obtained from lydrodvuamic simulations., At this point the interpretation of numerical simulations of MHD turbulence has been strongly affected by experience obtained from hydrodynamic simulations.
 Tn hwdrodyniuulcs. the correspondence with Kohuogorov slope has been fairly— for —about a decade. even though the same sumnnulatious produced Iohuosorov coustauts which were close to what has been observed carlicr in experiments.," In hydrodynamics, the correspondence with Kolmogorov slope has been fairly for about a decade, even though the same simulations produced Kolmogorov constants which were close to what has been observed earlier in experiments."
" The fact that such correspoudenuce has been found in simulations with relatively sinall. less than a thousand. Reynolds ΠΙΟΣ, demonstrated that lycvodvuamic turbulence is fairly local aud iu order to reproduce asvuiptotie cascading oulv a few steps iu log-k space is necessary."," The fact that such correspondence has been found in simulations with relatively small, less than a thousand, Reynolds numbers, demonstrated that hydrodynamic turbulence is fairly local and in order to reproduce asymptotic cascading only a few steps in log-k space is necessary."
 The cucrey slopes. however. were affected by the bottleneck effect.," The energy slopes, however, were affected by the bottleneck effect."
" Tn MIID turbulence. the observed flat (power-law) energv spectra bas been prematurely interpreted as ""Uóuertial range."," In MHD turbulence, the observed flat (power-law) energy spectra has been prematurely interpreted as “inertial range”."
 Towever. as it turued out. the fat spectra of MIID turbulence is an indication of aJack of a good inertial range. rather than ifs presence.," However, as it turned out, the flat spectra of MHD turbulence is an indication of a of a good inertial range, rather than its presence."
 ludeed. im simmlations with hwperdiffusion we compared lydrodvnamic and MIID slopes and found that while lydrodvnamic energy spectra are highly distorted by bottleneck effect. the MIID spectra stav very flat (see Fie. 2)).," Indeed, in simulations with hyperdiffusion we compared hydrodynamic and MHD slopes and found that while hydrodynamic energy spectra are highly distorted by bottleneck effect, the MHD spectra stay very flat (see Fig. \ref{bottle}) )."
 As it is not known a-priorv what is the coutribution of theerror of the spectral slope measurement that comes from bottleneck effect. it is therefore iupossible to measure true asviuptotic slopes directly.," As it is not known a-priory what is the contribution of the of the spectral slope measurement that comes from bottleneck effect, it is therefore impossible to measure true asymptotic slopes directly."
 Also. if is incorrect to claim that bottleneck effect is absent in sinulations with secoud-order (natural) viscosity. as the existence of the effect was clearly demonstrated in nmunercal simulations (Ixaneda," Also, it is incorrect to claim that bottleneck effect is absent in simulations with second-order (natural) viscosity, as the existence of the effect was clearly demonstrated in numerical simulations \citep{kaneda}."
etal., Fig.
2003).. Fig. 2 shows a comparison between hydrodvuamic aud MIID energy slopes i 512° simulations., \ref{bottle} shows a comparison between hydrodynamic and MHD energy slopes in $512^3$ simulations.
 As we sec. the spectra show a variety of bottleneck effects. depending ou the order of viscosity aud type of simulation. (MIID or hydro).," As we see, the spectra show a variety of bottleneck effects, depending on the order of viscosity and type of simulation (MHD or hydro)."
" Also. there are two tvpes of spectrum. £y and P, (see BLOOD) aud while £) is used in most. nmuuerical vapors. it is DX. a Fourier transform: of the structure Anetion which is directly predicted frou, IKolinogorov uodel."," Also, there are two types of spectrum, $E_k$ and $P_k$ (see BL09b) and while $E_k$ is used in most numerical papers, it is $P_k$, a Fourier transform of the structure function which is directly predicted from Kolmogorov model."
 While in the asviuptotic regine of exact aw scaling. D aud Ey has the same slope. iu a realistic Munerical simulation they differ quite a lot.," While in the asymptotic regime of exact power-law scaling, $P_k$ and $E_k$ has the same slope, in a realistic numerical simulation they differ quite a lot."
 From Fig., From Fig.
 2 it is not imunecdiately obvious that MIID slopes are shallower than livdro slopes., \ref{bottle} it is not immediately obvious that MHD slopes are shallower than hydro slopes.
 Most of the publicatious that uade aforementioned claim had performed onlv MIID sinuulations and compared MIID slope with asvuiptotic Iohuogorov slope. ie. 5/3.," Most of the publications that made aforementioned claim had performed only MHD simulations and compared MHD slope with asymptotic Kolmogorov slope, i.e. $-5/3$."
 Our study BLOOD reported that MIID turbulence is ess local than lycrodvuamic turbulence., Our study BL09b reported that MHD turbulence is less local than hydrodynamic turbulence.
 This is clearly demonstrated by a) the lack of visible bottleneck effect in MIID turbulence. while it was clearly present in lydire urbuleuce (Fig. 2)).," This is clearly demonstrated by a) the lack of visible bottleneck effect in MHD turbulence, while it was clearly present in hydro turbulence (Fig. \ref{bottle}) ),"
 b) the dependence of kinetic and uagnetie spectra on driving., b) the dependence of kinetic and magnetic spectra on driving.
 Iudecd. in case with Elsasser driving magnetic cucrey donates bv (see Fie. 3)).," Indeed, in case with Elsasser driving magnetic energy dominates by (see Fig. \ref{2048}) ),"
 while for velocity driving this is not the case., while for velocity driving this is not the case.
" An analytical bound for noulocalitv can be obtained hrough Πόσο"" inequality aud scalings of the turbulent fields (Απο&Eivuk2009).", An analytical bound for nonlocality can be obtained through Höllger inequality and scalings of the turbulent fields \citep{eyink09}.
 This bound is shown ou Fie. L., This bound is shown on Fig. \ref{nonlocality}.
 From practical viewpoint. however. this bouud does not set a strict constraint on the “width” of the enerev transter window. (ο4). which describe the enerev transfer between wavevectors Ay and À&. as the πιαπαν οποιο transfer at Aj could still be much lower that the estinate provided by Πόσο inequality.," From practical viewpoint, however, this bound does not set a strict constraint on the “width” of the energy transfer window, $T(k_0,k)$, which describe the energy transfer between wavevectors $k_0$ and $k$, as the maximally efficient transfer at $k_0$ could still be much lower that the estimate provided by Höllger inequality."
" We conclude that. from practical staudpoiut. MIID turbulence can stillbe ""diffuse local” ie. less local thai livdrodyuamic turbulence despite this analytical bound."," We conclude that, from practical standpoint, MHD turbulence can still be “diffuse local” i.e. less local than hydrodynamic turbulence despite this analytical bound."
 Although in this short paper we mostly relied on robust quantities. such as total energies and dissipation rates. we believe that πιοΊσα. simmlations have a wealth of data to be analyzed by theorists.," Although in this short paper we mostly relied on robust quantities, such as total energies and dissipation rates, we believe that numerical simulations have a wealth of data to be analyzed by theorists."
 Oue of the most important nieasures not mentioned in this paper is the anisotropy of ATID turbulence., One of the most important measures not mentioned in this paper is the anisotropy of MHD turbulence.
 It had been cousidered in ereat detail iu our earlier publication BLOOa., It had been considered in great detail in our earlier publication BL09a.
 Iu particular. we refer the," In particular, we refer the"
 , 
show Fe line 19]..,show complicated Fe line profiles \cite{Ueda98}.
 Jo interpret them as due to a single reflection. complicatedabsorption. or profilescisk-line component is dillieult. but Ueda et al.," To interpret them as due to a single reflection, absorption, or disk-line component is difficult, but Ueda et al."
 that the features near 7 keV seen in Japanese satellite ASCA 19].data are suggestdue to by He-like anc LH-like iron ions in an hot plasma.," \cite{Ueda98} suggest that the features near 7 keV seen in Japanese satellite ASCA data are due to absorption by He-like and H-like iron ions in an anisotropic, hot plasma."
 Such a absorption may be similar to that forming the hot ion anisotropic.torus in AGN., Such a plasma may be similar to that forming the hot ion torus in AGN.
 The second plasmashared. property of the superluminal sources is the steep. law spectral shape in the hard. X-ray/ rav regime (see Fig.," The second shared property of the superluminal sources is the steep, power law spectral shape in the hard X-ray/gamma ray regime (see Fig."
 4)., 4).
 powerPhoton number indices in the 20-200 keV. gammaband [rom 2.5 to 3.5. with slopes that do not seem to change rangedrastically or to be spectralcorrelated with luminosity as in other appear," Photon number indices in the 20-200 keV band range from $-$ 2.5 to $-$ 3.5, with spectral slopes that do not seem to change drastically or appear to be strongly correlated with luminosity as in other black hole candidates."
 OSSIZ has strongly from 1655-40 to blackτοῦ holekeV with no candidates.evidence of a cutoll observed Phis, OSSE has observed emission from GRO J1655-40 to 700 keV with no evidence of a cutoff \cite{Grov98}.
 emissionsuggests à GIOnonthermal origin for the emission: however. better statistics20].. are required for confirmation.," This suggests a nonthermal origin for the emission; however, better statistics are required for confirmation."
 The broadband spectral of the superluminal sources is usually associated with the high or shape states of BUC where the mass accretion rate may. reach near-ISddingtonultrahigh luminosities., The broadband spectral shape of the superluminal sources is usually associated with the high or ultrahigh states of BHC where the mass accretion rate may reach near-Eddington luminosities.
 The steep law shape can result from Comptonization of a nonthermal electron distributionpower such as might be encountered. inside the last stable orbit. (racial. bulk motion) around the black hole 21] This model has been used successfully tolit spectra for GRO 1655-40 and GRS 1915|105., The steep power law shape can result from Comptonization of a nonthermal electron distribution such as might be encountered inside the last stable orbit (radial bulk motion) around the black hole \cite{Chak95} This model has been used successfully \cite{Shra98} to fit spectra for GRO J1655-40 and GRS 1915+105.
 Phe Comptonization model22] must have a οὐ{ο and cannot emission above a few hundred keV. We highpoint energyout that a number of DIIC'. explainwhich apparently do not exhibit also have this energy. spectral e... Nova Aluscae. GRS jets.1000-45. and 4U 1543-47.high (," The Comptonization model must have a high energy cutoff, and cannot explain emission above a few hundred keV. We point out that a number of BHC, which apparently do not exhibit jets, also have this high energy spectral shape, e.g., Nova Muscae, GRS 1009-45, and 4U 1543-47. ("
See Fig.,See Fig.
 4)., 4).
 This shape.may be an observational bias. due to incompleteness in historical coverage of their outbursts in raclio/infrarecl bands.," This may be an observational bias, due to incompleteness in historical coverage of their outbursts in radio/infrared bands."
that equal the binding cuerey of all baryous in the halo.,that equal the binding energy of all baryons in the halo.
 This should provide au upper limit to the nunber of ionisius photous produced by shocks (itheabseuceofsieuificautfeedback.Miniatietal. 2001)... aud lence au upper Inuuit ou the contribution of shocks to reionization.," This should provide an upper limit to the number of ionising photons produced by shocks \citep[in the absence of significant feedback,][]{Miniati2004}, and hence an upper limit on the contribution of shocks to reionization."
 For this calculation. we again appeal to equation (3)). setting NV. to be Results ire shown iu the lower-left panel of Figure 1 assundue ΕΕ halo masses corresponding to eg=10dansHÀ aud eg=30hans!.," For this calculation, we again appeal to equation \ref{fcol}) ), setting $N_\gamma$ to be Results are shown in the lower-left panel of Figure \ref{plot1}
 assuming minimum halo masses corresponding to $v_{\rm vir}=10~{\rm
km~s^{-1}}$ and $v_{\rm vir}=30~{\rm km~s^{-1}}$."
 We find that the total eravitational energv available for ionisatiou of hydrogen corresponds to less than 1 ionising photon per 3 hydrogeus by 26 and less than 1 ionising photon per LO hvdrogeus by i8., We find that the total gravitational energy available for ionisation of hydrogen corresponds to less than 1 ionising photon per 3 hydrogens by $z\sim6$ and less than 1 ionising photon per 10 hydrogens by $z\sim8$.
 Next wo use the estimate of flux based ou our merger calculation of jonising radiation from shocks asthe source terii ina calculation of the reionizatiou history., Next we use the estimate of flux based on our merger calculation of ionising radiation from shocks asthe source term in a calculation of the reionization history.
 Miralda-Escudéetal.(2000) presented a model which allows the calculation of an effective recombination- rate iu an inhomogencous universe by assuning a naxinmn overdensity X.) peuctrated by ioniziug photous within ΠΠ τοσο”.," \citet[][]{Miralda2000} presented a model which allows the calculation of an effective recombination rate in an inhomogeneous universe by assuming a maximum overdensity $\Delta_{\rm
c}$ ) penetrated by ionizing photons within HII regions."
 The iodel assumues that reionization xoeresses rapidly through islands of lower density prior o the overlap ofindividual cosmological ionized regions., The model assumes that reionization progresses rapidly through islands of lower density prior to the overlap of individual cosmological ionized regions.
 Following the overlap epoch. the remaining regions of Heh density are eracually ionized.," Following the overlap epoch, the remaining regions of high density are gradually ionized."
 Writhe&Loch(2003) e1iploved this prescription within a semi-analvtie uodel of reionization. aud we refer the reader to that oper for details of the model.," \citet[][]{Wyithe2003} employed this prescription within a semi-analytic model of reionization, and we refer the reader to that paper for details of the model."
 Within this forinalizin. he epoch of overlap is precisely defined as the time when the volue fraction Q of the universe ionized up o an overdensity Ac. reaches unity.," Within this formalism, the epoch of overlap is precisely defined as the time when the volume fraction $Q$ of the universe ionized up to an overdensity $\Delta_{\rm c}$, reaches unity."
 After the overlap epoch. ionizing plotous will experience attenuation due ο residual overdense pockets of TT gas.," After the overlap epoch, ionizing photons will experience attenuation due to residual overdense pockets of HI gas."
 The model also ollows the mass averaged ionized fraction (μι)., The model also follows the mass averaged ionized fraction $Q_{\rm m}$ ).
 Fiewre 2 shows the resulting moclel for the reiouization of the IGAL and the subsequent post-overlap evolution due to ionising sources from fast accretion shocks (solid lines)., Figure \ref{plot2} shows the resulting model for the reionization of the IGM and the subsequent post-overlap evolution due to ionising sources from fast accretion shocks (solid lines).
 Ποσο we have used au ionising photon rate based on equation (1))., Here we have used an ionising photon rate based on equation \ref{merge}) ).
" The case shown corresponds to a value for the critical overdensity prior to the overlap epoch of A,—5. and both the volume averaged (dark lines) and imass-averaged (στον lines) jonisation fractions are shown."," The case shown corresponds to a value for the critical overdensity prior to the overlap epoch of $\Delta_{\rm c}=5$, and both the volume averaged (dark lines) and mass-averaged (grey lines) ionisation fractions are shown."
 We find that shocks can reionize less than of the ICM (by volume or mass} prior to z~6. and caunot coniplete reiouization until ;~ 3.," We find that shocks can reionize less than of the IGM (by volume or mass) prior to $z\sim6$, and cannot complete reionization until $z\sim3$ ."
 For comparison we conipute the reionization historv for stars (dashed lines). where the ionisng photon production rate is based on din.éng)di. with nefry based on equation (3)) with NS=15.," For comparison we compute the reionization history for stars (dashed lines), where the ionising photon production rate is based on $d(n_\gamma /n_{\rm H})/dz$, with $n_\gamma /n_{\rm H}$ based on equation \ref{fcol}) ) with $N_\gamma=15$."
 Iu this model. stars complete reionization by τον Sat which tune the relative coutributious from stars aud fast accretion shocks differ by a factor in excess of 100.," In this model, stars complete reionization by $z\sim8$, at which time the relative contributions from stars and fast accretion shocks differ by a factor in excess of 100."
 Iu thisLetter we have cemoustrated that recent estimates of the ionising huuinositv from fast accretion shocks associated with galaxy formation are not sufficient o drive reionization., In this we have demonstrated that recent estimates of the ionising luminosity from fast accretion shocks associated with galaxy formation are not sufficient to drive reionization.
 Ποπονο the ionising photons xoduced. by shocks are dominated by massive halos (Miniatictal.200L:Dopita2011).," However the ionising photons produced by shocks are dominated by massive halos \citep[][]{Miniati2004,Dopita2011}."
 This is in contrast to the jiouisine radiation from stars. which is both predicted and observed to be dominated by OW lnass galaxies.," This is in contrast to the ionising radiation from stars, which is both predicted and observed to be dominated by low mass galaxies."
 As a result. tle ionising radiation xoduced im shocks is siguificautlv more biased relative o the nuderlving large scale deusitv of the IGAL than are ionisiue photons produced in galaxies.," As a result, the ionising radiation produced in shocks is significantly more biased relative to the underlying large scale density of the IGM than are ionising photons produced in galaxies."
 It is easv to see he physics of the dominance of massive halos by notius hat the collapse energv available iu equation (6)) is xoportional to e (or MEA. whereas the stellar mass (αμας a constant mass-to-lelt ratio) is proportional ο ex (or Mg).," It is easy to see the physics of the dominance of massive halos by noting that the collapse energy available in equation \ref{binding}) ) is proportional to $v_{\rm vir}^6$ (or $M_{\rm halo}^{2}$ ), whereas the stellar mass (assuming a constant mass-to-light ratio) is proportional to $v_{\rm vir}^3$ (or $M_{\rm halo}$ )."
 The ionisatiou structure of the ICAL particularly the scale of TOT regions produced is a sensitive function of the bias of ionising sources (MeQuinuuetal.2007).," The ionisation structure of the IGM, particularly the scale of HII regions produced is a sensitive function of the bias of ionising sources \citep[][]{McQuinn2007}."
. It is this relation between the bias of ionising sources and the resulting ionisation structure during reionization that motivates redshifted. 2101 experiueuts with the ultimate aim of connecting ealaxy propertics to the power-spectrum of 21010. fluctuations. (Barkana 2009).., It is this relation between the bias of ionising sources and the resulting ionisation structure during reionization that motivates redshifted 21cm experiments with the ultimate aim of connecting galaxy properties to the power-spectrum of 21cm fluctuations \citep{Barkana2009}. .
 ere we quautify the effect of fast accretion shocks ou the bias of ionising sources., Here we quantify the effect of fast accretion shocks on the bias of ionising sources.
 The halo bias 5 for a halo mass AL at redshift 2 may be approximated using the Press&Schechter(1971). formalisi.modified to include non-spherical collapse (Shethetal.2001).," The halo bias $b$ for a halo mass $M$ at redshift $z$ may be approximated using the \citet[][]{press1974} formalism,modified to include non-spherical collapse \citep[][]{Sheth2001}."
. The power-spectima of the space distribution of sources is proportional to 5 squared., The power-spectrum of the space distribution of sources is proportional to $b$ squared.
 The luminosity weighted bias of ionisiug vacation produced bv shocks arising im merecrs can be evaluated using the expressionwhere the bias 5 is evaluated at a mass Af;| Ab., The luminosity weighted bias of ionising radiation produced by shocks arising in mergers can be evaluated using the expressionwhere the bias $b$ is evaluated at a mass $M_1+M_2$ .
 The resulting bias is plotted as a function of redshift in the upperpanel of Figure 3.., The resulting bias is plotted as a function of redshift in the upperpanel of Figure \ref{plot3}. .
 Prior to reiouization.," Prior to reionization,"
the orbital parameters and the internal dynamical properties of the systems (e.g.. Mihos 1992: Mihos IHlernquist. 1994. 1996: Barnes Llernquist. 1996).,"the orbital parameters and the internal dynamical properties of the systems (e.g., Mihos 1992; Mihos Hernquist 1994, 1996; Barnes Hernquist 1996)."
 Lt is. well known that ealaxies dominated by a central stellar component are more stable against tidal torques., It is well known that galaxies dominated by a central stellar component are more stable against tidal torques.
 In this case. tidal interactions are less ellicient in inducing star formation during the orbital decay phase (Binney ‘Tremaine LOST).," In this case, tidal interactions are less efficient in inducing star formation during the orbital decay phase (Binney Tremaine 1987)."
 By using cosmological simulations. Tissera et al. (," By using cosmological simulations, Tissera et al. ("
2002) found. that the response of a galactic system to tidal interactions varies along it evolutionary history. expected to be stronger at carly stages of evolution when the systems have internal properties not suitable for providing stability.,"2002) found that the response of a galactic system to tidal interactions varies along it evolutionary history, expected to be stronger at early stages of evolution when the systems have internal properties not suitable for providing stability."
 On the other hand. it is well known that galaxies in eroups and clusters have significantly reduced star formation with respect to those in the field and that. the star formation activity depends on the distance to the centre (Martínnez et al.," On the other hand, it is well known that galaxies in groups and clusters have significantly reduced star formation with respect to those in the field and that, the star formation activity depends on the distance to the centre nez et al."
 2002: Domínnguez et al., 2002; nguez et al.
 2002)., 2002).
 However. it ds stil uncertain how relevant the global environment is in the regulation of the star formation in galaxies.," However, it is still uncertain how relevant the global environment is in the regulation of the star formation in galaxies."
 Loveday. Tresse Maddox. (1999). found. that galaxies with prominen emission-lines display weaker clustering than more quicscen galaxies.," Loveday, Tresse Maddox (1999) found that galaxies with prominent emission-lines display weaker clustering than more quiescent galaxies."
 Tegmark Bromiley (1999) also found tha carly spectral types are more strongly clustered than late spectral types., Tegmark Bromley (1999) also found that early spectral types are more strongly clustered than late spectral types.
 Besides. Carter (2001) suggest tha the triggering of star formation occurs on a smaller spatia scale and whether a galaxy formis stars or not is strongly correlated. with the surrounding galaxy density average over a scale of a few Alpe.," Besides, Carter (2001) suggest that the triggering of star formation occurs on a smaller spatial scale and whether a galaxy forms stars or not is strongly correlated with the surrounding galaxy density averaged over a scale of a few Mpc."
 Lewis (2002) confirme his last result. by studying the environmental dependence of galaxy star-formation rates near clusters. finding that i is insensitive to the global large-scale. structure in. which he galaxy is embedded.," Lewis (2002) confirmed this last result by studying the environmental dependence of galaxy star-formation rates near clusters, finding that it is insensitive to the global large-scale structure in which the galaxy is embedded."
 The authors also obtained that the clistribution of star-formation rates is correlated. with both he distance from the cluster centre and the local projected density (see also Domínnguez ct al., The authors also obtained that the distribution of star-formation rates is correlated with both the distance from the cluster centre and the local projected density (see also nguez et al.
 2002)., 2002).
 ‘Taking into account these results. in this work we ocus on the analvsis of galaxv-galaxy. interactions within eroups and clusters with the aim at assessing if this ohvsical mechanism plays a significant role in star formation rigeering.," Taking into account these results, in this work we focus on the analysis of galaxy-galaxy interactions within groups and clusters with the aim at assessing if this physical mechanism plays a significant role in star formation triggering."
 For this purpose we constructed the hitherto argest sample of interacting pairs in groups ancl clusters rom the 2dEFCGIU., For this purpose we constructed the hitherto largest sample of interacting pairs in groups and clusters from the 2dFGRS.
 By means of spectroscopy ancl colour analysis. we explore the dependence of the star formation in galaxy pairs on relative projected separation. radial velocity and groupcentric distance.," By means of spectroscopy and colour analysis, we explore the dependence of the star formation in galaxy pairs on relative projected separation, radial velocity and groupcentric distance."
 The 2dE Galaxy Recshift Survey comprises over 220000 spectra of galaxies located in. two contiguos declination strips (Colles et al 2001)., The 2dF Galaxy Redshift Survey comprises over 220000 spectra of galaxies located in two contiguos declination strips (Colles et al 2001).
 Phe spectral properties of2dECRS galaxies are characterised. using the principal component analysis (PCA) described by Alaclewiek et al. (, The spectral properties of 2dFGRS galaxies are characterised using the principal component analysis (PCA) described by Madgwick et al. (
2002).,2002).
 This analysis makes use of the spectral information in the rest-frame wavelength range to6650. thereby including all the major optical diagnostic between Oll and Lla line.," This analysis makes use of the spectral information in the rest-frame wavelength range to, thereby including all the major optical diagnostic between OII and $\alpha$ line."
 For galaxies with z>0.15. the relation between the derived star formation rates and the spectral classification can he allectec by sky absortion bands contamination of the Ila line.," For galaxies with $z > 0.15 $, the relation between the derived star formation rates and the spectral classification can be affected by sky absortion bands contamination of the $\alpha$ line."
 Consequently. we restrict to galaxy pairs at z<01 in order to prevent the results from strong biases.," Consequently, we restrict to galaxy pairs at $z\leq 0.1$ in order to prevent the results from strong biases."
 The 2dECGIUS spectra are classified. by a parameter. 7. which is à linear combination of the first and. second principal components which isolates the relative strength of emission ancl absorption lines present in cach galaxy spectrum.," The 2dFGRS spectra are classified by a parameter, $\eta$, which is a linear combination of the first and second principal components which isolates the relative strength of emission and absorption lines present in each galaxy spectrum."
 Physically. 5g is related to the specific star formation rate in a galaxy. given the correlation with the equivalent width of llo found in emission lines galaxies (Bland-Llawthorn et al.," Physically, $\eta$ is related to the specific star formation rate in a galaxy, given the correlation with the equivalent width of $\alpha$ found in emission lines galaxies (Bland-Hawthorn et al."
 2002)., 2002).
 Galaxies with low star-formation rates have tvpica values p<Ld ancl actively star forming svstems yo1.4 (Alaclewick 2002)., Galaxies with low star-formation rates have typical values $\eta < -1.4$ and actively star forming systems $\eta > -1.4$ (Madgwick 2002).
 We study star formation induced by tidal interactions estimating the stellar birthrate parameter. b=SERA<SER> which indicates the present level of star formation activity of a galaxy related to its mean pas history.," We study star formation induced by tidal interactions estimating the stellar birthrate parameter, $b=SFR/<SFR>$ which indicates the present level of star formation activity of a galaxy related to its mean past history."
 Following Paper L throughout this work we use the linear correlation between b ancl η. b=0.255|1.06. as an estimate of the star formation activity in 2dGIU galaxies.," Following Paper I, throughout this work we use the linear correlation between $b$ and $\eta$, $b = 0.25 \eta + 1.06$, as an estimate of the star formation activity in 2dFGRS galaxies."
" In Paper 1. we analysed a sample of 1853 galaxy pairs in the LOO Ix release of the 2dE galaxy redshift) survey defined by a projected cistanee (rm,=1005! kpe and a relative racial velocity (AV=350kms+. ("," In Paper I, we analysed a sample of 1853 galaxy pairs in the 100 K release of the 2dF galaxy redshift survey defined by a projected distance $r_{\rm p} = 100 h^{-1} $ kpc and a relative radial velocity $\Delta V = 350 {\rm km s^{-1}}$. ("
"We adopt in this paper 44,=LO0Pkms'Alpe 13.",We adopt in this paper $H_0= 100 h {\rm km s^{-1} Mpc^{-1}}$ ).
 These limits proved to be reliable ones to select interacting pairs with enhanced star formation activity., These limits proved to be reliable ones to select interacting pairs with enhanced star formation activity.
 By applying the same selection criteria. we identified a total of 9174 pairs in the 2dEGIU.," By applying the same selection criteria, we identified a total of 9174 pairs in the 2dFGRS."
 In order to analyse in detail the properties of galaxy interactions in high density environments we constructed a catalog of pairs in groups by cross-correlating the total galaxy. pairs catalog with the 2dEXGIUS group catalog obtained by Merchánn Zandivarez (2004. in preparation).," In order to analyse in detail the properties of galaxy interactions in high density environments we constructed a catalog of pairs in groups by cross-correlating the total galaxy pairs catalog with the 2dFGRS group catalog obtained by Merchánn Zandivarez (2004, in preparation)."
 These authors identified eroups by using a slightly modified. version of the group finding algorithm develod bv Huchra Geller with a minimum number of 4 members. an outer number density enhancement of SO and a linking racial cutoll of 200 kms ," These authors identified groups by using a slightly modified version of the group finding algorithm developed by Huchra Geller with a minimum number of 4 members, an outer number density enhancement of 80 and a linking radial cutoff of 200 ${\rm km s^{-1}}$ ."
The sample in the catalog comprises 6076 &roups spanning over the redshift range of 0.003<20.25 with a mean redshift z20.1., The sample in the catalog comprises 6076 groups spanning over the redshift range of $0.003 \le z \le 0.25$ with a mean redshift $ z \simeq 0.1$.
 As a result. of this cross-correlation we obtain a sample of 4658 galaxies pairs in groups., As a result of this cross-correlation we obtain a sample of 4658 galaxies pairs in groups.
 Despite of the fact that the 2dE public catalog. is not complete. we argue that galaxy pairs searching is not severely alfected by completeness ellects.," Despite of the fact that the 2dF public catalog is not complete, we argue that galaxy pairs searching is not severely affected by completeness effects."
 This is based. on the fact that although the minimum fiber separation for 2015 spectroscopy is approximately 25 arcsec. the survey strategy was to repeat the measurements in each field with new fiber positions in order to achieve the highest completeness.," This is based on the fact that although the minimum fiber separation for 2dF spectroscopy is approximately 25 arcsec, the survey strategy was to repeat the measurements in each field with new fiber positions in order to achieve the highest completeness."
 Thus. [rom this point of view there is no bias against small angular separations which would introduce spurious results. specially at higher redshifts.," Thus, from this point of view there is no bias against small angular separations which would introduce spurious results, specially at higher redshifts."
 Fherefore. the inclusion of a pair in our catalog depends mostly on the inclusion of cach member in the survey. which were randomly selected within the target of each field.," Therefore, the inclusion of a pair in our catalog depends mostly on the inclusion of each member in the survey, which were randomly selected within the target of each field."
 We argue that there are not significant selection effects on the pair sample which could. bias our statistical results on star formation activity., We argue that there are not significant selection effects on the pair sample which could bias our statistical results on star formation activity.
 Following the procedure outlined of Paper 1. we focus our attention on the ellects of interactions on star formation bv comparing with a suitable control sample which cillers from the pair catalog only on the fact that. galaxies in eroups in the latter have a close companion.," Following the procedure outlined of Paper I, we focus our attention on the effects of interactions on star formation by comparing with a suitable control sample which differs from the pair catalog only on the fact that galaxies in groups in the latter have a close companion."
 Using Monte Carlo algorithm we select for cach galaxy pair. two other members of the 2DFGRS group catalog.," Using Monte Carlo algorithm we select for each galaxy pair, two other members of the 2DFGRS group catalog."
 Therefore. in this paper. the control sample corresponds to 9316galaxies in," Therefore, in this paper, the control sample corresponds to 9316galaxies in"
frequency decreases whenthei iferred iiass accretion rate decreases (0.2). Prius van «er Ils 1908: Mónudez ct al.,"frequency decreases when the inferred mass accretion rate decreases (e.g., Prins van der Klis 1998; Ménndez et al."
 1997: Ford van der EKlis 1998)., 1997; Ford van der Klis 1998).
 So far. onlv oue other source is known for which the break frequency has Όσοι observed to Increase with decreasing interred lnass accretion rate: the accretion-driven nuüllisecoud. N-rav pulsar SAN Jis0s.13658 (see Wijmands van der Isis 1998bj.," So far, only one other source is known for which the break frequency has been observed to increase with decreasing inferred mass accretion rate: the accretion-driven millisecond X-ray pulsar SAX J1808.4–3658 (see Wijnands van der Klis 1998b)."
 During the beegiuniug of he decay of the 1998 April outburst of this transient sQurce. the break frequency decreased Wih decreasiic N-rav flux.," During the beginning of the decay of the 1998 April outburst of this transient source, the break frequency decreased with decreasing X-ray flux."
 However. halfway the decay the |reals frequc‘LCV oSdeulv increased. again while the N-rax fiux kept ou ¢οσοasine.," However, half-way the decay the break frequency suddenly increased again while the X-ray flux kept on decreasing."
" Ανπας van der [lis (199s)) tentatively preposed that this unexpected behavior of the break frecnehey could |IO due to the uuique pulsaine nature of SAN Π150δ.11)658 compared to the nou-ptIsating neutron star LAINBs and black holes candidates. or it could be due to the first ever detailed study of tio finde properjos of a neutron star LMXD at such low mass accretion rates,"," Wijnands van der Klis (1998b) tentatively proposed that this unexpected behavior of the break frequency could be due to the unique pulsating nature of SAX J1808.4–3658 compared to the non-pulsating neutron star LMXBs and black holes candidates, or it could be due to the first ever detailed study of the timing properties of a neutron star LMXB at such low mass accretion rates."
 With our analysis of SEX. 1735269. which is a xsistent. LAINB aud for which no cohere ΠΠ pusations could be detected. it has been shown that the laτς yds most likely he case.," With our analysis of SLX 1735–269, which is a persistent LMXB and for which no coherent millisecond pulsations could be detected, it has been shown that the latter is most likely the case."
" Thus. the unexpected behavior of the accretiou-driven nullisecoud N-ray pulsar is not a ""uique feature of lis svstei. mereasine the suniluities of hat source with he other. nou-pulsatins neutron star LANBs."," Thus, the unexpected behavior of the accretion-driven millisecond X-ray pulsar is not a unique feature of this system, increasing the similarities of that source with the other, non-pulsating neutron star LMXBs."
 Diving the highest ¢count rates a bin is preseut on op of the band-limited nolse., During the highest count rates a bump is present on top of the band-limited noise.
 Wijnands van der EKlis (1999) showed that the frequency of this bump correlates well to the frequeuey of the break in low-hnunositv reutron star LMXDz (including tthe accretion-driven willisecoud X-ray pulsar) and bla‘Ak hole Caicidates., Wijnands van der Klis (1999) showed that the frequency of this bump correlates well to the frequency of the break in low-luminosity neutron star LMXBs (including the accretion-driven millisecond X-ray pulsar) and black hole candidates.
" Figure 3 shows the same data ploted in Fietue of Wijnands van der KIls (1999), 1""n1 now iachdins the data poiut of SEN 1735269 (triangle."," Figure \ref{break_vs_bump} shows the same data plotted in Figure of Wijnands van der Klis (1999), but now including the data point of SLX 1735–269 (triangle)."
" SEN 17335209 Avain,is right ou the relation defined by the oheY ", SLX 1735–269 is right on the relation defined by the other sources.
"ποσος, SLX 1735260 Is very sinular to oheT loxc-Inninositv LMXDs."," Again, SLX 1735–269 is very similar to other low-luminosity LMXBs."
 The point obtained for SLX 1735)5269 is at the low eud of the neutron star poiuts (he lower-frequeucyv points are mostly for Dlack-hole caxdidates) and very simular to the data of the N-rav Dursters IW 181212 aud 1E 17213015 (sce Wijnauds van der lis 1999)., The point obtained for SLX 1735–269 is at the low end of the neutron star points (the lower-frequency points are mostly for black-hole candidates) and very similar to the data of the X-ray bursters 4U 1812–12 and 1E 1724–3045 (see Wijnands van der Klis 1999).
 The latter two sources are. therefore. eood candidates to displav the saue merease of the break frequency wihi decreasing mass accretion rate.," The latter two sources are, therefore, good candidates to display the same increase of the break frequency with decreasing mass accretion rate."
 Tt is also incresting to note that the 325 keV huuinosity of SLN. 1735269 (~23 «1(pe Cres 13) is very close to the 325 keV unidnositv «tf SAN 1505.3658 when in this source t1ο break-frequeney aud the lass accretion rate became auti-correlated (ος τοῦ Cresls Wimauds van der lis 1999)., It is also interesting to note that the 3–25 keV luminosity of SLX 1735–269 $\sim$ 2–3 $\times10^{36}$ ergs ) is very close to the 3–25 keV luminosity of SAX J1808.4--3658 when in this source the break-frequency and the mass accretion rate became anti-correlated $\sim$ $\times10^{36}$ ergs; Wijnands van der Klis 1999).
 It is possible that this auti-correlation occtWs a a specific N-ray. Iuninosity. which might be sinular iu all neutron star LAINBs.," It is possible that this anti-correlation occurs at a specific X-ray luminosity, which might be similar in all neutron star LMXBs."
 This can easilv be checked 1Nw studving neutron star LAINBs in detail at such low huuinosities., This can easily be checked by studying neutron star LMXBs in detail at such low luminosities.
Flares are explosive events caused by magneüic reconnection in stellar atmospheres (Ilaischetal.1991.andreferencestherein)..,Flares are explosive events caused by magnetic reconnection in stellar atmospheres \citep[and references therein] {Haisch1991}.
 In the standard moclel. electrons are accelerated," In the standard model, electrons are accelerated"
at least 4-11 times higher than that in hot cores and dense cores.,at least 4-11 times higher than that in hot cores and dense cores.
 'The possible formation pathways of HNCO in shocks have never been modeled., The possible formation pathways of HNCO in shocks have never been modeled.
" In contrast, HNCO has been included in some models of dark clouds and hot core chemistry."," In contrast, HNCO has been included in some models of dark clouds and hot core chemistry."
" In the models by ?,, HNCO is produced by the ion- reaction Hy+HNCO*>H3NCO*H followed"," In the models by \cite{Iglesias77}, HNCO is produced by the ion-neutral reaction $\mathrm{H}_2 + \mathrm{HNCO}^+ \rightarrow \mathrm{H}_2 \mathrm{NCO}^+ + \mathrm{H} $ followed"
are only the early stages of the life of a massive star: in particular. many massive stars at solar metallicity go on to become Wolf-Rayet (WR) stars (Chiosi Maeder 1986).,"are only the early stages of the life of a massive star; in particular, many massive stars at solar metallicity go on to become Wolf-Rayet (WR) stars (Chiosi Maeder 1986)."
 WR stars are characterised by small or absent H envelopes as a result of high mass loss: therefore they generally arise from the most massive stars. which have higher mass-loss rates throughout their lives.," WR stars are characterised by small or absent H envelopes as a result of high mass loss; therefore they generally arise from the most massive stars, which have higher mass-loss rates throughout their lives."
 In a binary this process may be affected by Roche Lobe Overflow (RLOF). both as the donor (where the mass loss strips the envelope) and the gainer (which may become massive enough. via accretion. to later undergo a WR phase).," In a binary this process may be affected by Roche Lobe Overflow (RLOF), both as the donor (where the mass loss strips the envelope) and the gainer (which may become massive enough, via accretion, to later undergo a WR phase)."
 Some proportion of WR stars would. therefore also. be expected to be runaway. with the exact numbers depending on the dominant method of runaway production.," Some proportion of WR stars would therefore also be expected to be runaway, with the exact numbers depending on the dominant method of runaway production."
 Recently evidence has emerged that the fraction of runaways among Wolf-Rayet stars is similar to that amongst O stars (Mason et al., Recently evidence has emerged that the fraction of runaways among Wolf-Rayet stars is similar to that amongst O stars (Mason et al.
 1998. Moffat et al.," 1998, Moffat et al."
 1998. Foellmi et al.," 1998, Foellmi et al."
 2003) at around 10 per cent., 2003) at around 10 per cent.
 This has been interpreted as evidence in favour of dynamical ejection being the primary route for making massive runaway stars., This has been interpreted as evidence in favour of dynamical ejection being the primary route for making massive runaway stars.
 In this paper we consider whether the SN route may also produce similar runaway fractions for O and WR stars. and examine the implications of this.," In this paper we consider whether the SN route may also produce similar runaway fractions for O and WR stars, and examine the implications of this."
 The dynamical ejection scenario was first proposed by Poveda et al. (, The dynamical ejection scenario was first proposed by Poveda et al. (
1967).,1967).
 Tt involves binary encounters in the cores of the most massive OB associations., It involves binary encounters in the cores of the most massive OB associations.
 These encounters extract energy from the binary orbit through tightening of the orbit and generate runaway stars., These encounters extract energy from the binary orbit through tightening of the orbit and generate runaway stars.
 One system is known in which there is strong evidence for an origin through the dynamical ejection scenario., One system is known in which there is strong evidence for an origin through the dynamical ejection scenario.
 AAur and uCCol are both O9.5V stars with similar ages which are running away in opposite directions with velocities relative to the local standard of rest of 113.3 and | respectively (Hoogerwerf et al., Aur and $\mu$ Col are both O9.5V stars with similar ages which are running away in opposite directions with velocities relative to the local standard of rest of 113.3 and $^{-1}$ respectively (Hoogerwerf et al.
 2001)., 2001).
 Because of their similar but oppositely directed space velocities Blaauw Morgan (61954) first proposed a common origin for these runaway stars in the Orion nebula., Because of their similar but oppositely directed space velocities Blaauw Morgan (1954) first proposed a common origin for these runaway stars in the Orion nebula.
 Gies Bolton (1986) proposed a binary-binary interaction formed both of these runaway stars and the binary t OOri., Gies Bolton (1986) proposed a binary-binary interaction formed both of these runaway stars and the binary $\iota$ Ori.
 Supporting this hypothesis Hoogerwerf et al. (, Supporting this hypothesis Hoogerwerf et al. (
2001) have shown that these three objects occupied a very small region of space MMyr ago in the Trapezium cluster.,2001) have shown that these three objects occupied a very small region of space Myr ago in the Trapezium cluster.
 Gualandris. Portegies Zwart Eggleton (2004) have performed N-body simulations of the binary-binary encounter and have shown how a binary-binary encounter with an exchange occurring between the two binaries could produce the currently observed configuration.," Gualandris, Portegies Zwart Eggleton (2004) have performed N-body simulations of the binary-binary encounter and have shown how a binary-binary encounter with an exchange occurring between the two binaries could produce the currently observed configuration."
 Hoogerwerf et al. (, Hoogerwerf et al. (
2001) investigated the origin of twenty-two nearby runaway stars.,2001) investigated the origin of twenty-two nearby runaway stars.
 Parent associations were proposed for sixteen of these stars., Parent associations were proposed for sixteen of these stars.
 Of these sixteen eleven were proposed to have been produced via the binary supernova scenario as opposed to five through the dynamical ejection scenario., Of these sixteen eleven were proposed to have been produced via the binary supernova scenario as opposed to five through the dynamical ejection scenario.
 Two of the remaining runaways had more than one possible parent associations but were consistent with an origin via the binary supernova scenario., Two of the remaining runaways had more than one possible parent associations but were consistent with an origin via the binary supernova scenario.
 This implies a fraction of runaways formed through the dynamical ejection scenario as less than one third., This implies a fraction of runaways formed through the dynamical ejection scenario as less than one third.
 Leonard (1991) has performed a number of binary-binary encounters and finds that runaway velocities are greatest when the initial binaries are circular and the stars have similar masses., Leonard (1991) has performed a number of binary-binary encounters and finds that runaway velocities are greatest when the initial binaries are circular and the stars have similar masses.
 For the most-massive runaways in these binary-binary encounters Leonard (1991) finds that the maximum runaway velocity is half the surface escape velocity of that star - so escape velocities of 100s of | are possible., For the most-massive runaways in these binary-binary encounters Leonard (1991) finds that the maximum runaway velocity is half the surface escape velocity of that star - so escape velocities of 100s of $^{-1}$ are possible.
 There are a number of competing effects which will determine he relative sizes of the O and WR star runaway fraction in the case hat all runaways are created by dynamical interaction., There are a number of competing effects which will determine the relative sizes of the O and WR star runaway fraction in the case that all runaways are created by dynamical interaction.
 First. in à binary-single star interaction. the star which is most likely to be ejected as a runaway is the least massive of the three.," First, in a binary-single star interaction, the star which is most likely to be ejected as a runaway is the least massive of the three."
 It is thought hat runaway O stars arise from binary-binary (Clarke Pringle 1992) or higher-order multiple interactions. but even here it is the ess massive stars which will be ejected with the greatest velocities.," It is thought that runaway O stars arise from binary-binary (Clarke Pringle 1992) or higher-order multiple interactions, but even here it is the less massive stars which will be ejected with the greatest velocities."
 Selecting for lower-mass stars selects for O stars (the initial mass imit above which a star goes through an O phase being lower than he initial mass limit above which a star goes through a WR phase) and for evolved WR stars Gf the interaction happens late in the ifetime of the WR star when it has lost much of its mass via a windy., Selecting for lower-mass stars selects for O stars (the initial mass limit above which a star goes through an O phase being lower than the initial mass limit above which a star goes through a WR phase) and for evolved WR stars (if the interaction happens late in the lifetime of the WR star when it has lost much of its mass via a wind).
 Once a star is a runaway it is likely to remain that way. which selects for the later stages in a star's lifetime. i.e. against O stars.," Once a star is a runaway it is likely to remain that way, which selects for the later stages in a star's lifetime, i.e. against O stars."
 Between these considerations it is difficult to form a clear picture of the population occurring from dynamical interactions without large-scale numerical simulations., Between these considerations it is difficult to form a clear picture of the population occurring from dynamical interactions without large-scale numerical simulations.
 If the runaway fractions of such WR and O stars are equal. it may be only because of the balance of competing effects.," If the runaway fractions of such WR and O stars are equal, it may be only because of the balance of competing effects."
 Even if it is completely symmetric. a supernova in a binary system still occurs away from the centre of mass of the system and hence imparts a net velocity to the system as a whole.," Even if it is completely symmetric, a supernova in a binary system still occurs away from the centre of mass of the system and hence imparts a net velocity to the system as a whole."
 Whether the system is unbound by this and whether the resulting velocity of the companion is great enough for it to be observed as a runaway depends on its pre-SN parameters., Whether the system is unbound by this and whether the resulting velocity of the companion is great enough for it to be observed as a runaway depends on its pre-SN parameters.
 In particular. a binary will remain bound despite a SN explosion if less than half its total mass is lost.," In particular, a binary will remain bound despite a SN explosion if less than half its total mass is lost."
 For most binaries which have undergone mass transfer. it is he primary — initially the most massive star — which explodes first. but by the time of its SN its mass is less than that of its companion.," For most binaries which have undergone mass transfer, it is the primary – initially the most massive star – which explodes first, but by the time of its SN its mass is less than that of its companion."
 Therefore for perfectly symmetric SNe all of these systems would remain bound., Therefore for perfectly symmetric SNe all of these systems would remain bound.
 In these circumstances it is hard to explain the very ow binary fraction amongst runaway O stars (Mason et al., In these circumstances it is hard to explain the very low binary fraction amongst runaway O stars (Mason et al.
 1998)., 1998).
 Studies of single pulsar velocities (Lyne Lorimer 1994) finc hat an additional “kick” velocity of some 450kms (imparted by asymmetric mass loss or neutrino emission) is required to accoun or the extremely high velocity of some neutron stars.," Studies of single pulsar velocities (Lyne Lorimer 1994) find that an additional `kick' velocity of some $450\,{\rm kms}^{-1}$ (imparted by asymmetric mass loss or neutrino emission) is required to account for the extremely high velocity of some neutron stars."
 Brandt Podsiadlowski (1995) suggest that kicks of this magnitude wil unbind the binary in over 70 of cases., Brandt Podsiadlowski (1995) suggest that kicks of this magnitude will unbind the binary in over 70 of cases.
 In this case it is quite eusy to make massive runaways via the BSS., In this case it is quite easy to make massive runaways via the BSS.
 However. whilst the populations which go on to form runaway O and runaway WR stars are similar. they are not identical and in particular they are affected differently by the time at which the SN occurs and the size of the Kick.," However, whilst the populations which go on to form runaway O and runaway WR stars are similar, they are not identical and in particular they are affected differently by the time at which the SN occurs and the size of the kick."
 The simplest scenario in which O and WR runaway stars both arise from supernovae is when all Kicks are equal., The simplest scenario in which O and WR runaway stars both arise from supernovae is when all kicks are equal.
 The properties of the runaway are determined by any binary interaction it may have undergone and its state of evolution at the time of the SN of its companion., The properties of the runaway are determined by any binary interaction it may have undergone and its state of evolution at the time of the SN of its companion.
 The fraction of WR stars which are runaways should in this ease always be significantly greater than the fraction of O stars which are runaways., The fraction of WR stars which are runaways should in this case always be significantly greater than the fraction of O stars which are runaways.
 This arises from the relative positions of the O and WR phases in the star's lifetime., This arises from the relative positions of the O and WR phases in the star's lifetime.
 Stars either begin their lives as O stars or become O stars after undergoing accretion from RLOF., Stars either begin their lives as O stars or become O stars after undergoing accretion from RLOF.
 However. the O phase is always earlier than the WR phase.," However, the O phase is always earlier than the WR phase."
 In a binary it is reasonable to assume that both stars are formed at the same time., In a binary it is reasonable to assume that both stars are formed at the same time.
 By the time one of the stars has evolved to the point, By the time one of the stars has evolved to the point
uot exist.,not exist.
 Thus it could be conjectured that there has to be an explanation for the law from simple aud primitive principles of economic activity., Thus it could be conjectured that there has to be an explanation for the law from simple and primitive principles of economic activity.
 Oue of the striking economic activity that every society. iucludiug the most ancient ones. is capable of. is “give aud take’.," One of the striking economic activity that every society, including the most ancient ones, is capable of, is `give and take'."
 Someone gives vou a cup of coffee. vou haud him over a dollar.," Someone gives you a cup of coffee, you hand him over a dollar."
 This is a simple exchange of assets, This is a simple exchange of assets.
 Let us call itcadditive asset exchange’., Let us call it `additive asset exchange'.
 However. vou do not keep vour entire wealth at stake to a coffee shop owner.," However, you do not keep your entire wealth at stake to a coffee shop owner."
 But vou may keep it at stake in bank., But you may keep it at stake in bank.
 ere vou eet money which is proportionate to the moueyv vou own., Here you get money which is proportionate to the money you own.
 Let us call it unultiplicative asset exchange’., Let us call it `multiplicative asset exchange'.
 Researchers have looked at the models of wealth distribution im presence of additive aud imultiplicative asset oxchanec and results are intriguing., Researchers have looked at the models of wealth distribution in presence of additive and multiplicative asset exchange and results are intriguing.
 Somehow. simple asset exchanee models are unable to reproduce the power law tail which secs to be robust feature across economies.," Somehow, simple asset exchange models are unable to reproduce the power law tail which seems to be robust feature across economies."
 For multiplicative asset excliauge models. in which all ageuts start with same wealth. have similar capabilities (none is cleverer than the other iu auy seuse) the cmereine distribution of wealth is even less equitable than a power law.," For multiplicative asset exchange models, in which all agents start with same wealth, have similar capabilities (none is cleverer than the other in any sense) the emerging distribution of wealth is even less equitable than a power law."
 It turus out that in tree aud für trade. oue agent (by pure hick. since we have not assiened extra capabilities to auv aeeut) euds up swallowingo the entire wealth.," It turns out that in `free and fair' trade, one agent (by pure luck, since we have not assigned extra capabilities to any agent) ends up swallowing the entire wealth."
 Iu another theft and fraud rule. we eet an exponential distribution of wealth.," In another `theft and fraud' rule, we get an exponential distribution of wealth."
 What are these ποστ We cousider two models given by Brian Hayes., What are these \cite{Brian Hayes} We consider two models given by Brian Hayes.
 Iu these models. there is no coustuuption of wealth nor any production.," In these models, there is no consumption of wealth nor any production."
 Iu the first model. we assume that evervone knows the value of evervbody else's asset perfectly.," In the first model, we assume that everyone knows the value of everybody else's asset perfectly."
 This free and fain” (since nobody is able to conceal true value of his assets) model is called Yardsale models]., This 'free and fair' (since nobody is able to conceal true value of his assets) model is called Yardsale \cite{fnn}.
 It is the following: There are IN dudividuals in society aud they trade with cach other ou one-to-one basis., It is the following: There are $N$ individuals in society and they trade with each other on one-to-one basis.
 Evervoue is able to value evervoue else's assets perfectly while trading., Everyone is able to value everyone else's assets perfectly while trading.
 Naturally. the amount traded is a fraction of assets of poorer party.," Naturally, the amount traded is a fraction of assets of poorer party."
 However. we can lave another rule.," However, we can have another rule."
 In this rule. the amount to be exchaneed is a fraction of loscr’s wealth.," In this rule, the amount to be exchanged is a fraction of loser's wealth."
" Naturally, poorer ageuts have more to gain by plaving with richer oues and they can do so ouly by deception."," Naturally, poorer agents have more to gain by playing with richer ones and they can do so only by deception."
 Heuce it has been named theft aud fraud (TF) iiodel[9]., Hence it has been named theft and fraud (TF) \cite{fn}.
. The YS and TF rules can be given as follows., The YS and TF rules can be given as follows.
 Let us consider set of [N agents with wealth im(0).Πο(0ωνΕν(0) at time T=0.," Let us consider set of $N$ agents with wealth $m_1(0), m_2(0) \ldots
m_N(0)$ at time $T=0$."
 At cach thuestep T.—f we choose two ageuts { aud j aud thei wealtls ο) aud inj(f) are updated where Am is the net wealth exchanged between that two ageuts. (, At each timestep $T=t$ we choose two agents $i$ and $j$ and their wealths $m_i(t)$ and $m_j(t)$ are updated where $\Delta m$ is the net wealth exchanged between that two agents. (
Wealth of rest of the ageuts is uncliuged.),Wealth of rest of the agents is unchanged.)
 In the YS model. Am=oΠας).naj(t)).," In the YS model, $\Delta m=\alpha \min(m_i(t),m_j(t))$."
 Whereas. in the TF model the money. exchange is fraction of the wealth loser plaver.," Whereas, in the TF model the money exchange is fraction of the wealth loser player."
 Then. Aun=αμ) (if j is the loser).," Then, $\Delta m=\alpha(m_j(t))$ (if $j$ is the loser)."
 The parauieter à is a πα{οντη]ν distributed random nmmuber in the interval 0.1].," The parameter $\alpha$ is a uniformly distributed random number in the interval $\lbrack 0,1\rbrack$."
" However, noue of these models reproduces the power law distribution of wealth found im several societies."," However, none of these models reproduces the power law distribution of wealth found in several societies."
 The YS model essentially produces condensation, The YS model essentially produces condensation
satellite phase space for this equivalent circular orbit problem.,satellite phase space for this equivalent circular orbit problem.
" We examined resonances with /;€[—10,10] and |€[1,4]."," We examined resonances with $l_1\in[-10, 10]$ and $l\in[1,4]$."
" In addition to the -1:2:2 resonance, the 0:1:1, 1:1:1, and 1:0:2 resonances occur within the satellite's phase space."," In addition to the -1:2:2 resonance, the 0:1:1, 1:-1:1, and 1:0:2 resonances occur within the satellite's phase space."
" Comparing this to the results from the larger radius circular orbit calculation given refsec:rescorque)), thecouplingo fthelargerinstantaneousangular firrqulancybtpewitdarthe &alnighernréxigylieugméoy gorédósbhgtllavelar gerorbital ft Inaddi"," Comparing this to the results from the larger radius circular orbit calculation \\ref{sec:res_torque}) ), the coupling of the larger instantaneous angular frequency at pericentre to higher binding energy orbits that have larger orbital frequencies, moves the resonances inward in radius."
"tion, ial dubiin dderexdrhglea"," Hence, some resonances that were previously outside the satellite in \\ref{sec:res_torque} are now within the satellite."
 dign hasbinksrche estar engtho fthecouy," In addition, the stronger tidal field at smaller orbital radii in the host increases the strength of the coupling."
" resrorquearenowwithinthesatellite.landthel:0 2resonancesarenowcomparabletothestrengthofthe : 2resonance, whichismuchstrongerthanthe 2resonanceinthelargerradiuscircularorbit."," Using numerical perturbation theory, the strength of the 1:-1:1 and the 1:0:2 resonances are now comparable to the strength of the -1:2:2 resonance, which is much stronger than the -1:2:2 resonance in the larger radius circular orbit."
" In summary, resonant heating is enhanced for an eccentric orbit both because of the larger number of resonances within the satellite and the stronger tidal force felt by the satellite at pericentre."," In summary, resonant heating is enhanced for an eccentric orbit both because of the larger number of resonances within the satellite and the stronger tidal force felt by the satellite at pericentre."
" However, our approximate perturbation theory calculation does not include the full time dependence of the eccentric orbit, a calculation that is extremely difficult and is beyond the scope of this paper."," However, our approximate perturbation theory calculation does not include the full time dependence of the eccentric orbit, a calculation that is extremely difficult and is beyond the scope of this paper."
" Owing to satellite heating, particles in a satellite gain energy and angular momentum."," Owing to satellite heating, particles in a satellite gain energy and angular momentum."
 This reduces the satellite's binding energy and enhances the satellite's mass loss., This reduces the satellite's binding energy and enhances the satellite's mass loss.
 There are several mechanisms that heat a satellite and each one is effective over different ranges of binding energy., There are several mechanisms that heat a satellite and each one is effective over different ranges of binding energy.
" However, the re-equilibration of the satellite tends to globally redistribute the work throughout the satellite profile, washing out the nature of its origin."," However, the re-equilibration of the satellite tends to globally redistribute the work throughout the satellite profile, washing out the nature of its origin."
" The observational signatures of the subsequent mass loss, then, tend to be universal."," The observational signatures of the subsequent mass loss, then, tend to be universal."
 Fig., Fig.
 16 plots the fraction of bound particles remaining in different parts of phase space at different times for a satellite on a circular orbit., \ref{fig:2DPSP.XC1} plots the fraction of bound particles remaining in different parts of phase space at different times for a satellite on a circular orbit.
 Low binding energy particles are stripped at earlier times and high binding energy particles are stripped later., Low binding energy particles are stripped at earlier times and high binding energy particles are stripped later.
" In other words, the satellite stripping process is an outside-in process in energy space."," In other words, the satellite stripping process is an outside-in process in energy space."
 We can understand this behaviour as follows., We can understand this behaviour as follows.
 Weakly bound satellite orbits are affected and stripped by the tidal force beyond a characteristic radius., Weakly bound satellite orbits are affected and stripped by the tidal force beyond a characteristic radius.
 The apocentres of orbits with a energy are within a factor of two of the radius of a thestronganti," The apocentres of orbits with a given energy are within a factor of two of the radius of a circular orbit with the same energy, even for a zero-angular momentum orbit."
ea," For example, Fig."
t of a circular orbit (κ.= 1) and the thieapocentre of a radial orbit («= 0) for an energy of E=—0.044; the apocentre of the radial orbit is only larger than the radius of the circular orbit., \ref{fig:apo_peri} marks the radius of a circular orbit $\kappa=1$ ) and the apocentre of a radial orbit $\kappa=0$ ) for an energy of $E=-0.044$; the apocentre of the radial orbit is only larger than the radius of the circular orbit.
" Therefore, energy and not the relative angular momentum κ. determines the stripping boundary."," Therefore, energy and not the relative angular momentum $\kappa$ determines the stripping boundary."
" Although very low angular momentum orbits can be stripped at lower energies, Fig."," Although very low angular momentum orbits can be stripped at lower energies, Fig."
 16 shows that any trend towards a larger escape fraction for smaller « at fixed energy is very weak.," \ref{fig:2DPSP.XC1}
 shows that any trend towards a larger escape fraction for smaller $\kappa$ at fixed energy is very weak."
 We plot the fraction of particles remaining in different, We plot the fraction of particles remaining in different
shown by the dotted lines in Figur which were manually deeruined for each image.,shown by the dotted lines in Figure \ref{fig_tFOV1} which were manually determined for each image.
 The dark core elongates iuto the umbra in concert with the inward motion of the penuibral grain from 11:53UT to 12:28UT., The dark core elongates into the umbra in concert with the inward motion of the penumbral grain from 11:53UT to 12:38UT.
 The dark core breaks iuto two parts. aud tle ilier. (umbra-side) part shriuks iuto the umbra from 12:9UT to 13:11UT.," The dark core breaks into two parts, and the inner (umbra-side) part shrinks into the umbra from 12:49UT to 13:11UT."
 The outer yall agal1 eloigates into the ubὪ With another inward migrating penumbral eraiu [rom 13:22UT o 13:11U.T. and then the da‘k core gradually becomes uarrower aud less dark rou 13:HUT.," The outer part again elongates into the umbra with another inward migrating penumbral grain from 13:22UT to 13:44UT, and then the dark core gradually becomes narrower and less dark from 13:44UT."
 Finaly. πο cla‘k core is visible in he rane at LETSUT.," Finally, no dark core is visible in the frame at 14:18UT."
 Figure I shows the teiiporal evolttio1 of the Ci-baxli tensity along the dotted lites iu Figure 3ita.., Figure \ref{fig_stp1} shows the temporal evolution of the G-band intensity along the dotted lines in Figure \ref{fig_tFOV1}.
 This shows wo luwarcd noving penuimbral gralus. aud dark areas (dark cores) which also nove iuto the umbra.," This shows two inward moving penumbral grains, and dark areas (dark cores) which also move into the umbra."
 The Everslec flows also orieiuate at the peuumbral graius (Fig. | itb))., The Evershed flows also originate at the penumbral grains (Fig. \ref{fig_stp1} ).
" It is not observed. betwee1 the two successive peuumbral grains around 12:IUT. aud it 510os αἱ 13:15 with the clisappea""allce of the secoxd peuuiibral erain.", It is not observed between the two successive penumbral grains around 12:45UT and it stops at 13:45 with the disappearance of the second penumbral grain.
 Small recdshifts are observed aloig the dark-cored bright filau1011 in the frame at 13:56 in Figure 3ith.., Small redshifts are observed along the dark-cored bright filament in the frame at 13:56 in Figure \ref{fig_tFOV1}.
 One interesting result is hat the dark core is sillo pervect until 11:12 after the disappearane of the Evershed flow., One interesting result is that the dark core is still observed until 14:12 after the disappearance of the Evershed flow.
 Figure | shows that the areas wit1 more horizontal fieIs move a short distance toward the πα during the period when Evershec flows are observed (the white arrows) in comparison to the perio wilrout any Evershed flows (the black arrows)., Figure \ref{fig_stp1} shows that the areas with more horizontal fields move a short distance toward the umbra during the period when Evershed flows are observed (the white arrows) in comparison to the period without any Evershed flows (the black arrows).
 The 1magnetic fields at the dark core returu to the sale orleutatlon as heir διοιdiugs (more vertical) just alter the penumbral grain and Evershec low are no longer oπόνος] along the ¢ark core., The magnetic fields at the dark core return to the same orientation as their surroundings (more vertical) just after the penumbral grain and Evershed flow are no longer observed along the dark core.
 Figu 3 shows that the mo elorizoutal ields are observed along the dark core at 13:11 but uot seer at 13:56., Figure \ref{fig_tFOV1} shows that the more horizontal fields are observed along the dark core at 13:44 but not seen at 13:56.
 TIe 2D distributio oL nae.etic field inclination is not much changed after. 13:00. a1 hne area wit1 vertical fields sddeuly aypears along the dark core tn the period between 13:11 arc 13:56.," The 2D distribution of magnetic field inclination is not much changed after 13:00, and the area with vertical fields suddenly appears along the dark core in the period between 13:44 and 13:56."
 Higher time resolution is necessary to reveal the process of the disappearance of fine-scale uagnuetic fied structures in te penuluVa., Higher time resolution is necessary to reveal the process of the disappearance of fine-scale magnetic field structures in the penumbra.
 Another dlark-cored peuαυτα. filament (the vellow arrows in Fig 3)) and a dark penuumbral ilament (the eree] arrows) a‘e observed in the same fiekl-o£-view., Another dark-cored penumbral filament (the yellow arrows in Fig \ref{fig_tFOV1}) ) and a dark penumbral filament (the green arrows) are observed in the same field-of-view.
 These dark features also have nore horizoital fields than heir lateral surroundiugs. aud have similar spatial aud temporal 'elations wit1 the Evershecl flows.," These dark features also have more horizontal fields than their lateral surroundings, and have similar spatial and temporal relations with the Evershed flows."
 We σον that the Evershed flow originatese at peutuubral egrains and is associated with a more horizontal magnetic field., We confirm that the Evershed flow originates at penumbral grains and is associated with a more horizontal magnetic field.
 In this paper we describe a bright peuumbral filament with a dark core that survives for 10-20 minutes beyoud the end of the Evershed flows., In this paper we describe a bright penumbral filament with a dark core that survives for 10-20 minutes beyond the end of the Evershed flows.
 This ieaus that the convective upllow along the center of the bright pentumbral filament. which produces warping of," This means that the convective upflow along the center of the bright penumbral filament, which produces warping of"
(BID) and interred the limits between 10 and 30M...,(BH) and inferred the limits between $10$ and $30\ M_\odot$.
 Recently Greiner. Cuby. MeCaughrean (2001) used the inlrared observations to obtain the mass function.," Recently Greiner, Cuby, McCaughrean (2001) used the infrared observations to obtain the mass function."
 Thev were also able to identifv and characterize the donor., They were also able to identify and characterize the donor.
 Thev find that the svstem consists of a 14ελ. DII. with a 1.220.2Al. WAM UI type giant filling its Roche lobe. at an orbital separation of 108E448. (period of 33.5 days).," They find that the system consists of a $14\pm 4\,M_\odot$ BH, with a $1.2\pm 0.2\ M_\odot$ K-M III type giant filling its Roche lobe, at an orbital separation of $108 \pm 4 R_\odot$ (period of 33.5 days)."
 The formation of such svstem poses a problem lor the standard stellar evolutionary scenarios (Greiner οἱ al., The formation of such system poses a problem for the standard stellar evolutionary scenarios (Greiner et al.
 2001)., 2001).
 The mass of the DII is larger than the DII masses measured so far., The mass of the BH is larger than the BH masses measured so far.
 In the framework of stellar evolution it was argued. (Wellstein Langer 1999) that Inassive slags are not able {ο produce such massive DIIs., In the framework of stellar evolution it was argued (Wellstein Langer 1999) that massive stars are not able to produce such massive BHs.
 The hieh wind mass loss rates (or the mass transfer event) remove entire I-xich envelopes of massive stars. which become massive Woll-Ravet stars with vet more enhanced mass loss rates.," The high wind mass loss rates (or the mass transfer event) remove entire H-rich envelopes of massive stars, which become massive Wolf-Rayet stars with yet more enhanced mass loss rates."
 Therefore. at the time of core Collapse/SN explosion (hese massive stars are reduced to a fraction of (heir initial mass. and (μον can not be responsible for formation of massive DlIIs.," Therefore, at the time of core collapse/SN explosion these massive stars are reduced to a fraction of their initial mass, and they can not be responsible for formation of massive BHs."
 In order to avoid this problem. it was suggested that wind mass loss rates were overestimatecl (e.g. Nugis Lamers 2000).," In order to avoid this problem, it was suggested that wind mass loss rates were overestimated (e.g. Nugis Lamers 2000)."
 ]t was also proposed that probably. the mass transfer (MT) phase reveling bare helium core happens very late in the evolution of a star (case C MT). and thus remaining lifetime of phase is very short and wind mass loss is not that significant (Brown. Lee Tauris POOL: IXalogera 2001).," It was also proposed that probably the mass transfer (MT) phase reveling bare helium core happens very late in the evolution of a star (case C MT), and thus remaining lifetime of Wolf-Rayet phase is very short and wind mass loss is not that significant (Brown, Lee Tauris 2001; Kalogera 2001)."
 However. Nelemans van den Heuvel (2001) performed calculations with reduced. helium mass loss rates and allowed [or case C MT scenario. and thev have found that they are still not able to reproduce the formation of high mass Bis.," However, Nelemans van den Heuvel (2001) performed calculations with reduced helium mass loss rates and allowed for case C MT scenario, and they have found that they are still not able to reproduce the formation of high mass BHs."
 This was due to the fact. that the case C MT is attainable only for primaries initially less massive (han 19-25 AL... and thus not able to form high mass DlIs.," This was due to the fact, that the case C MT is attainable only for primaries initially less massive than 19-25 $M_\odot$, and thus not able to form high mass BHs."
 Nelemans van den Heuvel (2001) suggested (hat helium stars end their lives with higher masses than it is currently believed i.e.. either their lifetimes are shorter or the mass loss rates should be further reduced).," Nelemans van den Heuvel (2001) suggested that helium stars end their lives with higher masses than it is currently believed (i.e., either their lifetimes are shorter or the mass loss rates should be further reduced)."
" Recent developrient. of population svnthesis codes max. offer a solution for formation ""high mass DlIls in binaries.", Recent development of population synthesis codes may offer a solution for formation of high mass BHs in binaries.
 Delezvnski. Kalogera Bulik (2002. hereinafter. DINDO2) have shown that using detailed hydrodyvnanmical ealeulation of core collapse (Frver 1999) and lowing for a direct DII formation there is a possibility of forming BIIs of ~10... for a wide range of initial stellar masses.," Belczynski, Kalogera Bulik (2002, hereinafter BKB02) have shown that using detailed hydrodynamical calculation of core collapse (Fryer 1999) and allowing for a direct BH formation there is a possibility of forming BHs of $\sim 10 M_\odot$ for a wide range of initial stellar masses."
 They have also demonstrated that reduction of lowered helium star wind mass loss rates by. another factor o£ 2 (which is sll allowed by the observations) av increase maximum DII mass formed out of a single star up to ~15M... while reduction of all wind mass loss rates (both for H-rich and Le-rich stellar phases) increases the maximum DII mass to ~19.4...," They have also demonstrated that reduction of lowered helium star wind mass loss rates by another factor of 2 (which is still allowed by the observations) may increase maximum BH mass formed out of a single star up to $\sim 15 M_\odot$, while reduction of all wind mass loss rates (both for H-rich and He-rich stellar phases) increases the maximum BH mass to $\sim 19 M_\odot$."
 Belezvnski. Dulik. IXIuzniak (2002) have caleulated that the mass of DII may be maximally increased during binary interactions bv ~4A...," Belczynski, Bulik, Kluzniak (2002) have calculated that the mass of BH may be maximally increased during binary interactions by $\sim 4 M_\odot$."
 The highest mass DlIs appear because of MT in a binary. vel this is not likely in case of GRS 1915-105.," The highest mass BHs appear because of MT in a binary, yet this is not likely in case of GRS 1915+105."
 The BI of GRS 1915+105 is in a binary with a low mass star. and therefore DII mass could nol have been increased significantly.," The BH of GRS 1915+105 is in a binary with a low mass star, and therefore BH mass could not have been increased significantly."
 Currently (he mass ratio of the svstem components, Currently the mass ratio of the system components
.—,".,"
 provided uj.#0., provided $\mu\neq0$.
 The expressions (30)) and (34)) are the starting points of our analysis of the emissivity., The expressions \ref{schwinger1}) ) and \ref{schwinger2}) ) are the starting points of our analysis of the emissivity.
" It is worth noting that when (30)) is inserted into (4)) the emissivity can immediately be integrated over frequency and angle to give eammatfrWBE ise whereB=dB/dr. p""=me(y.yB) is the particle momentum 4-veetorand r the proper time."," It is worth noting that when \ref{schwinger1}) ) is inserted into \ref{emissivity}) ) the emissivity can immediately be integrated over frequency and angle to give ^2+ )^2 = | |^2 where $\dot{\bm{\beta}}=\diff\bm{\beta}/\diff t$, $p^\mu=mc\left(\gamma,\gamma\bm{\beta}\right)$ is the particle momentum $4$ -vectorand $\tau$ the proper time."
 The integrand on the hand side of (40)) is just the relativistic form of Larmor's formula for the instantaneous power radiated., The integrand on the right-hand side of \ref{larmor}) ) is just the relativistic form of Larmor's formula for the instantaneous power radiated.
 Thus. when integrated over a trajectory on which the acceleration is non-vanishing only within a finite time interval. this formula correctly gives the total radiated power.," Thus, when integrated over a trajectory on which the acceleration is non-vanishing only within a finite time interval, this formula correctly gives the total radiated power."
 It is. nevertheless. incorrect to regard it as a truly instantaneous power. for example byassociating a particular section of the trajectory with a part of the radiated power (e.g..Schwingeretal.1998.Chap. 37)..," It is, nevertheless, incorrect to regard it as a truly instantaneous power, for example byassociating a particular section of the trajectory with a part of the radiated power \citep[e.g.,][Chap.~37]{schwinger98}."
 The trajectory of a particle moving with constant acceleration (as measured in its instantaneous rest frame) 15 called bbecause of its shape in the (x. £)-plane (the acceleration and velocity are assumed parallel).," The trajectory of a particle moving with constant acceleration (as measured in its instantaneous rest frame) is called because of its shape in the $(x,t)$ -plane (the acceleration and velocity are assumed parallel)."
 In classical electrodynamies in flat space. a hyperbolic trajectory results when a particle moves in a constant electric. field which ts parallel to its velocity. and also to the magnetic field. if any is present.," In classical electrodynamics in flat space, a hyperbolic trajectory results when a particle moves in a constant electric field which is parallel to its velocity, and also to the magnetic field, if any is present."
 The sometimes controversial literature on the problem of the radiation emitted by a particle on such a trajectory. goes back over a century — see. for example. Ginzburg (1970)..," The sometimes controversial literature on the problem of the radiation emitted by a particle on such a trajectory, goes back over a century — see, for example, \citet{ginzburg70}. ."
 In the last few decades. interest has arisen in the associated quantum effects. theEffect and (e.g..Unruh 2009).," In the last few decades, interest has arisen in the associated quantum effects, the and \citep[e.g.,][]{unruh76,bellleinaas87,crispinoetal08,thirolfetal09}."
. At least in the classical limit. the conceptual problems associated with hyperbolic motion disappear if the particle experiences acceleration during only a finite time-interval. outside of which it moves with constant velocity.," At least in the classical limit, the conceptual problems associated with hyperbolic motion disappear if the particle experiences acceleration during only a finite time-interval, outside of which it moves with constant velocity."
 We will assume this to be the case in the application to pulsars., We will assume this to be the case in the application to pulsars.
 Consider aparticle of charge g and mass zi moving along the y-axis in an electric field E()=£EGO which 1s constant and of magnitude E between x=0 and x=ZL and vanishes elsewhere., Consider aparticle of charge $q$ and mass $m$ moving along the $x$ -axis in an electric field $\bm{E}(x)=\hat{\bm{x}}E(x)$ which is constant and of magnitude $E$ between $x=0$ and $x=L$ and vanishes elsewhere.
" Assuming the velocity 1s also directed along £. the trajectory Is forü «rrj2GPJe)eosh![(Lta"")fe|."," Assuming the velocity is also directed along $\hat{\bm{x}}$, the trajectory is for $0<\tau<\tau_L=
\left(\accel/c\right)\textrm{cosh}^{-1}\left[\left(L+\accel\right)/\accel\right]$."
 The length a’ is the distance over which the electrostatic potential changes by ποτή]: where wig=7i/mec is the Compton wavelength and E=lglfEfmc? is the electric field in units of the critical field — for an electron or positron this is the Schwinger field Esq.=13x105Vml.," The length $\accel$ is the distance over which the electrostatic potential changes by $mc^2/|q|$: , where $\lambdaC=\hbar/mc$ is the Compton wavelength and $\Ehat=|q|\hbar E/m^2c^3$ is the electric field in units of the critical field — for an electron or positron this is the Schwinger field $E_{\rm Schw}=1.3\times10^{18}
\,\textrm{V\,m}^{-1}$."
 The trajectory (42)) is an exact solution of the classical equations of motion. including the Lorentz-Abraham-Dirac form of the radiation reaction force (which vanishes identically for 0<7«τι).," The trajectory \ref{hyperbola}) ) is an exact solution of the classical equations of motion, including the Lorentz-Abraham-Dirac form of the radiation reaction force (which vanishes identically for $0<\tau<\tau_L$ )."
 In à gap near a pulsar surface. the magnetic field i5 sufficiently strong that electrons and positrons rapidly decay into the Landau ground state.," In a gap near a pulsar surface, the magnetic field is sufficiently strong that electrons and positrons rapidly decay into the Landau ground state."
 Then. if the radius of curvature of the field lines is large (see section 5)) the particle motion is approximately one-dimensional.," Then, if the radius of curvature of the field lines is large (see section \ref{pulsars}) ) the particle motion is approximately one-dimensional."
 The component along B of the electric field induced by rotation of the star accelerates particles in à trajectory that can be approximated by (42)). whereas the perpendicular component produces an £xB-drift that can be transformed away.," The component along $\bm{B}$ of the electric field induced by rotation of the star accelerates particles in a trajectory that can be approximated by \ref{hyperbola}) ), whereas the perpendicular component produces an $\bm{E}\times\bm{B}$ -drift that can be transformed away."
" Static models of gaps assume the (parallel) field vanishes below the surface (x= 0) and abovea"" pair-production aat height £L. where photons produced in the gap create a sufficient number of charges to screen the field."," Static models of gaps assume the (parallel) field vanishes below the surface $x=0$ ) and above a pair-production at height $L$, where photons produced in the gap create a sufficient number of charges to screen the field."
 Under pulsar conditions. one generally expects E«| and L/a®>>| (see Sect. 5)).," Under pulsar conditions, one generally expects $\Ehat\ll 1$ and $L/\accel\gg1$ (see Sect. \ref{pulsars}) )."
" A particle that starts at rest at the surface and is accelerated upwards achieves a Lorentz factor y=(y+a"")αἱ at height x.", A particle that starts at rest at the surface and is accelerated upwards achieves a Lorentz factor $\gamma=\left(x+\accel\right)/\accel$ at height $x$.
 The energy radiated inpassing from the surface to the pair production front can be computed from (30)) or (34))., The energy radiated inpassing from the surface to the pair production front can be computed from \ref{schwinger1}) ) or \ref{schwinger2}) ).
" For emission at 2-€= µ. a simple approximation can be found by first transforming into the particle rest frame at proper time To=(aJc)tanh”! QD. when it has reached the position x=and a Lorentz factor yo=xo+a"") /e."," For emission at $\bm{n}\cdot\hat{\bm{x}}=\mu$ , a simple approximation can be found by first transforming into the particle rest frame at proper time $\tau_0=\left(\accel/c\right)\textrm{tanh}^{-1}\left(\mu\right)$ , when it has reached the position $x_0=\accel\left[\cosh\left(c\tau_0/\accel\right)-1\right]$and a Lorentz factor $\gamma_0=\left(x_0+\accel\right)/\accel$ ."
 Denoting coordinates in this frame by GV. /). the trajectoryis," Denoting coordinates in this frame by $(x',t')$ , the trajectoryis"
In aclelition. we demonstrate the ellect of changing velocity. distribution.,"In addition, we demonstrate the effect of changing velocity distribution."
 As we use the bi-Maxwellian. clistribution proposed by 7.. to demonstrate the dependence of our results on the velocity distribution. we decided to change relative contributions of the two constituents.," As we use the bi-Maxwellian distribution proposed by , to demonstrate the dependence of our results on the velocity distribution, we decided to change relative contributions of the two constituents."
" In. Fie. the horizontal axis shows w, the contribution of the Iow-velocity part of the bi-Maxwellian distribution.", In \ref{results:numerical} the horizontal axis shows $w_1$ – the contribution of the low-velocity part of the bi-Maxwellian distribution.
" For wy,=0 we have a pure Maxwellian distribution with o—500kmsο. [ος οἱ21 a pure Maxwellian with στοὐkmst."," For $w_1=0$ we have a pure Maxwellian distribution with $\sigma= 500\ \kmps$, for $w_1=1$ – a pure Maxwellian with $\sigma= 90\ \kmps$."
 We show results of calculations for two clistributions of initial magnetic fields. described above (sec.2.1.2)., We show results of calculations for two distributions of initial magnetic fields described above (sec.2.1.2).
 The first is just a delta-function po1077 GG em., The first is just a delta-function $\mu=10^{30}$ G $^3$.
 B corresponds to the typical assumption mace in 90s., It corresponds to the typical assumption made in 90s.
 The second is based on recent results by?., The second is based on recent results by.
. Fractions of Ejectors. Propellers. subsonic Propellers. Accretors and Cieorotators demonstrate monotonic. nearly [linear behavior.," Fractions of Ejectors, Propellers, subsonic Propellers, Accretors and Georotators demonstrate monotonic, nearly linear behavior."
 The number of Ejectors strongly. decreases. with increasing wy., The number of Ejectors strongly decreases with increasing $w_1$.
 The behavior of Accretors ancl subsonic Propellers is opposite., The behavior of Accretors and subsonic Propellers is opposite.
 The behavior for the two studied. field distributions is similar in the cases of Aceretors. Ejectors. and subsonic Propellers.," The behavior for the two studied field distributions is similar in the cases of Accretors, Ejectors, and subsonic Propellers."
 In. the case of Propellers ancl Georotators the situation is different for two clistributions., In the case of Propellers and Georotators the situation is different for two distributions.
 In the most realistic case according to?.. wp=04 we have (in the case of initially cdecaved field clistribution) 55A of Ejectors. ~5% of supersonic and. ~20% of subsonic Propellers. 10% of Acerctors. and finally. 10% of Georotators.," In the most realistic case according to, – $w_1=0.4$ – we have (in the case of initially decayed field distribution) $\sim 55$ of Ejectors, $\sim 5$ of supersonic and $\sim 20$ of subsonic Propellers, $\sim 10$ of Accretors, and finally, $\sim 10$ of Georotators."
" As we sec. now for our ""the best choice” model we predict. more Accretors than in Paper Lt is what was expected on the basis of the semianalvtical model."," As we see, now for our “the best choice” model we predict more Accretors than in Paper I. It is what was expected on the basis of the semianalytical model."
 The increase in the relative number οἱ Accretors is due to the presence of INSs with large initial magnetic fields., The increase in the relative number of Accretors is due to the presence of INSs with large initial magnetic fields.
 This is illustrated in Iig.3.., This is illustrated in \ref{results: magnet}.
 We show there contributions of INSs with dillerent initial magnetic fields to the population of Xccretors., We show there contributions of INSs with different initial magnetic fields to the population of Accretors.
 Note. that the scale is logarithnic in both axis.," Note, that the scale is logarithmic in both axis."
 INSs with initial fields <31077 € are," INSs with initial fields $< 3\,10^{12}$ G are"
which is the focus of the next subsection.,which is the focus of the next subsection.
" In order to obtain a physically meaningful picture of a possible connection between rotation and activity. we derived relative Io. Iuminosiües Lj/L,4) rom the measured Ila EW."," In order to obtain a physically meaningful picture of a possible connection between rotation and activity, we derived relative $\alpha$ luminosities $L_{\mathrm{H}\alpha} / L_\mathrm{bol}$ ) from the measured $\alpha$ EW."
 We focused on the objects with clear chromospheric Hla. emission. and therefore excluded stars with spectral (wpe earlier than Ix2 (see relevact)).," We focused on the objects with clear chromospheric $\alpha$ emission, and therefore excluded stars with spectral type earlier than K2 (see \\ref{evact}) )."
 In a first step. we corrected the EW lor photospheric absorpüon. using the correlation between photospheric Wa absorption and spectral tvpes derived in relevact [rom non-active reference stars (see dotted line in Fig. 3)).," In a first step, we corrected the EW for photospheric absorption, using the correlation between photospheric $\alpha$ absorption and spectral types derived in \\ref{evact} from non-active reference stars (see dotted line in Fig. \ref{f4}) )."
 Objects with corrected EW «0.5 and thus insignificant chromospheric emission were excluded., Objects with corrected EW $<0.5$ and thus insignificant chromospheric emission were excluded.
 The continuum at the wavelength of Ha was estimated using the STAR«dusty1999 model spectra. which are based on the NextGen moclels refreshed with new water and TiO opacities (Allardetal.2000)..," The continuum at the wavelength of $\alpha$ was estimated using the STARdusty1999 model spectra, which are based on the NextGen models refreshed with new water and TiO opacities \citep{2000ApJ...540.1005A}."
 We measured the continuum flux al [or effective temperatures ranging [rom 30000 to NIX and logg=4.0 bv approximating (he spectrum around Io with a linear fit., We measured the continuum flux at for effective temperatures ranging from 000 to K and $\log g = 4.0$ by approximating the spectrum around $\alpha$ with a linear fit.
 This value was divided by (he bolometric luminosity for the respective elfective temperature., This value was divided by the bolometric luminosity for the respective effective temperature.
" As a result.we obtain scaling factors as a function ol elfective temperature to convert the Ila EW to Ly,/L,,4."," As a result,we obtain scaling factors as a function of effective temperature to convert the $\alpha$ EW to $L_{\mathrm{H}\alpha} / L_\mathrm{bol}$."
 Please note that this conversion depends neither on the radii of the objects nor on the distances. which are poorly constrained for many of our targets.," Please note that this conversion depends neither on the radii of the objects nor on the distances, which are poorly constrained for many of our targets."
 The ellective temperatures for our targets will be published in a forthcoming paper. see re[t ar..," The effective temperatures for our targets will be published in a forthcoming paper, see \\ref{tar}."
 Fie., Fig.
 7 shows the relative Ha huminosities as a function of esin/., \ref{f8} shows the relative $\alpha$ luminosities as a function of $v\sin i$.
 Please note (hat bv excluding non-active (earlier (wpe) objects. the clear majority of the objects in (he plot is fully convective.," Please note that by excluding non-active (earlier type) objects, the clear majority of the objects in the plot is fully convective."
 While the lower activity limit in this plot is a detection limit. the upper limit is reliably determined and can be compared with published samples.," While the lower activity limit in this plot is a detection limit, the upper limit is reliably determined and can be compared with published samples."
 In our sample. we obtain ~3x10' excluding the datapoint for 110. which possibly is affected by aflare event (see relvar)).," In our sample, we obtain $\sim 3 \times 10^{-4}$, excluding the datapoint for 10, which possibly is affected by aflare event (see \\ref{var}) )."
 For the mass ranee of our sample. (his value is roughly comparable with the upper limit in the Pleiades (ILodgkinetal.1995).. but clearly higher than in the Ivades ( 19970). again indicating a decline of the general activity with age. as already. discussed in relevact..," For the mass range of our sample, this value is roughly comparable with the upper limit in the Pleiades \citep{1995MNRAS.274..869H}, but clearly higher than in the Hyades \citep[$\sim 1.4 \times 10^{-4}$ , again indicating a decline of the general activity with age, as already discussed in \\ref{evact}. ."
 As can be seen in Fig. 7.. ," As can be seen in Fig. \ref{f8}, ,"
the upper limit of the range in activities is mostly flat., the upper limit of the range in activities is mostly flat.
 Thus.," Thus,"
We- lave also searched for. possible. correlations. betweenUnsο the X-ray huninosity aud the spectral index (fig.,"We have also searched for possible correlations between, the X-ray luminosity and the spectral index (fig."
 1)., 1).
 The spectral iudex im both soft and hard hands senis to be correlated to. while only a weal trend between the excess variance aud the ΕΕ is present.," The spectral index in both soft and hard bands seems to be correlated to, while only a weak trend between the excess variance and the luminosity is present."
 These results. which necd to be supported by further studies with a larger sample. appears to be inconsistent with the ASC'A results (Leighly 1999). where the excess variance σDUns is anticorrelated with the ταν Iuuinosity.," These results, which need to be supported by further studies with a larger sample, appears to be inconsistent with the ASCA results (Leighly 1999), where the excess variance $\sigma^{2}_{rms}$ is anticorrelated with the X-ray luminosity."
 From the spectral analysis of a sample of seven NLSIs observed by BeppoSAX. we confit that they have steeper spectral iudices aud faster X-ray variability with respect to BLSIs.," From the spectral analysis of a sample of seven NLS1s observed by BeppoSAX, we confirm that they have steeper spectral indices and faster X-ray variability with respect to BLS1s."
 The present results fit with the idea that NLS1s are powered by a relatively s102ll central black hole accreting near the Eddington limit., The present results fit with the idea that NLS1s are powered by a relatively small central black hole accreting near the Eddington limit.
solar atmosphere trieecr nuclear reactions. with relativistic positrons |seine one of the products of such interacions (Liugeufelter&Ramaty1967:IKozlovskyctal.Ww 102).,"solar atmosphere trigger nuclear reactions, with relativistic positrons being one of the products of such interactions \citep{Lingenfelter_Ramaty_1967, Kozlovsky_etal_2002}."
. These xc‘lativistic positrons are capable of producing sub-TIIz svuclirotrou radiation with a peak frequency aroun FreakFer? where fr. is the electron exvrofrequency and 5 is the Loreuz-factor. as sugeested by LingeufΜο&Ramaty(1967).," These relativistic positrons are capable of producing sub-THz synchrotron radiation with a peak frequency around $f_{peak}{\sim}f_{Be}\gamma^2$, where $f_{Be}$ is the electron gyrofrequency and $\gamma$ is the Lorenz-factor, as suggested by \citet{Lingenfelter_Ramaty_1967}."
. Althoush the svnchrotron peak frequency can easily fall iuto. the μιib-TIIz or THz range (Trottet considering typical maeuetic field (D— GC) aud Lorenz-factors 5~20. the low-frequeney svuchrotron specti1uà. Fyxflo. Figure 3((aj. is inconsistent with the whole range of the observed spectral index values uuless we adopt au additional absorption mechanisin leading to a sharper spectral shape.," Although the synchrotron peak frequency can easily fall into the sub-THz or THz range \citep{Trottet_etal_2008} considering typical magnetic field $B\sim1000$ G) and Lorenz-factors $\gamma\sim20$, the low-frequency synchrotron spectrum, $F_f{\propto}f^{1/3}$, Figure \ref{FIG_SR}( (a), is inconsistent with the whole range of the observed spectral index values unless we adopt an additional absorption mechanism leading to a sharper spectral shape."
" The only viable absorption mcechanisia is frec-free absorption. wlth again requires Ligh plasma density. ~1072 ""s Figure 2(00)."," The only viable absorption mechanism is free-free absorption, which again requires high plasma density, $\sim10^{12}$ $^{-3}$, Figure \ref{FIG_SR}( (b)."
 Even though a combination of ιο svuchrotron radiation frou relativistic positrous and free-free absorption ds capable of producing the required spectral shape. the correct flux density requires more relativistic positrons than seems to be available from nuclear interactions even in large flares.," Even though a combination of the synchrotron radiation from relativistic positrons and free-free absorption is capable of producing the required spectral shape, the correct flux density requires more relativistic positrons than seems to be available from nuclear interactions even in large flares."
 The total number of enersetic protons above 30 MeV for large solar flares as deduced from RITESSI observations is iu the range 1079—107 (e.g.Shihetal.2009). which is colparable to the instantaneous πο of positronus with Loreutz factor. >=20 required to explain observed sub-anillineter fixes.," The total number of energetic protons above 30 MeV for large solar flares as deduced from RHESSI observations is in the range $10^{29}-10^{33}$ \citep[e.g.][]{Shih_etal2009}, which is comparable to the instantaneous number of positrons with Lorentz factor, $\gamma=20$ required to explain observed sub-millimeter fluxes."
 The total thick-tarect positron yield is about 107 per proton of enerev above 10 MeV (IXozlovskyw—etal.2001).. so the total πο of positrons produced in a fare should be 10%.," The total thick-target positron yield is about $10^{-2}-10^{-4}$ per proton of energy above 10 MeV \citep{Kozlovsky_etal2004}, so the total number of positrons produced in a flare should be $\lesssim10^{31}$."
 Since the positron lifetime in a dense positron-production< site is likely to be less than duratiou ofa fare. the instantaneous positron number of ~10°! is difficult to achieve. uuless we allow a sienificant fraction of relativistic positrous to escape to aud then be trapped at a tenuous coronal part of the flaring loop. where the positrou lifetime is uch longer.," Since the positron lifetime in a dense positron-production site is likely to be less than duration of a flare, the instantaneous positron number of $\sim10^{31}$ is difficult to achieve, unless we allow a significant fraction of relativistic positrons to escape to and then be trapped at a tenuous coronal part of the flaring loop, where the positron lifetime is much longer."
 Svuchrotrou radiation from relativistic positrous is easily consistent with small sizes if the emission, Synchrotron radiation from relativistic positrons is easily consistent with small sizes if the emission
did not apply k-corrections. which become significant for the highest luminosity galaxies in their sample.,"did not apply k-corrections, which become significant for the highest luminosity galaxies in their sample."
 The second issue is that some of these galaxies have relatively Dat racio spectra. so correcting those observed at high redshift. back to 6GlIz using a nominal slope of 0.7 does not provide a good estimate.," The second issue is that some of these galaxies have relatively flat radio spectra, so correcting those observed at high redshift back to GHz using a nominal slope of $-0.7$ does not provide a good estimate."
 When nominal k-corrections are applied to the Yun et. al., When nominal k-corrections are applied to the Yun et al.
 sample. the best. fit ULIRG ratio of LoopfLiacga is 140.," sample, the best fit ULIRG ratio of $L_{\rm 60\um}/L_{\rm 1.4GHz}$ is $\sim140$."
 We have used the observations of Condon et al. (, We have used the observations of Condon et al. (
1991) to determine a more accurate slope.,1991) to determine a more accurate slope.
 We find a final ratio of Loogim/Liacgs=128 for a galaxy ab zo2 observed at 1.4CLIz ancl corrected. as if it had a slope of 0.7., We find a final ratio of $L_{\rm 60\um}/L_{\rm 1.4GHz} = 128$ for a galaxy at $z\sim2$ observed at GHz and corrected as if it had a slope of $-0.7$.
 This result. would. imply that the SETs estimated. above using the standard local ratio are uncder-estimated: by about ddex. a correction we have applied in our analvsis.," This result would imply that the SFRs estimated above using the standard local ratio are under-estimated by about dex, a correction we have applied in our analysis."
 After these corrections and our choice of a IME. our conversion from radio luminosity. to SER is 0.07 dex less than that of Bell (2003). [for a given racio luminosity we assume a SER 0.84 times that predicted by Bell (2003).," After these corrections and our choice of a IMF, our conversion from radio luminosity to SFR is $0.07\,$ dex less than that of Bell (2003), for a given radio luminosity we assume a SFR 0.84 times that predicted by Bell (2003)."
 We plot the SPRs of our SEG sample against redshift in Figure 4((a) using different svmbols for objects of cdillerent stellar masses., We plot the SFRs of our SFG sample against redshift in Figure \ref{fig:zsfr}( (a) using different symbols for objects of different stellar masses.
 Stellar mass estimates are calculated for the 138 sample of SECs by normalising a MS2 SED to our IRAC 3.65. fluxes Cy band for S sources not. covered by theSpifzer data) ane using a IME to determine a rest-frame Jf band luminosities and assuming a MS2 mass-to-(// band)-light ratio.," Stellar mass estimates are calculated for the $13^{\rm H}$ sample of SFGs by normalising a M82 SED to our IRAC $3.6\,\um$ fluxes $K-$ band for 8 sources not covered by the data) and using a IMF to determine a rest-frame $H-$ band luminosities and assuming a M82 $H-$ band)-light ratio."
 Similarly. we derived stellar masses for the Gell-NVSS sample from their observed ἐν band magnitudes assuming the same MS2 SED and nmiass-to-light-ratio.," Similarly, we derived stellar masses for the 6df-NVSS sample from their observed $K-$ band magnitudes assuming the same M82 SED and mass-to-light-ratio."
 Clearly using one mass-to-light ratio for a sample of ealaxies with a range of SETIts. amongst other »operties. is not ideal. but this approach sullices for the current investigation.," Clearly using one mass-to-light ratio for a sample of galaxies with a range of SFRs, amongst other properties, is not ideal, but this approach suffices for the current investigation."
 The possible selection effects of this choice are discussed in section 5.3.1.., The possible selection effects of this choice are discussed in section \ref{sec.se}.
 We [ind two striking results., We find two striking results.
 Firstly. there are many very righ SER. 300A4. vr.1. sources above z=1 compared to he local Universe.," Firstly, there are many very high SFR, $>300\,M_\odot$ $^{-1}$, sources above $z=1$ compared to the local Universe."
 The GdE-NVSS Survey covers a large area of the sky. 17/4. equivalent to ~TGpc? τος =03. rence is not biased against detecting rare. exceptionally ugh SER. sources.," The 6dF-NVSS Survey covers a large area of the sky, $17\%$ equivalent to $\sim7\,$ $^3$ to $z=0.3$, hence is not biased against detecting rare, exceptionally high SFR sources."
 Therefore. the lack of exceptionally. high SER sources locally is not a volume selection cllect and he presence of very high SER. galaxies at high redshift is observed in surveys at other wavelengths2006).," Therefore, the lack of exceptionally high SFR sources locally is not a volume selection effect and the presence of very high SFR galaxies at high redshift is observed in surveys at other wavelengths."
. Secondly. all our high SER. galaxies have very high. stellar masses.," Secondly, all our high SFR galaxies have very high stellar masses."
 We discuss this result more within the framework of current galaxy evolution moclels in Section 5.3.., We discuss this result more within the framework of current galaxy evolution models in Section \ref{sec.mvsfr}.
 We can compare the SER against stellar mass lor roth our. sample of SECs and the 6d[-NVSS sample in Figure 4((b) anc we find that a trend of SER. correlating with stellar mass is apparent in both samples from the local Universe up to z Z3)., We can compare the SFR against stellar mass for both our sample of SFGs and the 6df-NVSS sample in Figure \ref{fig:zsfr}( (b) and we find that a trend of SFR correlating with stellar mass is apparent in both samples from the local Universe up to $z\la 3$ ).
 As radio Dux limited surveys will always sample the highest SER objects at any eiven redshift. this result is consistent with the idea that here is an upper limit to the SER of a galaxy of a given mass.," As radio flux limited surveys will always sample the highest SFR objects at any given redshift, this result is consistent with the idea that there is an upper limit to the SFR of a galaxy of a given mass."
 We see a similar trend in the results of who find à “main sequence” relation between SER and stellar mass at a given. redshift. with increasing SET observed at higher stellar masses., We see a similar trend in the results of who find a “main sequence” relation between SFR and stellar mass at a given redshift with increasing SFR observed at higher stellar masses.
 Phe hypothesis that lower nmiass galaxies can only achieve lower maximum SEIts could be explained by the fact that more massive galaxies generally have more barvons in gas and dust which can act as raw, The hypothesis that lower mass galaxies can only achieve lower maximum SFRs could be explained by the fact that more massive galaxies generally have more baryons in gas and dust which can act as raw
for the mean redshift from our SDSS DR7 sample of K+A galaxies. would only allow us to detect star formation rates in excess of 30M. |.,"for the mean redshift from our SDSS DR7 sample of K+A galaxies, would only allow us to detect star formation rates in excess of 30 $_{\odot}$ $^{-1}$."
 For each of the 811 ΚΑ galaxies covered by the survey we cut out a 1 square from the FIRST database., For each of the 811 K+A galaxies covered by the survey we cut out a $1'$ square from the FIRST database.
 We use the median stacking method of Whiteetal.(2007) το create the resulting image of 811 K+A galaxies shown in the left panel of Fig. 1.., We use the median stacking method of \cite{white07} 	 to create the resulting image of 811 K+A galaxies shown in the left panel of Fig. \ref{stackedFits}.
 We then measure the flux from the combined image in an aperture equivalent to three FIRST beams from which we derive an average KA flux of 56+9 jiJy., We then measure the flux from the combined image in an aperture equivalent to three FIRST beams from which we derive an average K+A flux of $56\pm9$ $\mu$ Jy.
 To assess the significance of this result. we need to estimate the level of noise in the image.," To assess the significance of this result, we need to estimate the level of noise in the image."
 As FIRST is a survey. the image cutouts may not be fully cleaned of artifacts. such as side-lobes from distant radio sources.," As FIRST is a survey, the image cutouts may not be fully cleaned of artifacts, such as side-lobes from distant radio sources."
 To do this. we use a Monte Carlo simulation with a sample of known radio-quiet objects. 8495 white dwarfs from the SDSS (Eisensteinetal. 2006).," To do this, we use a Monte Carlo simulation with a sample of known radio-quiet objects, 8495 white dwarfs from the SDSS \citep{eisenstein06}."
. We create 10.000 stacks of 811 randomly selected white dwarfs (equivalent to the stack of K+A galaxies) and measure the flux in the same fashion to derive the mean flux from a supposedly radio-quiet sample.," We create 10,000 stacks of 811 randomly selected white dwarfs (equivalent to the stack of K+A galaxies) and measure the flux in the same fashion to derive the mean flux from a supposedly radio-quiet sample."
 This procedure allows us to estimate the level of noise present in the stacked image and therefore to determine the significance of our detection for K+A galaxies., This procedure allows us to estimate the level of noise present in the stacked image and therefore to determine the significance of our detection for K+A galaxies.
 A histogram of the fluxes from our Monte Carlo simulation is shown in Fig. 2.., A histogram of the fluxes from our Monte Carlo simulation is shown in Fig. \ref{wdHist}.
 Since we know that these sources are radio quiet. we can estimate à 5c significance flux for sources to be considered real.," Since we know that these sources are radio quiet, we can estimate a $5\sigma$ significance flux for sources to be considered real."
 We find this flux to be 13 Jy., We find this flux to be $43$ $\mu$ Jy.
 Our K+A stack is found to have a significant detection above the 56 noise level., Our K+A stack is found to have a significant detection above the $\sigma$ noise level.
 We can now compute the absolute lummosity at 1.4 GHz using our chosen cosmology and the average redshift of the K+A galaxies (2= 0.11)., We can now compute the absolute luminosity at 1.4 GHz using our chosen cosmology and the average redshift of the K+A galaxies $z=0.14$ ).
" where D; is the luminosity distance. Syτομ. 1s the flux density. (1|:)"" is the color correction and 1/(1|:) the bandwidth correction (Morrisonetal.2003)."," where $D_L$ is the luminosity distance, $S_{1.4 GHz}$ is the flux density, $(1+z)^{\alpha}$ is the color correction and $1/(1+z)$ the bandwidth correction \citep{morrison03}."
. We assume that the radio emission is dominated by synchrotron radiation such that Sx9? (Condon1992)., We assume that the radio emission is dominated by synchrotron radiation such that $S \propto \nu^{-0.8}$ \citep{condon92}.
. This yields our measurement of radio power. which we can convert to a SFR using from Yunetal.(2001).. which assumes a Salpeter initial mass function between 0.1 and 100 solar masses.," This yields our measurement of radio power, which we can convert to a SFR using from \cite{yun01}, which assumes a Salpeter initial mass function between 0.1 and 100 solar masses."
 This yields a star formation rate of 1.640:3 M.. + for our average ΚΑ galaxy at :>=0.11., This yields a star formation rate of $1.6 \pm 0.3$ $_{\odot}$ $^{-1}$ for our average K+A galaxy at $<z>=0.14$.
 However 79 of our sources are measured to have 1.4 GHz fluxes above the 30 noise level of the FIRST survey., However 79 of our sources are measured to have 1.4 GHz fluxes above the $\sigma$ noise level of the FIRST survey.
 The FIRST beam has an RMS of0.15 mJy and we find 79 galaxies (~10%)) have aperture fluxes in excess of 30 (450 jy) within an aperture of 3 beamsizes. 31 of which have fluxes in excess of Sa (750 jiJy).," The FIRST beam has an RMS of 0.15 mJy and we find 79 galaxies $\sim$ ) have aperture fluxes in excess of $\sigma$ (450 $\mu$ Jy) within an aperture of 3 beamsizes, 31 of which have fluxes in excess of $\sigma$ (750 $\mu$ Jy)."
 In Fig., In Fig.
 3. we show the redshift-luminosity distribution of the targets with aperture fluxes above the 36 and 5a limits., \ref{luminosityZ} we show the redshift–luminosity distribution of the targets with aperture fluxes above the $3\sigma$ and $5\sigma$ limits.
 Visual inspection of these individual outlier frames have shown that for the 31 galaxies above the 5o limit. about look like clear individual detections (1.e.. centrally concentrated. likely to be associated with our optical target. not in à frame that is significantly noisy). while for the 48 that are above the 30 limit but less than the Sa limit. only about of these are clear detections.," Visual inspection of these individual outlier frames have shown that for the 31 galaxies above the $\sigma$ limit, about look like clear individual detections (i.e., centrally concentrated, likely to be associated with our optical target, not in a frame that is significantly noisy), while for the 48 that are above the $\sigma$ limit but less than the $\sigma$ limit, only about of these are clear detections."
 Overall only about of our sample of 811 galaxies show evidence of significant ongoing radio activity. either from star formation or AGN activity.," Overall only about of our sample of 811 galaxies show evidence of significant ongoing radio activity, either from star formation or AGN activity."
 Removing all sources with measured fluxes in excess of 5c. we create a subsample of 780 galaxies.," Removing all sources with measured fluxes in excess of $\sigma$, we create a subsample of 780 galaxies."
 Stacking this subsample yields a mean flux of 36 j/Jy. which ts well below the 5o detection limit of 47 ;Jy found from a Monte Carlo simulation creating stacks of 780 white dwarfs.," Stacking this subsample yields a mean flux of 36 $\mu$ Jy, which is well below the $\sigma$ detection limit of 47 $\mu$ Jy found from a Monte Carlo simulation creating stacks of 780 white dwarfs."
 We can place an upper limit on the SFR of 1.3 .. + for this subsample with <:2-—U.1l., We can place an upper limit on the SFR of $1.3$ $_{\odot}$ $^{-1}$ for this subsample with $<z> = 0.14$.
" When star formation ceases in a galaxy. we expect it to decrease exponentially to low levels. rather than an abrupt truncation. unless some ""catastrophic? event has removed all the available fuel or ionized the gas and prevented further star formation."," When star formation ceases in a galaxy, we expect it to decrease exponentially to low levels, rather than an abrupt truncation, unless some `catastrophic' event has removed all the available fuel or ionized the gas and prevented further star formation."
 Evidence for a rapid shutdown of star formation in these galaxies has been presented by Brownetal.(2009)., Evidence for a rapid shutdown of star formation in these galaxies has been presented by \cite{brown09}.
" We therefore carry out the same analysis on a subsample of young"" K+A galaxies and attempt to detect residual star formation in these objects.", We therefore carry out the same analysis on a subsample of `young' K+A galaxies and attempt to detect residual star formation in these objects.
 In Fig. 4..," In Fig. \ref{agePlot},"
 we plot Hó and D4000 from SDSS spectra and overplot models calculated with GALAXEV (Bruzual&Charlot2003)., we plot $\delta$ and D4000 from SDSS spectra and overplot models calculated with GALAXEV \citep{bruzual2003}.
. We plot the galaxies with significant 1.4 GHz detections as red squares. the rest as gray dots.," We plot the galaxies with significant 1.4 GHz detections as red squares, the rest as gray dots."
 We adopt a Salpeter initial. mass function (IMF) and solar metallicity as initial conditions., We adopt a Salpeter initial mass function (IMF) and solar metallicity as initial conditions.
 The model galaxies evolved over 10 Gyr with an exponentially decreasing star formation rate (7 = | Gyr)., The model galaxies evolved over 10 Gyr with an exponentially decreasing star formation rate $\tau$ = 1 Gyr).
 At 10 Gyr. we added an instantaneous starburst (delta function) of mass 1. 5. 10. 30 and (relative to the old stellar population) after which the SFR returns to zero.," At 10 Gyr, we added an instantaneous starburst (delta function) of mass 1, 5, 10, 30 and (relative to the old stellar population) after which the SFR returns to zero."
 The dotted lines demarcate the values of the spectral indices observed 30. 50. 100. 250 and 500 Myr after the burst.," The dotted lines demarcate the values of the spectral indices observed 30, 50, 100, 250 and 500 Myr after the burst."
 These are the same models used by Yagietal.(2006) and al.(2008)., These are the same models used by \cite{yagi2006} and \cite{goto2008}.
. We then select the 456 K+A galaxies with burst ages less than 250 Myr and an average redshift of <2>=(113 and stack these galaxies in the same fashion as the complete sample., We then select the 456 K+A galaxies with burst ages less than 250 Myr and an average redshift of $<z> = 0.13$ and stack these galaxies in the same fashion as the complete sample.
 The stacked image is shown in the right panel of Fig., The stacked image is shown in the right panel of Fig.
 1. from which we measure a mean flux of 61 sry., \ref{stackedFits} from which we measure a mean flux of 61 $\mu$ Jy.
 The Monte Carlo simulation with white dwarfs gives a 5c detection limit of 59 μὴν., The Monte Carlo simulation with white dwarfs gives a $\sigma$ detection limit of 59 $\mu$ Jy.
 Our younger sample of K+A galaxies 1s found to be at the 5o detection limit. giving a SFR of 1.5+ 0.3M.. yr. +.," Our younger sample of K+A galaxies is found to be at the $5\sigma$ detection limit, giving a SFR of $1.5~\pm~0.3$ $_{\odot}$ $^{-1}$ ."
 This is consistent with a rapid decline of star formation in these galaxies as shown by Brown (2009)., This is consistent with a rapid decline of star formation in these galaxies as shown by \cite{brown09}.
 We have found an average star formation rate of only 1.6 ΕΜ. yr+t from stacking radio observations of 811field K+A galaxies in the local universe., We have found an average star formation rate of only $1.6~\pm~0.3$ $_{\odot}$ $^{-1}$ from stacking radio observations of 811 K+A galaxies in the local universe.
 However. much of this signal appears to originate from ~4% of active galaxies.," However, much of this signal appears to originate from $\sim$ of active galaxies."
 Based on the definition of Sadleretal. (2002).. which requires radio power above 10°? W | and the absence of emission lines. this sample is approximately equally split between star forming galaxies and AGN (with the latter more prominent at higher redshifts because of selection effects).," Based on the definition of \cite{sadler02}, which requires radio power above $10^{23}$ W $^{-1}$ and the absence of emission lines, this sample is approximately equally split between star forming galaxies and AGN (with the latter more prominent at higher redshifts because of selection effects)."
 For the remainder of the sample. we find an upper limit on the SFR of 1.34 M... yr+.," For the remainder of the sample, we find an upper limit on the SFR of 1.4 $_{\odot}$ $^{-1}$."
 Even a subsample of spectroscopically young galaxies does not show a significant detection of residual star formation., Even a subsample of spectroscopically young galaxies does not show a significant detection of residual star formation.
 Our results are in good agreement with previous work., Our results are in good agreement with previous work.
 Goto did not detect evidence of star formation from VLA observations in 36 galaxies drawn from the SDSS DRI but he was able to set an upper limitof <15 M.. yr+ for 15 of the nearest K+A galaxies., \cite{goto04} did not detect evidence of star formation from VLA observations in 36 galaxies drawn from the SDSS DR1 \citep{goto03} but he was able to set an upper limitof $< 15$ $_\odot$ $^{-1}$ for 15 of the nearest K+A galaxies.
 Miller found that only 2 out of 15 K+A galaxies in his sample show signs of obscured star formation., \cite{miller01} found that only 2 out of 15 K+A galaxies in his sample show signs of obscured star formation.
 Nevertheless.," Nevertheless,"
In all three datasets. the multi-band fluxes of a given object were effectively measured in identical physical apertures outside the atmosphere (and with identical spatial weighting) for all filters. assuming that seeing produces a Gaussian-shaped PSF.,"In all three datasets, the multi-band fluxes of a given object were effectively measured in identical physical apertures outside the atmosphere (and with identical spatial weighting) for all filters, assuming that seeing produces a Gaussian-shaped PSF."
 Colours could still be biased by non-Gaussianity of the PSF and by suboptimal background subtraction., Colours could still be biased by non-Gaussianity of the PSF and by suboptimal background subtraction.
 The properties of these three imaging datasets are summarised in Table |.., The properties of these three imaging datasets are summarised in Table \ref{tab:imaging}.
 Since the limiting magnitudes are estimated in completely different ways in the three data release papers. we decided to calculate hypothetical 10cm limiting magnitudes with the GaBoDS values as a reference.," Since the limiting magnitudes are estimated in completely different ways in the three data release papers, we decided to calculate hypothetical $\sigma$ limiting magnitudes with the GaBoDS values as a reference."
 These Miner correspond to the IOc sky noise under the following assumption: with G denoting GaBoDS quantities and X denoting quantities of the other dataset.," These $m_{\mathrm{lim,eff}}$ correspond to the $\sigma$ sky noise under the following assumption: with $\mathrm{G}$ denoting GaBoDS quantities and $\mathrm{X}$ denoting quantities of the other dataset."
 FWHM is the measured seeing. fosp Is the exposure time. and D is the diameter of the telescope.," FWHM is the measured seeing, $t_{\mathrm{exp}}$ is the exposure time, and $D$ is the diameter of the telescope."
 By doing so we neglect differences between similar filter transmission curves and variations in observing conditions (moon. sky transparency ete.)," By doing so we neglect differences between similar filter transmission curves and variations in observing conditions (moon, sky transparency etc.)"
" Thus. the limiting magnitudes are only rough estimates for approximate comparison,"," Thus, the limiting magnitudes are only rough estimates for approximate comparison."
 The ΕΡΕ limiting magnitudes in the ZJKs-bands are the ones given in?) and ?) corresponding to completeness.," The FDF limiting magnitudes in the $ZJKs$ -bands are the ones given in \cite{2003A&A...398...49H} and \cite{2004Gabasch_PhD_Thesis}
 corresponding to completeness."
 The dependence of photometric errors on magnitude and redshift in the three datasets 1s shown in Fig. |.., The dependence of photometric errors on magnitude and redshift in the three datasets is shown in Fig. \ref{fig:errors}.
 The errors for the COMBO data are derived from multiple measurements of the same sources. where photon shot-noise is assumed to be a lower limit.," The errors for the COMBO data are derived from multiple measurements of the same sources, where photon shot-noise is assumed to be a lower limit."
 The GaBoDS and FDF errors are purely derived from shot-noise as no multiple measurements were made., The GaBoDS and FDF errors are purely derived from shot-noise as no multiple measurements were made.
energetic electron beams impinging at the sites of higher densitv and strong magnetic fields.,energetic electron beams impinging at the sites of higher density and strong magnetic fields.
 In a recent. study. (Alaurva&Ambastha2009.hereafterMAO)... we had discovered moving (ransient magnetic and Doppler velocity features during the peak-phases of two major N17/4B and X10/2D white light [lares (WLE) of 2003 October 28 and 29. respectively. in NOAA 10486.," In a recent study \citep[][hereafter MA09]{Maurya2009}, we had discovered moving transient magnetic and Doppler velocity features during the peak-phases of two major X17/4B and X10/2B white light flares (WLF) of 2003 October 28 and 29, respectively, in NOAA 10486."
 IIXR. sources were also observed. during these flares., HXR sources were also observed during these flares.
 For the flare of 2003 October 28. the IIXI. sources showed a separation of 2223 Main matching well with the chromospheric Ho flare ribbons.," For the flare of 2003 October 28, the HXR sources showed a separation of $\approx23$ Mm matching well with the chromospheric $\alpha$ flare ribbons."
 This observation is consistent with the flare mocdels (hat sugeest formation of INR [ootpoint sources in the chromosphere or lower corona depending on the enerev of penetrating particles., This observation is consistent with the flare models that suggest formation of HXR footpoint sources in the chromosphere or lower corona depending on the energy of penetrating particles.
 The magnetic and Doppler velocity transients. on the other hand. showed a somewhat greater separation of zz20 MMm similar to the photospheric WLE kernels.," The magnetic and Doppler velocity transients, on the other hand, showed a somewhat greater separation of $\approx29$ Mm similar to the photospheric WLF kernels."
 At the transients’ sites. we detected anomalous magnetic polarity sign reversals during the impulsive phases of these flares.," At the transients' sites, we detected anomalous magnetic polarity sign reversals during the impulsive phases of these flares."
 The transients were first detected at the weaker field location of polarity reversal line (PIL). and not in the cooler. stronger magnetic field sites of sunspot umbra/penumbra. as found earlier by Qiu&Gary.(2003).," The transients were first detected at the weaker field location of polarity reversal line (PIL), and not in the cooler, stronger magnetic field sites of sunspot umbra/penumbra, as found earlier by \cite{Qiu2003}."
.. Llowever. as ihe flares in NOAA 10436 progressed. (he (ransients moved away from the PIL towards the stronger fields.," However, as the flares in NOAA 10486 progressed, the transients moved away from the PIL towards the stronger fields."
 We inferred from the analysis of the N17/4B flare of 2003 October 28 that the moving (rausients were better related to the INR: sources. ie.. the non-(hermal processes associated with electron-beam injection. and not to the WLF kernels. i.e.. thermal heating.," We inferred from the analysis of the X17/4B flare of 2003 October 28 that the moving transients were better related to the HXR sources, i.e., the non-thermal processes associated with electron-beam injection, and not to the WLF kernels, i.e., thermal heating."
 There have been a very [ew cases reported so far on the transient magnetic and Doppler velocily features driven by the flares., There have been a very few cases reported so far on the transient magnetic and Doppler velocity features driven by the flares.
" It appears (hat these transients mar reach detectable levels only in some very energetic. impulsive Πάνος,"," It appears that these transients may reach detectable levels only in some very energetic, impulsive flares."
 In. this paper. we report the detection ol a similar event associated with the first N-class flare of the current solar cycle 24.," In this paper, we report the detection of a similar event associated with the first X-class flare of the current solar cycle 24."
 This {wo-ribhon WL flare occurred in NOAA AR 11158 during its central meridian passage on 2011 February 15., This two-ribbon WL flare occurred in NOAA AR 11158 during its central meridian passage on 2011 February 15.
 [Tt was well observed by the Helioseismic ancl Magnetic Imager (IIMI) and Atmospheric Imaging Assembly (ALA) on hoard Solar Dynamics Observatory (900)., It was well observed by the Helioseismic and Magnetic Imager (HMI) and Atmospheric Imaging Assembly (AIA) on board Solar Dynamics Observatory (SDO).
 From the movies of high resolution magnetic and Doppler velocity images. we detected the transients appearing first near (he umbral boundary of the main sunspot.," From the movies of high resolution magnetic and Doppler velocity images, we detected the transients appearing first near the umbral boundary of the main sunspot."
 It persisted only for a few minutes during the peak phase of the Hare., It persisted only for a few minutes during the peak phase of the flare.
 As found earlier in MAO09. the magnetic polarity went through a sign reversal at the location of the transients.," As found earlier in MA09, the magnetic polarity went through a sign reversal at the location of the transients."
 The Doppler velocity. however. did not show such a sign reversal.," The Doppler velocity, however, did not show such a sign reversal."
 Instead. (here occurred a large magnitude velocity enhancement at the transients site.," Instead, there occurred a large magnitude velocity enhancement at the transient's site."
 Using multi-wavelength flare observation from SDO. we intend to study the association ol the observed transients with various signatures of the X2.2 flare of 2011 February 15.," Using multi-wavelength flare observation from SDO, we intend to study the association of the observed transients with various signatures of the X2.2 flare of 2011 February 15."
 The spectral data available from SDO-IIMI will also be used to investigate the changes in Stokes profiles occurring during the peak phase of the flare., The spectral data available from SDO-HMI will also be used to investigate the changes in Stokes profiles occurring during the peak phase of the flare.
 Characteristics of these transients will be examined to explain (heir cause ancl ellects using the present theoretical models., Characteristics of these transients will be examined to explain their cause and effects using the present theoretical models.
 The paper is, The paper is
a few M. ? to a few tens of M. 7 (Buat et al.,a few $_{\odot}$ $^{-2}$ to a few tens of $_{\odot}$ $^{-2}$ (Buat et al.
 1989) or up to a few hundreds of ML. 7 (Mureia et al., 1989) or up to a few hundreds of $_{\odot}$ $^{-2}$ (Murgia et al.
 2002)., 2002).
 Heiner et al. (, Heiner et al. (
2010) presented a new method in which the volume number densities in the gas clouds surrounding OB associations were determined using a model which considers the atomic hydrogen as a photodissociation product on the clouds surfaces and the UV huninosities were used as a proxy lor the SER.,2010) presented a new method in which the volume number densities in the gas clouds surrounding OB associations were determined using a model which considers the atomic hydrogen as a photodissociation product on the clouds surfaces and the UV luminosities were used as a proxy for the SFR.
 The latter authors obtained an exponent lor the Schmidt law of 1.4250.2., The latter authors obtained an exponent for the Schmidt law of $1.4 \pm 0.2$.
 Bigiel et al. (, Bigiel et al. (
"2008) combined GALEX ultraviolet and t 24 jm observations to derive the SER for a sample of nearby galaxies on scales of ~"") pc.",2008) combined GALEX ultraviolet and Spitzer 24 $\micron$ observations to derive the SFR for a sample of nearby galaxies on scales of $\sim 750$ pc.
" They derived X, using the HI observations of the TIIINGS survey (Walter et al.", They derived $\Sigma_{g}$ using the HI observations of the THINGS survey (Walter et al.
 200 and the CO emission by the DIMA survey of nearby galaxies. (Llelfer et al., 2008) and the CO emission by the BIMA survey of nearby galaxies (Helfer et al.
 2003) and the WERA CO-Line Extragalactic survey (Lerov et al., 2003) and the HERA CO-Line Extragalactic survey (Leroy et al.
 2009)., 2009).
 These new results showed a more complex dependence of τσ on X., These new results showed a more complex dependence of $\Sigma_{SFR}$ on $\Sigma_{g}$.
 Digiel et al. (, Bigiel et al. (
"2008) found that ~| lorH XM,4 inB the range5 9—8S0 AL. > and that the τομ4SLR—X,EI4 relation. has a much steeper slope in the regime of X,<9 M. 77.",2008) found that $n \sim 1$ for $\Sigma_{g}$ in the range $9-80$ $_{\odot}$ $^{-2}$ and that the $\Sigma_{SFR}-\Sigma_{g}$ relation has a much steeper slope in the regime of $\Sigma_{g} < 9$ $_{\odot}$ $^{-2}$.
 several ideas have been proposed in order to explain the origin of the KS law., Several ideas have been proposed in order to explain the origin of the KS law.
" One of the early explored scenarios is one in which stars form as a result of gravitational instabilities in galactic disks over a characteristic timescale which is the local [ree-Iall time of the gas and which is given by {ρεxp,0.57. where pg is the local gas volume density."," One of the early explored scenarios is one in which stars form as a result of gravitational instabilities in galactic disks over a characteristic timescale which is the local free-fall time of the gas and which is given by $t_{ff,g} \propto \rho_{g}^{-0.5}$, where $\rho_{g}$ is the local gas volume density."
" For a constant scale height of the disk. p,xX, and thus μμxοτειXp? (Madore 1977: Li οἱ al."," For a constant scale height of the disk, $\rho_{g} \propto \Sigma_{g}$ and thus $\Sigma_{SFR} \propto \Sigma_{g}/t_{ff,g} \propto \Sigma_{g}^{1.5}$ (Madore 1977; Li et al."
 2006)., 2006).
" Wong Blitz (2002) argued that the value of the NS Jaw slope is related to the value of the molecular fraction fi,=Xj,/X, and Blitz Rosolowsky (2006) showed that fj, is related to the pressure of the interstellar medium.", Wong Blitz (2002) argued that the value of the KS law slope is related to the value of the molecular fraction $f_{H_{2}}=\Sigma_{H_{2}}/\Sigma_{g}$ and Blitz Rosolowsky (2006) showed that $f_{H_{2}}$ is related to the pressure of the interstellar medium.
 Tassis (2007) ancl Wada Norman (2007) suggested that Che value of à» is related to the width of the density probability distribution function of the interstellar eas and {ο the threshold clensity (hat is associatecl with the gas tracer., Tassis (2007) and Wada Norman (2007) suggested that the value of $n$ is related to the width of the density probability distribution function of the interstellar gas and to the threshold density that is associated with the gas tracer.
 The origin of the IXS laws has also been extensively investigated using numerical simulations which were able (ο reproduce NS laws with slopes ol ~1.5—2 (IXravisov. 2003: Tasker Bryan 2006: Shetty Ostriker 2008: Robertson Ixravisov 2008: Schave Dalla Vecchia 2008: Gnedin οἱ al., The origin of the KS laws has also been extensively investigated using numerical simulations which were able to reproduce KS laws with slopes of $\sim 1.5-2$ (Kravtsov 2003; Tasker Bryan 2006; Shetty Ostriker 2008; Robertson Kravtsov 2008; Schaye Dalla Vecchia 2008; Gnedin et al.
 2009: Papadopoulos Pelupessy POLO: Gnedin hNravisov 2011: Hopkins et al., 2009; Papadopoulos Pelupessy 2010; Gnedin Kravtsov 2011; Hopkins et al.
 2011)., 2011).
 Escala. (2011) pointed out that a correlation exists between the largest mass-scale for structures not stabilised by rotation and ihe SER while Abelardo Zamora-Aviles Vazzquez-Semadeni (2011) argued that the SER in gravitationally molecular clouds is regulated by feedback. [rom massive stars., Escala (2011) pointed out that a correlation exists between the largest mass-scale for structures not stabilised by rotation and the SFR while Abelardo Zamora-Aviles Vázzquez-Semadeni (2011) argued that the SFR in gravitationally collapsing molecular clouds is regulated by feedback from massive stars.
 ]xrumholz et al. (, Krumholz et al. (
20098. MNAIXMTO09) proposed a model for the star formation laws in galaxies which combines: a) a prescription lor the molecular gas fraction as a function of My. b) a description of the behaviour of Giant Molecular Clouds (GMCS) as a function of My. and c) a model. based on turbulence. which describes the conversion of a fraction of the GMCSs mass into stars per unit time.,"2009a, KMT09) proposed a model for the star formation laws in galaxies which combines: a) a prescription for the molecular gas fraction as a function of $\Sigma_{g}$, b) a description of the behaviour of Giant Molecular Clouds (GMCs) as a function of $\Sigma_{g}$, and c) a model, based on turbulence, which describes the conversion of a fraction of the GMCs mass into stars per unit time."
 IXMTO9 computed several star formation laws for various values of (he interstellar gas metallicities and compared their results to a compilation of observational, KMT09 computed several star formation laws for various values of the interstellar gas metallicities and compared their results to a compilation of observational
Table 2 also iucludes the updated solar ucutrino fluxes inferred from all available neutrino data.,Table \ref{tab:neutrinos} also includes the updated solar neutrino fluxes inferred from all available neutrino data.
 The analysis inchiles the recent more precise. “Bo measurcinent. which is the main change with respect to previous analysis (Bahleall&Pena-Caray2003:Pena-CaravSerencll2008:Couzalez-Garciaetal. 2010).," The analysis includes the recent more precise, $^7$ Be measurement, which is the main change with respect to previous analysis \citep{roadmap,bps08,concha:2010}."
. Details of the analysis will be shown clsewhere (Borexinocollabo-vation 2011)., Details of the analysis will be shown elsewhere \citep{borex:2011}.
. In order to compare the SSAL predictions with the fluxes inferred frou neutrino data. we use the 4? function defined iu Gouzález-Cuucíactal. (2010)... with updated errors and correlations;," In order to compare the SSM predictions with the fluxes inferred from neutrino data, we use the $\chi^2$ function defined in \citet{concha:2010}, , with updated errors and correlations."
 We find νέων=3.5 and css=3.4 leading in both cases to POSvesano= 90%.," We find $\chi^2_{\rm GS98}=3.5$ and $\chi^2_{\rm AGSS09}=3.4$, leading in both cases to $P^{\rm agr}_{\rm GS98,AGSS09}=90\%$ ."
" The new fusion cross sectious frou: SEIT and the new Dorexino results lead to both models predicting solar neutrino fluxes in excellent agrecment with inferred ones: frou Table 2 it can be seen that solar ‘Be aud ""D fiuxes are intermediate between SSAL predictions for GS9S and AGSSO9 compositions.", The new fusion cross sections from SFII and the new Borexino results lead to both models predicting solar neutrino fluxes in excellent agreement with inferred ones; from Table \ref{tab:neutrinos} it can be seen that solar $^7$ Be and $^8$ B fluxes are intermediate between SSM predictions for GS98 and AGSS09 compositions.
 Currently: solar neutrinos eau not differentiate between different solar compositions.," Currently, solar neutrinos can not differentiate between different solar compositions."
 Bricily. the construction of an SSM requires finding two parameters that determine the initial composition of the model. 344 and Zany (Vauw=τίVig Zing). aud the nusing leusth parameter Αντ.," Briefly, the construction of an SSM requires finding two parameters that determine the initial composition of the model, $\yini$ and $\zini$ $\xini=1-\yini-\zini$ ), and the mixing length parameter $\alpha_{\rm MLT}$."
 The three parameters are determined iteratively by requinug the model to reproduce the present-day solu lwuinosity. radius aud surface metal-to-bydrogen abundance ratio.," The three parameters are determined iteratively by requiring the model to reproduce the present-day solar luminosity, radius and surface metal-to-hydrogen abundance ratio."
" We remind the reader that the choice of a solar composition determines not ouly the present-day (2/4). value. but also the relative abundances of metals within the bulk metallicity,"," We remind the reader that the choice of a solar composition determines not only the present-day $\left(Z/X\right)_{\rm
 S}$ value, but also the relative abundances of metals within the bulk metallicity."
 Ta what follows. all models are computed using the ACGSSOO solar composition.," In what follows, all models are computed using the AGSS09 solar composition."
 The algorithm used to construct SSAIs can be casily modified to compute nonstandard models with accretion. ouce the properties of the accreted matter CGuass aud composition) aud the timescales and accretion rates are specified.," The algorithm used to construct SSMs can be easily modified to compute nonstandard models with accretion, once the properties of the accreted matter (mass and composition) and the timescales and accretion rates are specified."
 Below. aud in the remainder of the paper. we use the following nomenclature: Mj. is the mass of the accreted material. Zac. Vac. aud Vy. are. respectively. its metal. hydrogen and helimu mass fractions. Το aud Tae. are the initial and eudiug times of the accretion process.," Below, and in the remainder of the paper, we use the following nomenclature: $\mac$ is the mass of the accreted material, $\zac$, $\xac$, and $\yac$ are, respectively, its metal, hydrogen and helium mass fractions, $\tau_{\rm ac,i}$ and $\tau_{\rm ac,e}$ are the initial and ending times of the accretion process."
 Schelmatically. the algorithu consists of the following steps: Iu the above scheme the free parameters of the model aro the same as those of SSAIs. namely Mugs Zug and ντ.," Schematically, the algorithm consists of the following steps: In the above scheme the free parameters of the model are the same as those of SSMs, namely $\yini$, $\zini$, and $\alpha_{\rm MLT}$."
 But they now depend om properties of the accreted mnaterial. particularly its composition. because the müxture of initial aud accreted matter that forms the preseut-«dav solar surface nist satisfv the (λα constraint.," But they now depend on properties of the accreted material, particularly its composition, because the mixture of initial and accreted matter that forms the present-day solar surface must satisfy the $\left(Z/X\right)_{\rm S}$ constraint."
 So far. woe have assumed. that the parameters characterizing the accretion process are known.," So far, we have assumed that the parameters characterizing the accretion process are known."
 We now discuss how we selected the rauges for those parameters., We now discuss how we selected the ranges for those parameters.
 The properties of the resulting solar models will clearly depend on the parameters that describe both the properties of the accreted mater and the timing aud duration of the accretion process., The properties of the resulting solar models will clearly depend on the parameters that describe both the properties of the accreted mater and the timing and duration of the accretion process.
 Our goal was to cover a relatively large paraicter space. in order to better define the rauge of possible solar model outcomes.," Our goal was to cover a relatively large parameter space, in order to better define the range of possible solar model outcomes."
 Below we describe our clioices., Below we describe our choices.
" Tutuitively, a hvpothetical solution to the solar abundance problemi would seen to require that metalpoor or even metal-free material is accreted outo the Sun."," Intuitively, a hypothetical solution to the solar abundance problem would seem to require that metal-poor or even metal-free material is accreted onto the Sun."
 This has been the assumption in the models explored previously (Castrootal.2007:Garzik&Mussack 2010)..," This has been the assumption in the models explored previously \citep{castro:2007,guzik:2010}. ."
 Tere we explore metal-free. metal-poor. aud metal-rich accretion.," Here we explore metal-free, metal-poor, and metal-rich accretion."
 Surprisingly. as described in L. we find that motalvich accretion can lead to partial iniprovenienuts imn the helioscisinic properties of some models.," Surprisingly, as described in \ref{sec:results}, we find that metal-rich accretion can lead to partial improvements in the helioseismic properties of some models."
" We explore Z4, Values ranging from 0 to 0.03. the latter beine roughly twice the solar surface metallicity."," We explore $\zac$ values ranging from 0 to 0.03, the latter being roughly twice the solar surface metallicity."
 The relative abundances of metals is uot varied. but is fixed to AGSSOO values.," The relative abundances of metals is not varied, but is fixed to AGSS09 values."
 This is an assumption that may be a reasonable starting poiut for initial explorations. but probably should be relaxed in future calculations given that auv miechanisui for scerceating metals would likely reflect condensation teniperatures and other elemenut-specific chemistry.," This is an assumption that may be a reasonable starting point for initial explorations, but probably should be relaxed in future calculations given that any mechanism for segregating metals would likely reflect condensation temperatures and other element-specific chemistry."
 We cousider accretion of lass from the protoplanetary disk with a composition different from that of the unprocessed iaterial of the proto-solar nebula., We consider accretion of mass from the protoplanetary disk with a composition different from that of the unprocessed material of the proto-solar nebula.
 The amount of such material the Sun müeht have accreted in its carly evolutionary phases in not well coustrained. as estimates of both the mass of the proto-planctary disk aud the fraction of that mass that remained in the solar system vary.," The amount of such material the Sun might have accreted in its early evolutionary phases in not well constrained, as estimates of both the mass of the proto-planetary disk and the fraction of that mass that remained in the solar system vary."
 Asstunine that initially the proto-solar cloud. was well mixed. one cau set a lowerlinut to the mass of the protoplanetary disk. the so-called 1uiiuuun- solar nebula (ATAISN) limit. from estimates ofthe metal content of the planets;," Assuming that initially the proto-solar cloud was well mixed, one can set a lowerlimit to the mass of the protoplanetary disk, the so-called minimum-mass solar nebula (MMSN) limit, from estimates ofthe metal content of the planets."
 The calculation. however. still depends ou model assmuptions.," The calculation, however, still depends on model assumptions."
 Early estimates (Weideuschilling1977:Havashi1981). give," Early estimates \citep{weiden:1977,hayashi:1981} give"
the shrinking umbral fragment.,the shrinking umbral fragment.
 The scan made during 21:36-21:41 UT reveals a drastic shrinkage of the umbra with only a small area of strong downflows that appear close to where the umbra existed earlier (black arrow in the continuum image of Figure 11))., The scan made during 21:36-21:41 UT reveals a drastic shrinkage of the umbra with only a small area of strong downflows that appear close to where the umbra existed earlier (black arrow in the continuum image of Figure \ref{down_oct}) ).
" In comparison to AR 10953, the area of the downflowing patch near the umbra-penumbra boundary decreases with time."," In comparison to AR 10953, the area of the downflowing patch near the umbra-penumbra boundary decreases with time."
" While the downflows occupy an area as large as 6 arcsec? at 15:01 UT, this decreases to 72.3 arcsec? by 21:36 UT."," While the downflows occupy an area as large as 6 $^2$ at 15:01 UT, this decreases to $\approx$ 2.3 $^2$ by 21:36 UT."
 Common characteristics of the downflows observed in ARs 10953 and 11029 are their lifetimes of more than 6 hr and the fact that the long-lived ones appear to be located near the umbra-penumbra boundary., Common characteristics of the downflows observed in ARs 10953 and 11029 are their lifetimes of more than 6 hr and the fact that the long-lived ones appear to be located near the umbra-penumbra boundary.
 The more short-lived downflows are observed elsewhere in the ARs., The more short-lived downflows are observed elsewhere in the ARs.
 Supersonic downflows associated with the Evershed flow are usually observed in the outer penumbra ToroIniestaetal.2001;BellotRubio2004) or even beyond the sunspot boundary Pil-letetal.2009).," Supersonic downflows associated with the Evershed flow are usually observed in the outer penumbra \citep{Josecarlos2001,Luis2004} or even beyond the sunspot boundary \citep{Valentin2009}."
. These downflows represent(Martínez mass flux returning to the photosphere with a polarity opposite to that of the sunspot., These downflows represent mass flux returning to the photosphere with a polarity opposite to that of the sunspot.
 As they are seen in the outer penumbra they cannot explain the strong downflows we have detected in the inner penumbra., As they are seen in the outer penumbra they cannot explain the strong downflows we have detected in the inner penumbra.
 One could suppose that the supersonic downflows near the umbra-penumbra boundary are the photospheric manifestations of some kind of inverse Evershed flow seen in the chromosphere., One could suppose that the supersonic downflows near the umbra-penumbra boundary are the photospheric manifestations of some kind of inverse Evershed flow seen in the chromosphere.
" However, it is difficult to ascertain how such a chromospheric phenomenon could produce supersonic downflows in the inner penumbra at the photosphere."," However, it is difficult to ascertain how such a chromospheric phenomenon could produce supersonic downflows in the inner penumbra at the photosphere."
 Another mechanism that could perhaps explain the supersonic downflows is suggested below based on the orientation of the filaments in which they occur., Another mechanism that could perhaps explain the supersonic downflows is suggested below based on the orientation of the filaments in which they occur.
" The continuum images were morphologicallyopened (Curtoetal.2008) and subtracted from their original image in order to increase the contrast and isolate bright structures from the dark background, filament crossings, and diffuse edges."," The continuum images were morphologically \citep{Curto2008} and subtracted from their original image in order to increase the contrast and isolate bright structures from the dark background, filament crossings, and diffuse edges."
 is the result of two operations namelyerosion followed bydilation., is the result of two operations namely followed by.
 These two operators look for the neighborhood minimum and maximum where the search domain is defined by a structuring element (SE)., These two operators look for the neighborhood minimum and maximum where the search domain is defined by a structuring element (SE).
 The size of the SE used for opening the images was 7x pixels for the first two ARs while a 3x pixel SE was sufficient for AR. 11029., The size of the SE used for the images was $7\times7$ pixels for the first two ARs while a $3\times3$ pixel SE was sufficient for AR 11029.
" The above morphological operation was chosen after discarding the Sobel and Roberts edge enhancement operator, unsharp masking, and intensity thresholding."," The above morphological operation was chosen after discarding the Sobel and Roberts edge enhancement operator, unsharp masking, and intensity thresholding."
 The results are shown in Figure 12 with reversed signs., The results are shown in Figure \ref{unsharp} with reversed signs.
" It is observed that in NOAA AR 10923, the strong downflows encompass two bisecting filaments P1 and P2 and their likely point of intersection is marked by a blue arrow."," It is observed that in NOAA AR 10923, the strong downflows encompass two bisecting filaments P1 and P2 and their likely point of intersection is marked by a blue arrow."
" Such locations have been similarly marked for the other ARs, although they are less obvious."," Such locations have been similarly marked for the other ARs, although they are less obvious."
" The orientation of the filaments resemble the post reconnection configuration illustrated in Figure 5c of Ryutovaetal. suggesting that the origin of the downflows is the (2008a),,slingshot effect associated with the reconnection of the filaments."," The orientation of the filaments resemble the post reconnection configuration illustrated in Figure 5c of \citet{Ryutova2008a}, suggesting that the origin of the downflows is the slingshot effect associated with the reconnection of the filaments."
 The bisecting angles shown by the solid green lines in AR. 10923 were estimated to be = 51° and 46? respectively., The bisecting angles shown by the solid green lines in AR 10923 were estimated to be $\approx$ $^{\circ}$ and $^{\circ}$ respectively.
" In AR 10953 only one half of theintersecting filaments are visible, with the other end is possibly obscured by overlying filaments."," In AR 10953 only one half of theintersecting filaments are visible, with the other end is possibly obscured by overlying filaments."
"for such activity is found to be 3.0. 10. photon enm7s. tat 20-70 Κον,",for such activity is found to be 3.0 $\times 10^{-3}$ photon $^{-2}$ $^{-1}$ at 20-70 kev.
 We compare this limit with the X-ray spectrum obtained with Avicl V (White&Carpenter1978). at the peak of the July 1977 outburst., We compare this limit with the X-ray spectrum obtained with Ariel V \cite{wc} at the peak of the July 1977 outburst.
 By assuming à mean photon enerev of 45 keV over a spectral range of 20-70 keV for the BATSE observations we estimate a maximum Ilux density of 2.7 10 keV em7s ! ft., By assuming a mean photon energy of 45 keV over a spectral range of 20-70 keV for the BATSE observations we estimate a maximum flux density of 2.7 $\times 10^{-3}$ keV $^{-2}$ $^{-1}$ $^{-1}$.
 Phe fitted spectrum of White Carpenter (LOTS) is extremely steep and. dominated by a thermal component., The fitted spectrum of White Carpenter \shortcite{wc} is extremely steep and dominated by a thermal component.
 By extrapolating their model. our lower limit for detection by BALTSE in the data presented here is consistent with the Dux that would be expected on the basis of this model to within errors.," By extrapolating their model, our lower limit for detection by BATSE in the data presented here is consistent with the flux that would be expected on the basis of this model to within errors."
 Thus we conclude that had AOS38-668 been active at its previous level BATS would have detected it., Thus we conclude that had A0538-668 been active at its previous level BATSE would have detected it.
 This source was detected in BATSE data at 296 with a period. 2.08., This source was detected in BATSE data at $\sigma$ with a period 2.087d.
 Con. N-3 is the only 1AIXND to have a well determined. orbital period. derivative (Nagaseet however thi sis too small to show up in our analvsis., Cen X-3 is the only HMXB to have a well determined orbital period derivative \cite{nag} however this is too small to show up in our analysis.
 The power svectrum in Fieure 2. sdows two peaks. but comparison with the power spectrum. for simulated: data showed. the uigher-frequeney peak to be an artelact of aliasing.," The power spectrum in Figure \ref{fig:lsdata} shows two peaks, but comparison with the power spectrum for simulated data showed the higher-frequency peak to be an artefact of aliasing."
 The folded lishteurve Figure 1 is a simple sawtooth like form. brightening more rapidly than it decays.," The folded lightcurve Figure \ref{fig:lightcurves} is a simple sawtooth like form, brightening more rapidly than it decays."
 Two peaks with —36 significance are found. at. periods of 16.8d and 7.39d., Two peaks with $\sim$ $\sigma$ significance are found at periods of 16.8d and 7.39d.
 Ehe orbital period of the svstem is believed to be S.38d (Marshall ancl Ricketts 1980. Cook and Page 1987) thus the 16.8d. X-ray modulation is consistent with twice the binary period.," The orbital period of the system is believed to be 8.38d (Marshall and Ricketts 1980, Cook and Page 1987) thus the 16.8d X-ray modulation is consistent with twice the binary period."
 However. there is no evidence for a peak in the power spectrum at ο - this is not surprising if one considers the folded lighteurve in Figure 1: which shows just a single broad peak when folded at 16.8d.," However, there is no evidence for a peak in the power spectrum at $\sim$ 8.4d - this is not surprising if one considers the folded lightcurve in Figure 1 which shows just a single broad peak when folded at 16.8d."
 Constructing a simulated. dataset. containing a sinewave at S.38d. with amplitude taken as 0.002 (measured from a lighteurve folded at this period) failed to reproduce the 16.8d. modulation., Constructing a simulated dataset containing a sinewave at 8.38d with amplitude taken as 0.002 (measured from a lightcurve folded at this period) failed to reproduce the 16.8d modulation.
 Thus it appears that the emission is really modulated. at twice the binary period in these BATSE data., Thus it appears that the emission is really modulated at twice the binary period in these BATSE data.
 Early BATSE occulation data from this source have already been the subject ofa paper by Rubin et al.," Early BATSE occulation data from this source have already been the subject of a paper by Rubin et al.,"
 1996., 1996.
 Our PDAL period agrees with 1S0-+0.00003c from. Copernicus X-rav observation (Bracuarcli1978)., Our PDM period agrees with $\pm$ 0.00003d from Copernicus X-ray observation \cite{bran}.
. We also detect significant peaks in the power spectrum at 13.808d. at a significance of 11.3o. and at exactly half this period.," We also detect significant peaks in the power spectrum at 13.808d at a significance of $\sigma$, and at exactly half this period."
 This period has been previously reported. by Ixonig Maisack. (..1997)., This period has been previously reported by Konig Maisack \shortcite{km97}.
. We further investigated: this period. by subtracting the orbital modulation from the lighteurve. using Figure 1 as a template.," We further investigated this period by subtracting the orbital modulation from the lightcurve, using Figure \ref{fig:lightcurves} as a template."
 This procedure resulted in reduction of spectral power at the orbital period by a factor of 24., This procedure resulted in reduction of spectral power at the orbital period by a factor of 24.
 No attenuation of the 13.808d. period. was observed. in [act a significant increase resulted.," No attenuation of the 13.808d period was observed, in fact a significant increase resulted."
 Hence we are confident that the 13.8508d period is an independent modulation and not an harmonic of the orbital period., Hence we are confident that the 13.808d period is an independent modulation and not an harmonic of the orbital period.
 A peak was detected in LS periodogram at 190.238d. with INLIEIMITT.AS days., A peak was detected in LS periodogram at 190.238d with FWHM=17.48 days.
 A PDAL periodogram determination of 186.60. zE0.348068d. measured. by centroiding is consistent with the established value of 186.5 cays., A PDM periodogram determination of 186.6d $\pm$ 0.348068d measured by centroiding is consistent with the established value of 186.5 days.
 The PDAL period of 1L0O.462640.0011e is in agreement with the period of 10.44364:0.0038d. (Chakrabartyctal1993) from BATSE pulse timing stuclies., The PDM period of $\pm$ 0.0011d is in agreement with the period of $\pm$ 0.0038d \cite{ch1} from BATSE pulse timing studies.
 The 14d binary period is not detected., The 1.4d binary period is not detected.
" Phe ""average"" Nyquist period of the daily average data is 2.4d so the single- data was also analvsed. again with no detection."," The ""average"" Nyquist period of the daily average data is 2.4d so the single-step data was also analysed, again with no detection."
 The 30.5d X-ray modulation believed to be due to the precession ofa warped accretion disk (Langetal1981). is detected and is shown to be persistent throughout the full span of the data Figure 1.., The 30.5d X-ray modulation believed to be due to the precession of a warped accretion disk \cite{lang} is detected and is shown to be persistent throughout the full span of the data Figure \ref{fig:lightcurves}.
 MI period finding techniques tried. (Lomb- PDM. CLEAN) derive a period for this modulation slightly shorter than usually quoted.," All period finding techniques tried, (Lomb-Scargle, PDM, CLEAN) derive a period for this modulation slightly shorter than usually quoted."
 A PDM periodogram constructed at a resolution of 10.7 eveles and measured bv centroiding. derived a period. of 30.3490. while the L-ο periodogram. viclded 30.355d.," A PDM periodogram constructed at a resolution of $\times 10^{-5}$ cycles and measured by centroiding, derived a period of 30.349d while the L-S periodogram yielded 30.355d."
. Monte. Carlo simulations of sinusoidal signals at. 30.5c and: 30.35d. superimposed. on noise created by randomizing the original dataset show that the LS periodogram. frequency resolution is 10.7 at the S/N level seen in the data., Monte Carlo simulations of sinusoidal signals at 30.5d and 30.35d superimposed on noise created by randomizing the original dataset show that the LS periodogram frequency resolution is $\times 10^{-5}$ at the S/N level seen in the data.
 A solution at 30.5d is thus seeminglv in conlliet with the BATSE dataset., A solution at 30.5d is thus seemingly in conflict with the BATSE dataset.
 A remarkable fact is the stability of this modulation over the 7 vears of data. since no jitter is evident from the values in Table 1 This system is clearly the brightest. most regular source studied here.," A remarkable fact is the stability of this modulation over the 7 years of data, since no jitter is evident from the values in Table \ref{tab:summary}
 This system is clearly the brightest, most regular source studied here."
 Phe phase-binned. folded. Lghteurve shows increasing Lux levels consistent with phase 0.5. each of which reached tvpe-lI outburst levels.," The phase-binned folded lightcurve shows increasing flux levels consistent with phase 0.5, each of which reached type-I outburst levels."
 This result confirms previous work by Pravdo et al. 1995 and Woh et al. 1997 - both of these works also present. evidence for apastron outbursts from this system.," This result confirms previous work by Pravdo et al, 1995 and Koh et al, 1997 - both of these works also present evidence for apastron outbursts from this system."
 The power spectrum for CN301-2 shows a pattern of strong peaks which after comparison to simulated data are found to be real., The power spectrum for GX301-2 shows a pattern of strong peaks which after comparison to simulated data are found to be real.
 “Phese [requeney. components. appearing at integer submultiples of the orbital period are a signature of the hiehly non-sinusoidal liehteurve.," These frequency components, appearing at integer submultiples of the orbital period are a signature of the highly non-sinusoidal lightcurve."
" The spectrum shown is that generated. after the removal of 4 particularly bright apastron Εαν points. as expected. their inclusion boosts the £2,,,/2 component."," The spectrum shown is that generated after the removal of 4 particularly bright apastron flux points, as expected their inclusion boosts the $P_{orb}/2$ component."
is low. the magnetic torque is significant only if the angular velocity is close to Keplerian velocity and the magnetic field inclination angle to the disk surface is low (low #y. see Fig.,"is low, the magnetic torque is significant only if the angular velocity is close to Keplerian velocity and the magnetic field inclination angle to the disk surface is low (low $\kappa_0$, see Fig."
 2)., 2).
 The numerically determined stability boundaries for the neutral wave mode are plotted in Figs., The numerically determined stability boundaries for the neutral wave mode are plotted in Figs.
 3 and 4., 3 and 4.
 It 1s seen that instability happens in basically two region of parameter space., It is seen that instability happens in basically two region of parameter space.
 One is at high wind torque (right side of the diagrams): the instability then happens roughly independent of the strength of the magnetic field., One is at high wind torque (right side of the diagrams); the instability then happens roughly independent of the strength of the magnetic field.
 At low wind torques. instability is possible Cnly when the rotation rate is close enough to Keplerian.," At low wind torques, instability is possible only when the rotation rate is close enough to Keplerian."
 Examples of the growth rate of the neutral wave mode for different parameter values are shown in Figures 5-11., Examples of the growth rate of the neutral wave mode for different parameter values are shown in Figures 5-11.
 We have presented a linear stability analysis of disks with magnetically driven winds. and confirm the instability by the mechanism proposed by LPP.," We have presented a linear stability analysis of disks with magnetically driven winds, and confirm the instability by the mechanism proposed by LPP."
 In the presence of a strong magnetic field. the disk is compressed by the vertical component of gravitational force as Well as vertical magnetic pressure. and the vertical structure of the disk is significantly altered. which affects the position of sonic point and the wind torque.," In the presence of a strong magnetic field, the disk is compressed by the vertical component of gravitational force as well as vertical magnetic pressure, and the vertical structure of the disk is significantly altered, which affects the position of sonic point and the wind torque."
 I this strong field case. the angular velocity of accretion flow significantly deviates from the Keplerian velocity due to the radial magnetic force. and the magnetic torque is then negligible for any magnetic field inclination angle (see Figs.," In this strong field case, the angular velocity of accretion flow significantly deviates from the Keplerian velocity due to the radial magnetic force, and the magnetic torque is then negligible for any magnetic field inclination angle (see Figs."
 | and 2. see also Ogilvie and Livio 1998).," 1 and 2, see also Ogilvie and Livio 1998)."
" We have taken these effects into account in present investigation,", We have taken these effects into account in present investigation.
 The system of equations analyzed has four modes., The system of equations analyzed has four modes.
 In the absence of a magnetic field. two are a neutral displacements.," In the absence of a magnetic field, two are a neutral displacements."
 One of these two is not specifically related to the magnetic wind torque. and we have excluded it from quantitative analysis.," One of these two is not specifically related to the magnetic wind torque, and we have excluded it from quantitative analysis."
 The other has a frequency proportional to the magnetic torque (real and imaginary parts of the frequency are of the same order of magnitude). it can become unstable.," The other has a frequency proportional to the magnetic torque (real and imaginary parts of the frequency are of the same order of magnitude), it can become unstable."
 The final two modes represent an inward and an outward traveling wave., The final two modes represent an inward and an outward traveling wave.
 The restoring force in. the wave Is a combination of the coriolis force (epicyelic motion) and the magnetic forces., The restoring force in the wave is a combination of the coriolis force (epicyclic motion) and the magnetic forces.
 Both inward and outward traveling waves are stable in the range of validity of our assumptions., Both inward and outward traveling waves are stable in the range of validity of our assumptions.
 In Fig., In Fig.
 5. the growth rate of the instability is plotted for angular velocity very close to Keplerian velocity (Qy= 0.995). which may approximate the case considered in LPP.," 5, the growth rate of the instability is plotted for angular velocity very close to Keplerian velocity $\tilde\Omega_0=0.995$ ), which may approximate the case considered in LPP."
 The disk becomes more unstable if the angular velocity of the flow i5 close to Keplerian (see Figs., The disk becomes more unstable if the angular velocity of the flow is close to Keplerian (see Figs.
 5-8)., 5-8).
 For high inclination angles of magnetic field line. with respect to the surface of the disk (large ny). the magnetic torque is very small.," For high inclination angles of magnetic field line with respect to the surface of the disk (large $\kappa_0$ ), the magnetic torque is very small."
 Instability is then suppressed by magnetic diffusion., Instability is then suppressed by magnetic diffusion.
 The magnetic torque makes the disk unstable. while magnetic diffusion has a_ stabilizing effect. suppressing instability at low Oy and/or torque (see Figs.," The magnetic torque makes the disk unstable, while magnetic diffusion has a stabilizing effect, suppressing instability at low $\tilde\Omega_0$ and/or torque (see Figs."
 3 and 4)., 3 and 4).
 Comparing Figs., Comparing Figs.
 6 and 9. we see that the disk ts less unstable in low temperature case QI= 0.001) while the instability occurs for lower values of μυ.," 6 and 9, we see that the disk is less unstable in low temperature case $\tilde H=0.001$ ) while the instability occurs for lower values of $\kappa_0$."
 To see the effect of magnetic diffusion. Figs.," To see the effect of magnetic diffusion, Figs."
 10 and 11 show the growth rates for the cases with η=0., 10 and 11 show the growth rates for the cases with $\tilde\eta=0$.
 In the absence of magnetic diffusion. the disk is always unstable. though the growth rates can be very small.," In the absence of magnetic diffusion, the disk is always unstable, though the growth rates can be very small."
"from the ZAEHB (Zero Age Extreme Horizontal Branch) and should therefore, according to evolutionary calculations (e.g. Dorman et al. 1993)),","from the ZAEHB (Zero Age Extreme Horizontal Branch) and should therefore, according to evolutionary calculations (e.g. Dorman et al. \cite{dorman}) ),"
 have a similar age as 00101+039 and 448 (see Fig. 3))., have a similar age as $+$ 039 and 48 (see Fig. \ref{tefflogg}) ).
 We thus conclude that the assumption of orbital sychronisation is fully justified in the case of 6687., We thus conclude that the assumption of orbital sychronisation is fully justified in the case of 687.
 In about 100Myr the helium-burning in the core of the sdB will come to an end.," In about $100\,{\rm Myr}$ the helium-burning in the core of the sdB will come to an end."
" After a short period of helium-shell-burning this star will eventually become a white dwarf consisting of C and O. 6687 is one of only a few known DD progenitor systems, where both components are C/O white dwarfs and which will merge in less than a Hubble time."," After a short period of helium-shell-burning this star will eventually become a white dwarf consisting of C and O. 687 is one of only a few known DD progenitor systems, where both components are C/O white dwarfs and which will merge in less than a Hubble time."
" Compared to the sdB+WD binary 11930-2752 d, Maxted et al. 2000;;"," Compared to the sdB+WD binary $+$ 2752 $P\approx0.1\,{\rm d}$ , Maxted et al. \cite{maxted1};"
" Geier et al. 2007)),"," Geier et al. \cite{geier1}) ),"
" which is the best known candidate for DD SN Ia progenitor, the orbital period of 6687 is rather long."," which is the best known candidate for DD SN Ia progenitor, the orbital period of 687 is rather long."
" This leads to a merging time of 11.1Gyr, which is just a little shorter than the Hubble time, compared to only 200Myr for 1193042752."," This leads to a merging time of $11.1\,{\rm Gyr}$, which is just a little shorter than the Hubble time, compared to only $200\,{\rm Myr}$ for $+$ 2752."
 With a total mass of 1.187027Μο for the most likely subdwarf mass it may come close to the Chandrasekhar limit of 1.4Μο and is therefore placed at the edge of the progenitor parameter space (see Fig. 4)).," With a total mass of $1.18_{-0.21}^{+0.22}\,M_{\rm \odot}$ for the most likely subdwarf mass it may come close to the Chandrasekhar limit of $1.4\,M_{\rm \odot}$ and is therefore placed at the edge of the progenitor parameter space (see Fig. \ref{progen}) )."
" In contrast to 1193042752, where the primary mass could be constrained by an additional analysis of the subdwarfs ellipsoidal deformation visible as variation in its lightcurve, no such constraint can be put on the primary mass of 6687 yet."," In contrast to $+$ 2752, where the primary mass could be constrained by an additional analysis of the subdwarfs ellipsoidal deformation visible as variation in its lightcurve, no such constraint can be put on the primary mass of 687 yet."
" Instead of exploding as SN Ia, the merger of the two white dwarfs will most likely lead to the formation of a supermassive white dwarf with O/Ne/Mg-core."," Instead of exploding as SN Ia, the merger of the two white dwarfs will most likely lead to the formation of a supermassive white dwarf with O/Ne/Mg-core."
 Up to now four binaries with total masses between about 1.2 and 1.4Μο have been discovered.," Up to now four binaries with total masses between about $1.2$ and $1.4\,{\rm M_{\odot}}$ have been discovered."
" In two of them the visible component is an sdB. Since the sdB close binary fraction is much higher than the one of white dwarfs, it may be easier to find double-degenerate binary progenitors in the hot subdwarf population."," In two of them the visible component is an sdB. Since the sdB close binary fraction is much higher than the one of white dwarfs, it may be easier to find double-degenerate binary progenitors in the hot subdwarf population."
" Two other massive DD systems, a central star of a planetary nebula (Tovmassian et al. 2004;;"," Two other massive DD systems, a central star of a planetary nebula (Tovmassian et al. \cite{tovmassian};"
 Napiwotzki et al. 2005)), Napiwotzki et al. \cite{napiwotzki8}) )
 and a white dwarf from the SDSS survey (Badenes et al. 2009;;, and a white dwarf from the SDSS survey (Badenes et al. \cite{badenes};
 Marsh et al. 2010;;, Marsh et al. \cite{marsh};
" Kulkarni van Kerkwijk 2010)), were discovered serendipitously."," Kulkarni van Kerkwijk \cite{kulkarni}) ), were discovered serendipitously."
" Even though 6687 does not qualify as SN Ia progenitor candidate, the discovery of a population of double degenerate binaries (and progenitor systems) with total masses close to the Chandrasekhar limit in the course of the SPY survey (see Fig. 4))"," Even though 687 does not qualify as SN Ia progenitor candidate, the discovery of a population of double degenerate binaries (and progenitor systems) with total masses close to the Chandrasekhar limit in the course of the SPY survey (see Fig. \ref{progen}) )"
 provides evidence for a similar population exceeding this limit., provides evidence for a similar population exceeding this limit.
 The same binary evolution channel that produces the sub- systems will also produce super-Chandrasekhar systems with slight changes in the initial conditions only., The same binary evolution channel that produces the sub-Chandrasekhar systems will also produce super-Chandrasekhar systems with slight changes in the initial conditions only.
"with increasing densities would be expected as the [N textscii] 46548 A line becomes more-and-more affected by collisional de-excitations (i.e., decreases in intensity).","with increasing densities would be expected as the $[$ $]$ $\lambda$ 6548 $\mbox{\AA}$ line becomes more-and-more affected by collisional de-excitations (i.e., decreases in intensity)."
" As expected, the linear relation shows a positive slope although its value, very close to 0, largely suggests no correlation at all."," As expected, the linear relation shows a positive slope although its value, very close to 0, largely suggests no correlation at all."
" Indeed, the quality of the linear fit is relatively poor with a correlation coefficient of 0.35."," Indeed, the quality of the linear fit is relatively poor with a correlation coefficient of 0.35."
" Hence, we believe that no conclusion can be drawn from Figure 15."," Hence, we believe that no conclusion can be drawn from Figure 15."
 Two possibilities are however provided in order to explain such behavior., Two possibilities are however provided in order to explain such behavior.
" First, the reader should note that the uncertainties are relatively large for both parameters investigated."," First, the reader should note that the uncertainties are relatively large for both parameters investigated."
 The mean uncertainty for the line ratio is 0.17 while typical uncertainties for the Inelectron-densityesas measurements p are provided in the last paragraph of § 4.2.3.," The mean uncertainty for the $\frac{[\textnormal{N}\,\textsc{ii}]\,\lambda6584}{[\textnormal{N}\,\textsc{ii}]\,\lambda6548}$ line ratio is 0.17 while typical uncertainties for the electron-density measurements $\rho$ are provided in the last paragraph of $\S$ 4.2.3."
 The poor correlation of the linear fit in Figure 15 could be attributed to large error bars., The poor correlation of the linear fit in Figure 15 could be attributed to large error bars.
" Moreover, the absence of a well-defined correlation between p and agers would not be surprising if the N* and S* material are not perfectly cospatial in the vicinity of Melotte 15."," Moreover, the absence of a well-defined correlation between $\rho$ and $\frac{[\textnormal{N}\,\textsc{ii}]\,\lambda6584}{[\textnormal{N}\,\textsc{ii}]\,\lambda6548}$ would not be surprising if the $^{+}$ and $^{+}$ material are not perfectly cospatial in the vicinity of Melotte 15."
" Given a difference of more than 4 eV between the ionization potentials of neutral nitrogen and sulfur, it can be assumed that the electron densities, computed from the [S textscii]doublet, maynotre flectaccuratelythephysicalconditionspitetitia considering ionic⋅⋅ volume."," Given a difference of more than 4 eV between the ionization potentials of neutral nitrogen and sulfur, it can be assumed that the electron densities, computed from the $[$ $]$ doublet, may not reflect accurately the physical conditions prevailing in the $^{+}$ ionic volume."
" Therefore, the p vs. ∐∖↧∐∣⋋∂⊟∂∠↨ diagram⋅ of Figure 15 could be an interesting [NT]diagnostic46548 tool although our data set may not provide the appropriate spectral information to reliably construct such a diagram."," Therefore, the $\rho$ vs. $\frac{[\textnormal{N}\,\textsc{ii}]\,\lambda6584}{[\textnormal{N}\,\textsc{ii}]\,\lambda6548}$ diagram of Figure 15 could be an interesting diagnostic tool although our data set may not provide the appropriate spectral information to reliably construct such a diagram."
" Alternatively, given the first ionization potential of nitrogen (14.5 eV) and oxygen (13.6 eV), the eas line ratio would likely give a more accurate indication of the density behavior inside the N* volume."," Alternatively, given the first ionization potential of nitrogen (14.5 eV) and oxygen (13.6 eV), the $\frac{[\textnormal{O}\,\textsc{ii}]\,\lambda3726}{[\textnormal{O}\,\textsc{ii}]\,\lambda3729}$ line ratio would likely give a more accurate indication of the density behavior inside the $^{+}$ volume."
" Panels (a) of Figures 12 to 14 reveal that a large fraction of the nebular-gas content in the vicinity of the Melotte 15 star cluster appears to be dominated by photoionization, typical of standard regions."," Panels (a) of Figures 12 to 14 reveal that a large fraction of the nebular-gas content in the vicinity of the Melotte 15 star cluster appears to be dominated by photoionization, typical of standard regions."
" However, points identified outside the expected regime for regions and located near the “SNRs” area demand to be closely investigated (see § 4.2.5)."," However, points identified outside the expected regime for regions and located near the “SNRs” area demand to be closely investigated (see $\S$ 4.2.5)."
" In all three figures, these are symbolized as red filled circles and potentially indicate the presence of shocks in the targeted nebular volume."," In all three figures, these are symbolized as red filled circles and potentially indicate the presence of shocks in the targeted nebular volume."
" These areas of our FOV, suggesting shock excitation, are identified as red dots in all three Panels (b) of the same figures."," These areas of our FOV, suggesting shock excitation, are identified as red dots in all three Panels (b) of the same figures."
" However, at this point, shock excitation in 11805 remains highly hypothetical."," However, at this point, shock excitation in 1805 remains highly hypothetical."
 This is somewhat surprising the presence of relatively massive stars in gináhdNlleir associated strong stellar winds (see 8 2)., This is somewhat surprising considering the presence of relatively massive stars in Melotte 15 and their associated strong stellar winds (see $\S$ 2).
" In order to deeply investigate the impact of shock excitation in 11805, we assume that, if present, the shock-excited ionized material is relatively confined and localized along"," In order to deeply investigate the impact of shock excitation in 1805, we assume that, if present, the shock-excited ionized material is relatively confined and localized along"
"of the quasar, although the centroid is not well constrained by the current data.","of the quasar, although the centroid is not well constrained by the current data."
 This paper reports oobservations of the X-ray emission from the vicinity of 2270.1., This paper reports observations of the X-ray emission from the vicinity of 270.1.
 This includes unresolved emission from the quasar itself and extended X-ray emission within ~10” of the core., This includes unresolved emission from the quasar itself and extended X-ray emission within $\sim 10 \arcsec$ of the core.
" The extended X-rays have two components: softer emission associated with the radio emission north and south of the core; and harder, more diffuse emission which may originate in gas associated with the cluster in which the quasar is embedded (?) or in iC/CMB emission from low-surface brightness or older radio emission that is not easily detectable (?).."," The extended X-rays have two components: softer emission associated with the radio emission north and south of the core; and harder, more diffuse emission which may originate in gas associated with the cluster in which the quasar is embedded \citep{2009ApJ...695..724H}
 or in iC/CMB emission from low-surface brightness or older radio emission that is not easily detectable \citep{2003MNRAS.341..729F}."
" We assume a ACDM cosmology with H,=71 km s! Mpc!, Qy=0.27, and Qyac=0.73 (?).. 2"," We assume a $\Lambda$ CDM cosmology with $_o$ =71 km $^{-1}$ $^{-1}$, $\Omega_M=0.27$, and $\Omega_{vac}=0.73$ \citep{2011ApJS..192...16L}."
270.1 was observed on-axis with the ACIS-S for 9.673 ks on 2008 February 16 9255))., 270.1 was observed on-axis with the ACIS-S for 9.673 ks on 2008 February 16 ).
" The data were reprocessed in 2011 January with CIAO 4.3 to take advantage of the latest calibration files and CTI (charge transfer inefficiency) calibration as well as sub-pixel event repositioning, which improves the spatial resolution."," The data were reprocessed in 2011 January with CIAO 4.3 to take advantage of the latest calibration files and CTI (charge transfer inefficiency) calibration as well as sub-pixel event repositioning, which improves the spatial resolution."
 The reprocessed data were used in the analysis presented here., The reprocessed data were used in the analysis presented here.
 The quasar is well-detected with >700 counts consistent with the spatial distribution of a point source., The quasar is well-detected with $>700$ counts consistent with the spatial distribution of a point source.
 There are also 740 excess counts within oof the quasar but outside its' point spread function (PSF)., There are also $>$ 40 excess counts within of the quasar but outside its' point spread function (PSF).
" Radio data from the VLA archive were reprocessed to generate high-resolution images at 1.43, 8.46, and 14.94 GHz, to provide comparison images at resolution similar to, or better than, that of the ddata."," Radio data from the VLA archive were reprocessed to generate high-resolution images at 1.43, 8.46, and 14.94 GHz, to provide comparison images at resolution similar to, or better than, that of the data."
" All processing was done in AIPS, and followed the usual steps of calibration, imaging, and a cycle."," All processing was done in AIPS, and followed the usual steps of calibration, imaging, and a CLEANing/self-calibration cycle."
" The datasets used are listed in Table 1,, with the angular sizes of the synthesized beams generated from the full datasets at uniform sampling."," The datasets used are listed in Table \ref{tb:vla}, with the angular sizes of the synthesized beams generated from the full datasets at uniform sampling."
Spitzer/IRAC data for 2270.1 were obtained on 2007 June 28 and are reported by ??..," data for 270.1 were obtained on 2007 June 28 and are reported by \citet{2008ApJ...688..122H,2009ApJ...695..724H}."
 The on-source exposure times of 430s in each band allow us to detect point sources to ~3 wy (30) at 3.6 and 4.5 um and ~25 uJy at 5.8 and 8 um., The on-source exposure times of $\times$ 30s in each band allow us to detect point sources to $\sim 3~\mu$ Jy $\sigma$ ) at 3.6 and 4.5 $\mu$ m and $\sim 25~\mu$ Jy at 5.8 and 8 $\mu$ m.
performing second-skip measurements.,performing second-skip measurements.
" However, their measurements employed a scheme of"," However, their measurements employed a scheme of"
It is clear that only galaxies [rom the first two categories. wwith Ro<0.25. can help constrain halo models.,"It is clear that only galaxies from the first two categories, with $R\le 0.25$, can help constrain halo models."
 A glance at Table 1 shows that most of the solutions that are consistent with CDM are actually badly constrained., A glance at Table \ref{table:fit} shows that most of the solutions that are consistent with CDM are actually badly constrained.
 This is investigated further in Fig. 19.. Ile, This is investigated further in Fig. \ref{fig:resolve}.
re His plotted against the number of data points in each rotation curve., Here $R$ is plotted against the number of data points in each rotation curve.
 A distinction is made between rotation curves that are consistent wilh CDM ancl those that are inconsistent with CDM using the constraints introduced here., A distinction is made between rotation curves that are consistent with CDM and those that are inconsistent with CDM using the constraints introduced here.
 Table 1. and Fig., Table \ref{table:fit} and Fig.
 19. lead to several conclusions.," \ref{fig:resolve}
 lead to several conclusions."
 Firstly. of the 15 galaxies that are consistent wilh CDM. 13 have less than 30 data points.," Firstly, of the 15 galaxies that are consistent with CDM, 13 have less than 30 data points."
 Furthermore. of (hese 13 galaxies. only 1 has 2<0.25 iis well-constrainecd).," Furthermore, of these 13 galaxies, only 1 has $R\le 0.25$ is well-constrained)."
 Looking at the 21 galaxies (hat are inconsistent with CDM. only 10 have less than 30 data points.," Looking at the 21 galaxies that are inconsistent with CDM, only 10 have less than 30 data points."
 Of these 10 ealaxies. all except one have 2x0.25.," Of these 10 galaxies, all except one have $R\le 0.25$."
 Rotation curves with more than 30 data points tend (to be better constrained on average. as well as have a tendency to be inconsistent with CDM.," Rotation curves with more than 30 data points tend to be better constrained on average, as well as have a tendency to be inconsistent with CDM."
 It is also interesting to note that even amongst galaxies with only a limited number of data points. the most constrained solutions (small A2) tend to be those inconsistent wilh CDM.," It is also interesting to note that even amongst galaxies with only a limited number of data points, the most constrained solutions (small $R$ ) tend to be those inconsistent with CDM."
 The majority of solutions (85 per cent) that are consistent. with CDM have only a small number of data points are ill-constrained., The majority of solutions $(\sim 85$ per cent) that are consistent with CDM have only a small number of data points are ill-constrained.
 These ill-constrained solutions therefore do not decide between any model one way or the other. aud statements that these galaxies are consistent wilh CDM are {hus not very strong.," These ill-constrained solutions therefore do not decide between any model one way or the other, and statements that these galaxies are consistent with CDM are thus not very strong."
 Of the well-constrained solutions the large majority is inconsistent wilh CDA., Of the well-constrained solutions the large majority is inconsistent with CDM.
 Furthermore. of the 13 galaxies with more (han 30 data points only 2 are consistent wilh CDM.," Furthermore, of the 13 galaxies with more than 30 data points only 2 are consistent with CDM."
 These (wo galaxies (NGC 3274 and NGC 4455) also happen to have the smallest optical seale-lengtlis ancl highest surface brightnesses from all galaxies with available photometry in the MeGaughοἱal.(2001).. deBlok&Dosma(2002). and Swatersetal.(2003) samples: both galaxies have αν<20.0 mag 7.," These two galaxies (NGC 3274 and NGC 4455) also happen to have the smallest optical scale-lengths and highest surface brightnesses from all galaxies with available photometry in the \citet{mcgaugh2001}, \citet{dBB02} and \citet{swaters2003} samples: both galaxies have $\mu_{0,B} \la 20.0$ mag $^{-2}$."
 These galaxies are therefore unlikely to be dominated by dark matter in (heir inner parts ancl it is very likely that the steep slopes in (hese two galaxies simply reflect the stellar mass distribution (see also the discussion on NGC 3274 in Sec., These galaxies are therefore unlikely to be dominated by dark matter in their inner parts and it is very likely that the steep slopes in these two galaxies simply reflect the stellar mass distribution (see also the discussion on NGC 3274 in Sec.
 9.2.2 of deBlok&Bosma. 2002))., 9.2.2 of \citealt{dBB02}) ).
 Amonest the rotation eurves with less than 30 points there is only one galaxy. with Ho«0.25 that seems consistent with CDM., Amongst the rotation curves with less than 30 points there is only one galaxy with $R<0.25$ that seems consistent with CDM.
 This is UGC 131. a bona-fide LSB cdwarf. and," This is UGC 731, a bona-fide LSB dwarf, and"
stars and might well coustitute the main source of Li in the galaxy.,stars and might well constitute the main source of Li in the galaxy.
 The production of Li in ACB stars las received special attention in receut vears (c.g. Sackiiaun Boothrovd 1992)., The production of Li in AGB stars has received special attention in recent years (e.g. Sackmann Boothroyd 1992).
" Basically, Li is produced bv the reaction ?IIetΠο,+)""Be. followed by “Bolewv)’Li in a hot convective region hat brings the “Be or ‘Li. to cooler regions before the * Li is destrove by Τα».o)Hle."," Basically, Li is produced by the reaction $\rm{^3He(^4He,\gamma)^7Be}$, followed by $\rm{^7Be(e^-,\nu)^7Li}$ in a hot convective region that brings the $\rm{^7Be}$ or $\rm{^7Li}$ to cooler regions before the $^7$ Li is destroyed by $\rm{^7Li(p,\alpha)^4He}$."
 This is the so-called * Be-trauspor πιολαπάσι (Cameroun Fowler 1971)., This is the so-called $^7$ Be-transport mechanism (Cameron Fowler 1971).
 Results of these theoretical studies quantitatively agree with the Li abuudances derived iu ACD stars of the ealaxy aud the Magellanic Clouds. although there are still many open questions related to the Li production in these stars.," Results of these theoretical studies quantitatively agree with the Li abundances derived in AGB stars of the galaxy and the Magellanic Clouds, although there are still many open questions related to the Li production in these stars."
 Amoue others we find questions about the minium initial stellar mass which can eventually become a SLIR star during the AGB phase. the duration of the SLIR phase or the actual Li vield iuto the interstellar miediuin.," Among others we find questions about the minimum initial stellar mass which can eventually become a SLiR star during the AGB phase, the duration of the SLiR phase or the actual Li yield into the interstellar medium."
 Our purpose in this work is related to the reality of the Li abundances im SLIR stars iud its consequences ou the Li vield., Our purpose in this work is related to the reality of the Li abundances in SLiR stars and its consequences on the Li yield.
 At preseut. the uncertainty in the derivation of he Li abundances in ACB stars is not lower than 0.10.5 dex (see references above). mainly due to uucertainties iu he stellar parameters aud the fit to the observed spectra.," At present, the uncertainty in the derivation of the Li abundances in AGB stars is not lower than 0.4-0.5 dex (see references above), mainly due to uncertainties in the stellar parameters and the fit to the observed spectra."
 Note. that iu many situatious no single set of stellar yaralucters Is found to fit the observations.," Note, that in many situations no single set of stellar parameters is found to fit the observations."
" Ποπονο, here are also systematic errors that are not usually aken iuto account that nüeht dramatically chauge the Li abundance derived: uncertainties in the atmosphere nodels. the existence of velocity stratificatious (1u0st SLIR stars are actually variable). sphericity aud NLTE effects are not currently considered as possible svstCluatic sources of error."," However, there are also systematic errors that are not usually taken into account that might dramatically change the Li abundance derived: uncertainties in the atmosphere models, the existence of velocity stratifications (most SLiR stars are actually variable), sphericity and NLTE effects are not currently considered as possible systematic sources of error."
" Of course. the consequences of each of these phenomena on Li abundance merit indiviual study aud are bevond the scope of this work (sec. hosvever, Scholtz 1992: Jorseusen et al."," Of course, the consequences of each of these phenomena on Li abundance merit individual study and are beyond the scope of this work (see, however, Scholtz 1992; rgensen et al."
 1992)., 1992).
 Here. we will focus our attention on the effects of departures from LTE in the formation of the Li lines in C-stars.," Here, we will focus our attention on the effects of departures from LTE in the formation of the Li lines in C-stars."
 The study of NLTE effects iu the formation of lithimu lines iu stellar atinospheres was begun by the work of ALulller et al. (, The study of NLTE effects in the formation of lithium lines in stellar atmospheres was begun by the work of Mülller et al. (
1975).,1975).
 They performed NETE analysis of the very weak lithimm resonance line A6708 in the spectrmm of the Sun.," They performed NLTE analysis of the very weak lithium resonance line $\lambda
6708$ in the spectrum of the Sun."
 Later. Luck (1977) investigated the statistical balance of lithium in the atinospheres of C-I& elauts for a [level atom model of Li.," Later, Luck (1977) investigated the statistical balance of lithium in the atmospheres of G-K giants for a 4-level atom model of Li."
 A similar atom model was used by de a Reza Querci (1978) aud de la Reza e al. (, A similar atom model was used by de la Reza Querci (1978) and de la Reza et al. (
1981).,1981).
 Historically these papers considered. for the first tine the impact of a stellar chromosphere on the lithimm lines.," Historically, these papers considered for the first time the impact of a stellar chromosphere on the lithium lines."
 A new stage of research was beeun with the work of Steenbock Uolweeer (1981). who TisCC the technique of complete linearization for an ὃ-leve atom model.," A new stage of research was begun with the work of Steenbock Holweger (1984), who used the technique of complete linearization for an 8-level atom model."
 They studied NLTE effects in ith lines in atmospheres of dwarfs aud giauts., They studied NLTE effects in lithium lines in atmospheres of dwarfs and giants.
 Pavleuko (1991) considered iu detail the effects of devialon from LTE in the atmosphere of red eiauts., Pavlenko (1991) considered in detail the effects of deviation from LTE in the atmosphere of red giants.
 Later. Magazzü et al. (," Later, Magazzú et al. ("
1992). [ανα et al. (,"1992), Martin et al. ("
1991) and. Pavlenko (199 continued the NLTE studies in T-Tau stars. €C-I& giauts. subeianuts and dwarfs,"1994) and Pavlenko (1994), continued the NLTE studies in T-Tau stars, G-K giants, subgiants and dwarfs."
 The main results of these studies were confirmed by the independent work of Carlsson et al. (, The main results of these studies were confirmed by the independent work of Carlsson et al. (
199D). who uade a similar investigation using atinosplhere models with various effective. teniperatures. DIunuuosities aud metallicities.,"1994), who made a similar investigation using atmosphere models with various effective temperatures, luminosities and metallicities."
 Finally. Houdebiue et al. (," Finally, Houdebine et al. ("
1095). Pavleuko et al. (,"1995), Pavlenko et al. ("
1995). Pavleuko Magazzü (1996) aud Martiu ct al. (,"1995), Pavlenko Magazzú (1996) and Martin et al. ("
1997) have coutinued the stucdies of different aspects of NLTE formation of lithimm lines 1- stellar atinosplieres.,1997) have continued the studies of different aspects of NLTE formation of lithium lines in stellar atmospheres.
 As far as we know. the sole study ou this subject for ACD stars is that by de la Reza Querci (1978) who performe kinetic equilibrium calculations of neutral lithinan lines in C-stars aud determined the influence of the possible clromospheric radiation into the photosphere.," As far as we know, the sole study on this subject for AGB stars is that by de la Reza Querci (1978) who performed kinetic equilibrium calculations of neutral lithium lines in C-stars and determined the influence of the possible chromospheric radiation into the photosphere."
 Iu the preseut work we revise this study using up to date atomic data. collisional aud radiative rates. an extended Li atom model aud more reliable model atinosphlieres. for CUstars in a wider range of effective temperatures CI=2500—3100 IK) and C/O ratios (1.0-1.35) (see below).," In the present work we revise this study using up to date atomic data, collisional and radiative rates, an extended Li atom model and more reliable model atmospheres for C-stars in a wider range of effective temperatures $\rm{_{eff}}=2500-3100$ K) and C/O ratios (1.0-1.35) (see below)."
 We explicitly apply our results deriviug Li abuudances from svuthetic spectra. both in LTE aud NLTE. in three wol known SLIR stars (WX Cre. WZ Cas and IY να) frou four accessible Li I lines: he resonance line at AGTOS and the subordinate transitions at A1603. AGLOL and AS126A. respectively. benefiting frou the high sigual-to-noise ratio and high resolution spectra of these stars.," We explicitly apply our results deriving Li abundances from synthetic spectra, both in LTE and NLTE, in three well known SLiR stars (WX Cyg, WZ Cas and IY Hya) from four accessible Li I lines: the resonance line at $\lambda6708$ and the subordinate transitions at $\lambda4603$, $\lambda6104$ and $\lambda8126$, respectively, benefiting from the high signal-to-noise ratio and high resolution spectra of these stars."
 The consequences on the real Li abundances in ACB stars and ou their net Li vield iuto the imterstellar medimm is then reexiundinecd., The consequences on the real Li abundances in AGB stars and on their net Li yield into the interstellar medium is then reexamined.
" The observatious were made during 1997 and 1998 iu ""o different observatories.", The observations were made during 1997 and 1998 in two different observatories.
 We used the L2 m WOT at the Observatory of El Roque de los Mucliachos with he Utrecht Echelle Spectrograph as the main iustrunenut and a 2048 CCD with 21 gan pixel size., We used the 4.2 m WHT at the Observatory of El Roque de los Muchachos with the Utrecht Echelle Spectrograph as the main instrument and a $\times$ 2048 CCD with 24 $\mu$ m pixel size.
 We used he 79.0 linesfim erating which provides less wavelength coverage. but more space between orders (20-30 aresec).," We used the 79.0 lines/mm grating which provides less wavelength coverage, but more space between orders (20-30 arcsec)."
 The projected size of the slit on the chip was around wo pixels which gave a resolving power of 50000. the effective resolution ranging between 0.05-0.19 from the due orders to the red ones.," The projected size of the slit on the chip was around two pixels which gave a resolving power of 50000, the effective resolution ranging between 0.05-0.19 from the blue orders to the red ones."
 The total nuuber of orders ou the chip were 30 covering the waveleneth range 0.1-1.0 fan with some gaps between orders., The total number of orders on the chip were 30 covering the wavelength range 0.4-1.0 $\mu$ m with some gaps between orders.
 WZ Cas and WX Cye were also observed by the 2.2 τι telescope at the Calar Alto Observatory., WZ Cas and WX Cyg were also observed by the 2.2 m telescope at the Calar Alto Observatory.
 For this observational run a fibre optics cassegrain echelle spectrograph (FOCES) (Pfeiffer et al., For this observational run a fibre optics cassegrain echelle spectrograph (FOCES) (Pfeiffer et al.
 1998) was used., 1998) was used.
 This time the chip was a 10211021 Tektronik CCD with 2l sau pixel size., This time the chip was a $\times$ 1024 Tektronik CCD with 24 $\mu$ m pixel size.
 The FOCES image covers the visible spectral region from 0.38 to 0.96. ju in about SO orders with full spectral coverage., The FOCES image covers the visible spectral region from 0.38 to 0.96 $\mu$ m in about 80 orders with full spectral coverage.
 Spectral OLCLCYS are separatec by 20 pixels iu the blue aud 10 iu the red., Spectral orders are separated by 20 pixels in the blue and 10 in the red.
 The maxiuun resolving power is 10000 with a two pixel resolution clement., The maximum resolving power is 40000 with a two pixel resolution element.
"the RG-Novae are KT Eri, EU Sct and M31N 2007-12b.","the RG-Novae are KT Eri, EU Sct and M31N 2007-12b."
" However, the question of whether these are recurrent novae with missed outbursts or part of a population of long inter-outburst timescale evolved systems is one we cannot address here as a short recurrence time also requires a high mass WD."," However, the question of whether these are recurrent novae with missed outbursts or part of a population of long inter-outburst timescale evolved systems is one we cannot address here as a short recurrence time also requires a high mass WD."
" However, we would strongly urge searches of observational archives to uncover any missed outbursts (as was done for V2487 Oph)."," However, we would strongly urge searches of observational archives to uncover any missed outbursts (as was done for V2487 Oph)."
" We predict that the secondary of the recurrent nova CI Agl is a sub-giant star, akin to the secondary in the U Sco system, and that the of the recurrent V2487 Oph is a red-giant similar tosecondary that in the KT Eri system."," We predict that the secondary of the recurrent nova CI Aql is a sub-giant star, akin to the secondary in the U Sco system, and that the secondary of the recurrent V2487 Oph is a red-giant similar to that in the KT Eri system."
 There is also some evidence that the secondary in DI Lac is also a sub-giant star., There is also some evidence that the secondary in DI Lac is also a sub-giant star.
" Whilst preparing the catalog of novae analyzed in this paper, it quickly became clear that reliable, multi-color, quiescent photometry is lacking for a large number of Galactic novae."," Whilst preparing the catalog of novae analyzed in this paper, it quickly became clear that reliable, multi-color, quiescent photometry is lacking for a large number of Galactic novae."
" reliance on a single epoch of quiescent photometry is Additionally,problematic due to the large range in quiescent luminosity exhibited by many systems."," Additionally, reliance on a single epoch of quiescent photometry is problematic due to the large range in quiescent luminosity exhibited by many systems."
" Whilst this technique has been shown to produce results consistent with the current understanding of most nova generallysystems, although revealing several interesting systems, there are a number of limitations that are worth of discussion."," Whilst this technique has been shown to produce results generally consistent with the current understanding of most nova systems, although revealing several interesting systems, there are a number of limitations that are worth of discussion."
" In systems where the accretion disk has a significant contribution to the luminosity, the magnitude of this contribution is a function of the inclination of that disk (or of the system)."," In systems where the accretion disk has a significant contribution to the luminosity, the magnitude of this contribution is a strong function of the inclination of that disk (or of the system)."
 strongWarner(1987) showed a correlation between the disk inclination and the apparent brightness of nova remnants and the amplitude of their outburst., \citet{1987MNRAS.227...23W} showed a correlation between the disk inclination and the apparent brightness of nova remnants and the amplitude of their outburst.
 The inclination correction to be applied to the magnitude of a quiescent CN system was initially derived for the dwarf nova U Geminorum by Paczynski&Schwarzenberg-Czerny (1980)., The inclination correction to be applied to the magnitude of a quiescent CN system was initially derived for the dwarf nova U Geminorum by \citet{1980AcA....30..127P}.
". They modeled the disk luminosity in U Gem by assuming flat optically thick accretion disk and derived the following arelation showing the change in magnitude of the disk as a function of inclination: where i is the inclination of the system, defined such that i=O° is a polar/face-on system and i=90° is edge-on."," They modeled the disk luminosity in U Gem by assuming a flat optically thick accretion disk and derived the following relation showing the change in magnitude of the disk as a function of inclination: where $i$ is the inclination of the system, defined such that $i=0^{\circ}$ is a polar/face-on system and $i=90^{\circ}$ is edge-on."
 This relationship is independent of the disk luminosity and hence the accretion rate and is normalized to the mean disk luminosity (which occurs at i= 56.7°)., This relationship is independent of the disk luminosity and hence the accretion rate and is normalized to the mean disk luminosity (which occurs at $i=56.7^{\circ}$ ).
 We adapt Equation 1 such that it may be normalized to any inclination: where J is the inclination at which one chooses as a standard., We adapt Equation \ref{eq:inc} such that it may be normalized to any inclination: where ${\cal I}$ is the inclination at which one chooses as a standard.
" The Paczynski&Schwarzenberg-Czerny(1980) model is applicable for any system in which the accretion disk is the dominant luminosity source, and is therefore only reasonable to apply to MS-Nova systems, the effect of the magnitude change would be expected to decrease significantly for SG-Novae and RG-Novae, i.e. with increasing secondary "," The \citet{1980AcA....30..127P} model is applicable for any system in which the accretion disk is the dominant luminosity source, and is therefore only reasonable to apply to MS-Nova systems, the effect of the magnitude change would be expected to decrease significantly for SG-Novae and RG-Novae, i.e. with increasing secondary luminosity."
To the effect of inclination in each nova luminosity.system we use investigateEquation 2 to minimize the effect of the accretion disk (i.e. edge-on)., To investigate the effect of inclination in each nova system we use Equation \ref{eq:inc2} to minimize the effect of the accretion disk (i.e. edge-on).
" However, as the accretion disks in novae are not flat and the secondary has some luminosity in V (originalassumptionsfromPaczyn-Schwarzenberg-Czerny1980) we adopt an inclination I=80° to be indicative of the minimum V-band flux of an edge-on CN system."," However, as the accretion disks in novae are not flat and the secondary has some luminosity in $V$ \citep[original assumptions from][]{1980AcA....30..127P} we adopt an inclination ${\cal I}=80^{\circ}$ to be indicative of the minimum $V$ -band flux of an edge-on CN system."
" Therefore, to estimate the absolute magnitude My of the secondary in a given system at quiescence, it follows that: where V is the apparent magnitude, d distance to the system in (parsecs) and Ay the extinction correction."," Therefore, to estimate the absolute magnitude $M_V$ of the secondary in a given system at quiescence, it follows that: where $V$ is the apparent magnitude, $d$ distance to the system in (parsecs) and $A_V$ the extinction correction."
" However, such an is only to be valid when it can be assumed that the approachaccretion disk likelydominates the luminosity and the accretion rate is low (hence the disk is approximately flat)."," However, such an approach is only likely to be valid when it can be assumed that the accretion disk dominates the luminosity and the accretion rate is low (hence the disk is approximately flat)."
" Hence in SG-Novae and particular RG-Novae systems, where the flux contribution of the secondary is significant, we would expect the effect of system inclination to be substantially reduced."," Hence in SG-Novae and particular RG-Novae systems, where the flux contribution of the secondary is significant, we would expect the effect of system inclination to be substantially reduced."
" Additionally, the luminosity ratio of the accretion disk to the secondary will be at its smallest for the Ks data."," Additionally, the luminosity ratio of the accretion disk to the secondary will be at its smallest for the $K_{S}$ data."
" Hence, if we assume that the Ks flux of each quiescent nova system is due only to the secondary, we can produce a color magnitude diagram showing the location of just the secondary star in each system (see 3))."," Hence, if we assume that the $K_{S}$ flux of each quiescent nova system is due only to the secondary, we can produce a color magnitude diagram showing the location of just the secondary star in each system (see Figure \ref{inclination}) )."
" As can be seen in Figure 3 this very simple approach to inclination has the expected effect of repositioning most MS-nova systems redwards, towards the true position of the secondary star on the main sequence."," As can be seen in Figure \ref{inclination} this very simple approach to inclination has the expected effect of repositioning most MS-nova systems redwards, towards the true position of the secondary star on the main sequence."
" However, in order to apply such a technique to all novae, more detailed models of the disks in these systems are required."," However, in order to apply such a technique to all novae, more detailed models of the disks in these systems are required."
" Such attempts also suffer from the difficulty in obtaining, and hence lack of, accurate inclination measurements of most nova systems."," Such attempts also suffer from the difficulty in obtaining, and hence lack of, accurate inclination measurements of most nova systems."
"Two extraordinary features the strong increase of aneular rotation velocity aud of stellar velocity dispersion inside a radius of aand the shift of the bright poiut-like nucleus with respect to the center of the galaxy were ndwally explained iu the frames of two equally successfi""ul models: a strcng anisotropy (cud-on tumbling minuiAL: Cerhard1988)) and alo axisvnunuetric potential disribution with a supermassive black hole iu he center (I&oriieudy. 1988).",Two extraordinary features – the strong increase of angular rotation velocity and of stellar velocity dispersion inside a radius of and the shift of the bright point-like nucleus with respect to the center of the galaxy – were initially explained in the frames of two equally successful models: a strong anisotropy (end-on tumbling minibar: \cite{gerhard}) ) and an axisymmetric potential distribution with a supermassive black hole in the center (Kormendy \cite{k88}) ).
 The former model lookec preferable because of the isophote twist aOS the radius of and because of a noticeaJe line-of-sigh velocity eradient along the photometric nüuor axis (Ciardullo « tal. d1988)) ., The former model looked preferable because of the isophote twist along the radius of and because of a noticeable line-of-sight velocity gradient along the photometric minor axis (Ciardullo et al. \cite{ciar}) ) –
 these observationa facts had allowed Stark aid Binney (199ty) to Sugeest the presence of a large-scale bar in extended up to ffrom the ceuer., these observational facts had allowed Stark and Binney \cite{sb94}) ) to suggest the presence of a large-scale bar in extended up to from the center.
 However Bacon ct al. (1991)) «, However Bacon et al. \cite{bemn94}) )
"utesbservec a central part. rzx:5"", of with the La Field Spectregraph TIGER and could conipare the surface brighHOSS lap with the liinc-ofsight veloc Ποια: they have found a coimeideuc(e oft1ο chynaCa and photonieric lajor axes and in this wav proves he circularity of stellar rotation luside a radius of5""."," observed a central part, $r \le 5\arcsec$, of with the Integral Field Spectrograph TIGER and could compare the surface brightness map with the line-of-sight velocity field; they have found a coincidence of the dynamical and photometric major axes and in this way proved the circularity of stellar rotation inside a radius of."
 The unecar region of 1las appeared to be axisviunietric., The nuclear region of has appeared to be axisymmetric.
 After that a model of Tremaine (19953) iis become very popular he has prOPOSc an eccentric disk rotating in accordance with the hepers law and raving a supermassive black hole iu one of its foci. P2.," After that a model of Tremaine \cite{tr}) ) has become very popular: he has proposed an eccentric disk rotating in accordance with the Kepler's law and having a supermassive black hole in one of its foci, P2."
 Tn the frame of this model the bright nuuccus Pl is ali apocenter where stars decelerate aud their orbits crowd. hen forming a surface brightuess excess.," In the frame of this model the bright nucleus P1 is an apocenter where stars decelerate and their orbits crowd, then forming a surface brightness excess."
 The inodel of Tremaine (1995)) is often cited as the most realislc: rowever If has been dismissed two voars ago., The model of Tremaine \cite{tr}) ) is often cited as the most realistic; however it has been dismissed two years ago.
 Crorssen. et al. (19953) , Gerssen et al. \cite{gkm95}) )
"had observed with a lorest spectroerajh: hey hack oricutes the slit alone the minor axis of he cleus (PAL tls"") axd set its width as 1725. SO hat the putative disk of Trαμαπιο faIs completely witiu he slit."," had observed with a long-slit spectrograph; they had oriented the slit along the minor axis of the nucleus $P.A.=148\degr$ ) and set its width as $1\farcs25$, so that the putative disk of Tremaine falls completely within the slit."
 Due to augular momentu conservation. he uiinositv-welehted velocits νο a filed Iweplerian orhit about a stationary object s vould1 OZZOTO: but the analySIS : the observations show the preseuce of two distiict jeniatical componcits at r=0!," Due to angular momentum conservation, the luminosity-weighted velocity of a filled Keplerian orbit about a stationary object should be zero; but the analysis of the observations showed the presence of two distinct kinematical components at $r=0$!"
 Thcced. only one model is not rejected: that of a giant stellar cluster falling to he ceuter of uuder the attrac‘tion of a black hole (Eqauscllom&Combes 1997)): but such a configuration is unstable aud very short-lived. so it implies that is observed during au τιiique evolutionary stage.," Indeed, only one model is not rejected: that of a giant stellar cluster falling to the center of under the attraction of a black hole \cite{emcomb97}) ); but such a configuration is unstable and very short-lived, so it implies that is observed during an unique evolutionary stage."
 The results«jbtained in this work even worsen the situation., The results obtained in this work even worsen the situation.
" Earlier whe1 we discovered a chemically distinct uucleus in galaxies iore distaut thanATD3M.. we supposed it to be a compact nuclear disk: In several cases where the chemically distinct nuclei appeared to be resolved. our supposition was confirmed In"" a colucideuce of chemically. kinematically auc photometrically distinct area radi Silchek.1995... Sil'eheuko1997: bit uote that they are ο]lipti ealaxies)."," Earlier when we discovered a chemically distinct nucleus in galaxies more distant than, we supposed it to be a compact nuclear disk; in several cases where the chemically distinct nuclei appeared to be resolved, our supposition was confirmed by a coincidence of chemically, kinematically and photometrically distinct area radii – \cite{me95}, – \cite{me97}; but note that they are elliptical galaxies)."
 The case of has «estroved our presuniptiou: the nuclear disk detecB by dts pliXtometiic signature has a radius | SOLOO vw. While the chemically cüstiuct imcleus Is iesolved. being less than 3 pe.," The case of has destroyed our presumption: the nuclear disk of detected by its photometric signature has a radius of 80–100 pc, while the chemically distinct nucleus is unresolved, being less than 3 pc."
 Moreover. it is not P1 whicli is «iomicallv distinet. though only P1 is themelt to he a eiut stellar cluster. but P2 which is assume to IC d πιpernmassive black hole the stellar couteut around swuch is not vet known.," Moreover, it is not P1 which is chemically distinct, though only P1 is thought to be a giant stellar cluster, but P2 which is assumed to be a supermassive black hole the stellar content around which is not yet known."
 The central region with a radis of 273 oei Fig., The central region with a radius of $2\farcs3$ in Fig.
 3 looks three times vouuger than the Inlee: but P2 coutributes oulv a small fraction iuto the Iuniijositv of Dis region. nanielv. lif to asstune t16 photometric decomposition modeLC from the work of Bacon ct al. (199 D):," \ref{diag} looks three times younger than the bulge; but P2 contributes only a small fraction into the luminosity of this region, namely, if to assume the photometric decomposition model C from the work of Bacon et al. \cite{bemn94}) );"
 so we nust conc‘lide that the stellar ]x»ilation of P2 is siguificautY vouieroy thaw 5 billion vears., so we must conclude that the stellar population of P2 is significantly younger than 5 billion years.
 Hence a relatively recen star forniation burst exactly at the dyvuanücal ceuter of SCCLUS iudubitable., Hence a relatively recent star formation burst exactly at the dynamical center of seems indubitable.
" It mav not be the onlv aux last one: «ust spiral avis in the nuclear disk of31.. the loca splitting ofewission lines in several spots within a dozen ix""""econds from the center seen in our data and also in fhe data of Clardlo et al. (1985))."," It may not be the only and last one: dust spiral arms in the nuclear disk of, the local splitting of emission lines in several spots within a dozen arcseconds from the center seen in our data and also in the data of Ciardullo et al. \cite{ciar}) ),"
 the brielt nucleus Pl which rot be ona stable orbit — all these Cs are evideuces favour of a contimous matter dif the «nter ofal., the bright nucleus P1 which cannot be on a stable orbit – all these facts are evidences in favour of a continuous matter drift to the center of.
" Trough less probable. there exists still another expanation of the ooervational facts reported by us: if in the proximity of the supermassive slack hole located 1insicle P2 the stars lavo sOLnQC lua Structure. say, if ticr external atmiosplheres are removed bv tidal effects. then we see them immer leavers which are enriched by metals."," Though less probable, there exists still another explanation of the observational facts reported by us: if in the proximity of the supermassive black hole located inside P2 the stars have some unusual structure, say, if their external atmospheres are removed by tidal effects, then we see their inner layers which are enriched by metals."
 I1 this case the uneeus P2 av look like a chemically decoupled uucleus too., In this case the nucleus P2 may look like a chemically decoupled nucleus too.
"found by Yinetal.(2007),, who compared oxygen estimates via N> and m]/H8)/([N π]/Ηα) with those via T,-method for a sample of 695 galaxies and regions.","found by \citet{yin07}, who compared oxygen estimates via $N_{2}$ and $\beta$ $\alpha$ ) with those via $T_{e}$ -method for a sample of 695 galaxies and regions."
" This occurs because in this regime of metallicity the nitrogen and oxygen have both mainly a primary nucleosynthesis origin, doing nitrogen emission lines to be relatively independent on oxygen abundance and consequently the use of metallicity indicators based on these emission lines are not reliable. ("," This occurs because in this regime of metallicity the nitrogen and oxygen have both mainly a primary nucleosynthesis origin, doing nitrogen emission lines to be relatively independent on oxygen abundance and consequently the use of metallicity indicators based on these emission lines are not reliable. ("
e.g. Levesqueetal.2010;; Dopitaetal.2000)).,e.g. \citealt{levesque10}; \citealt{dopita00}) ).
 The origin of the dispersion found by us is probable due to the difference between the real N/O-O/H abundance relation of the object sample and the one assumed in our models., The origin of the dispersion found by us is probable due to the difference between the real N/O-O/H abundance relation of the object sample and the one assumed in our models.
" In fact, Pérez-Montero&Contini(2009) analyzed the dependence of N/O with O/H estimation obtained via the metallicity indicators using nitrogen line ratios and compared these estimations with the ones obtained via T,-method."," In fact, \citet{perez09} analyzed the dependence of N/O with O/H estimation obtained via the metallicity indicators using nitrogen line ratios and compared these estimations with the ones obtained via $T_{\rm e}$ -method."
" They found approximately the same dispersion as the one derived by us, and also showed that if the N/O ratio is taken into account in strong-line methods, the dispersion can be reduced by about 0.1 dex."," They found approximately the same dispersion as the one derived by us, and also showed that if the N/O ratio is taken into account in strong-line methods, the dispersion can be reduced by about 0.1 dex."
" Moreover, the scattering of N/O for a fixed O/H value is larger for the low metallicity regime (see e.g. Pilyuginetal.2003)), which introduces a larger dispersion for oxygen estimations in this regime, such as the one observed in our results."," Moreover, the scattering of N/O for a fixed O/H value is larger for the low metallicity regime (see e.g. \citealt{pilyugin03}) ), which introduces a larger dispersion for oxygen estimations in this regime, such as the one observed in our results."
" This is confirmed by the use of detailed models, for which the N/O-O/H relation is a free parameter, yielding a lower dispersion (0.08 dex) than the ones obtained from diagnostic diagrams."," This is confirmed by the use of detailed models, for which the N/O-O/H relation is a free parameter, yielding a lower dispersion (0.08 dex) than the ones obtained from diagnostic diagrams."
" Yinetal.(2007) also obtained similar results comparing oxygen abundances derived from T,-method and those via the photoionization models of Charlot&Longhetti(2001).", \citet{yin07} also obtained similar results comparing oxygen abundances derived from $T_{\rm e}$ -method and those via the photoionization models of \citet{charlot01}.
". Another important test is to verify if abundance gradients estimates by using diagnostic diagrams agree with those via T,- method.", Another important test is to verify if abundance gradients estimates by using diagnostic diagrams agree with those via $T_{\rm e}$ -method.
" For that, in Fig."," For that, in Fig."
 7 we show a comparison of oxygen gradient slope computed using the [Omj/[On] vs. u]/[Ou] diagram presented in Fig., \ref{f55} we show a comparison of oxygen gradient slope computed using the ] vs. ] diagram presented in Fig.
" 2 and those via Τε-πιείποά for spiral galaxies M1101, M551, M333, and NGC22403 obtained by Kennicuttetal.(2003), Bresolinetal. (2004),, Magrinietal. (2007),, and Garnettetal.(1997), respectively."," \ref{f1}
 and those via $T_{\rm e}$ -method for spiral galaxies 101, 51, 33, and 2403 obtained by \citet{kennicutt03}, \citet{bresolin04}, \citet{magrini07}, and \citet{garnett97}, respectively."
" We can see that, within the uncertainties given by the linear fitting, the diagnostic diagram above yields abundance gradient consistent with the ones via T,-method."," We can see that, within the uncertainties given by the linear fitting, the diagnostic diagram above yields abundance gradient consistent with the ones via $T_{\rm e}$ -method."
" Again, the difference between the gradient estimates is probable due to the N/O-O/H relation assumed in our models and the one of the galaxies."," Again, the difference between the gradient estimates is probable due to the N/O-O/H relation assumed in our models and the one of the galaxies."
" This is supported by the detailed model results, since a linear fitting on oxygen abundance from these, presented in Table 2,, yields a gradient for 1101 of 12+log(O/H)= 0.90(+0.26) R/Ros + 8.77(+0.15), the same gradients found by Kennicuttetal.(2003) using the T,-method."," This is supported by the detailed model results, since a linear fitting on oxygen abundance from these, presented in Table \ref{tab2}, yields a gradient for 101 of 12+log(O/H)= $\pm0.26$ ) $R/R_{25}$ + $\pm0.15$ ), the same gradients found by \citet{kennicutt03} using the $T_{\rm e}$ -method."
" In general, oxygen determination obtained from strong- methods, which use emission line intensities predicted by photoionization models, are overestimated up to 0.5 dex when compared with those obtained from T.-method (Kewley&El-nettetal.2004;Stasiáska 2002)."," In general, oxygen determination obtained from strong-line methods, which use emission line intensities predicted by photoionization models, are overestimated up to 0.5 dex when compared with those obtained from $T_{\rm e}$ -method \citep{kewley08,dors05,kennicutt03,garnett04,stasinska02}."
". This discrepancy is attributed to the fact that photoionization codes are not realistic enough, do not treat all the relevant physical processes correctly, use inaccurate atomic data, etc (Kennicuttetal.2003)."," This discrepancy is attributed to the fact that photoionization codes are not realistic enough, do not treat all the relevant physical processes correctly, use inaccurate atomic data, etc \citep{kennicutt03}."
". However, as seen previously, using the state of art of photoionization models and the combination of two line ratio, one sensitive to the metallicity and another sensitive to the ionization parameter, which does taken into account the physical conditions (hardness of the ionizing radiation and geometrical factor) of star-forming regions (Pilyugin 2001), minimizes the effects mentioned above and gives O/H estimates close to the 7.-method."," However, as seen previously, using the state of art of photoionization models and the combination of two line ratio, one sensitive to the metallicity and another sensitive to the ionization parameter, which does taken into account the physical conditions (hardness of the ionizing radiation and geometrical factor) of star-forming regions \citep{pilyugin01}, minimizes the effects mentioned above and gives O/H estimates close to the $T_{\rm e}$ -method."
" As explained in Sect. 3,,"," As explained in Sect. \ref{phot},"
 the match between solar abundances for the gas and star has little influence on metallicity indicators (i.e. u]) showing that the metallicity estimates by our models are indepent of this fact., the match between solar abundances for the gas and star has little influence on metallicity indicators (i.e. ]) showing that the metallicity estimates by our models are indepent of this fact.
" The ionization parameter is expected to be dependent on the metallicity because stellar atmospheres of massive O stars become cooler with increasing metallicity as a result of enhanced line and wind blanketing (Masseyetal. 2005), decreasing consequently the ionization parameter."," The ionization parameter is expected to be dependent on the metallicity because stellar atmospheres of massive O stars become cooler with increasing metallicity as a result of enhanced line and wind blanketing \citep{massey05}, , decreasing consequently the ionization parameter."
" Moreover, when stellar"," Moreover, when stellar"
The modulation index 7 is defined as the ratio of the RMS deviation to the mean value of the observed flux densities Table ] presents the values of the measured modulation indices for each individual session.,The modulation index $m$ is defined as the ratio of the RMS deviation to the mean value of the observed flux densities Table \ref{t1} presents the values of the measured modulation indices for each individual session.
 The average values of 7 in the bottom section of the table. just as the flux density averages (see previous section). are calculated with and without last two sessions.," The average values of $m$ in the bottom section of the table, just as the flux density averages (see previous section), are calculated with and without last two sessions."
 For these sessions the quasi-stable flux behaviour means that the relative strength of the modulation drops and also causes the increase of (F)., For these sessions the quasi-stable flux behaviour means that the relative strength of the modulation drops and also causes the increase of $\left<F\right>$.
 Both these effects contribute to the decrease of the measured modulation index for the two ultimate sessions., Both these effects contribute to the decrease of the measured modulation index for the two ultimate sessions.
 For the remaining sessions the modulation index varies from 0.71 (November 2002) to 1.32 (August 2002). with an average value of ;i=0.96+0.04. which means that the observed flux density of the source Is undergoing significant variations.," For the remaining sessions the modulation index varies from 0.71 (November 2002) to 1.32 (August 2002), with an average value of $m=0.96\pm0.04$, which means that the observed flux density of the source is undergoing significant variations."
 One has to ask a question: what contributes to the observed flux modulation?, One has to ask a question: what contributes to the observed flux modulation?
 We expected that at the frequency of 4.8 GHz PSR B0329454 will be still in strong scintillation regime. which means that its signal will be undergoing diffractive as well as refractive scintillations.," We expected that at the frequency of 4.8 GHz PSR B0329+54 will be still in strong scintillation regime, which means that its signal will be undergoing diffractive as well as refractive scintillations."
 This came from. the observational experience with this pulsar and strong flux variability observed at 5 GHz. when we observed it for the purpose of estimating its spectrum (Maron et al. 2000)).," This came from the observational experience with this pulsar and strong flux variability observed at 5 GHz, when we observed it for the purpose of estimating its spectrum (Maron et al. \cite{maro00}) )."
 The theory (see Lorimer Kramer. 2005.. for summary) predicts that at 4.8 GHz a pulsar with DM=26.8 pe οι should be close to its transition frequency. but on the strong scintillation side as well.," The theory (see Lorimer Kramer, \cite{lori}, for summary) predicts that at 4.8 GHz a pulsar with $DM = 26.8$ pc $^{-3}$ should be close to its transition frequency, but on the strong scintillation side as well."
 For the DISS the intrinsic modulation index should be close to unity., For the DISS the intrinsic modulation index should be close to unity.
 In usual. low-frequency observations. where the decorrelation bandwidth Avpjss is significantly less than the observing bandwidth. the number of observed scintles within the bandwidth. at any given time. will be large.," In usual, low-frequency observations, where the decorrelation bandwidth $\Delta\nu_{\rm DISS}$ is significantly less than the observing bandwidth, the number of observed scintles within the bandwidth, at any given time, will be large."
 That would lead to the decrease of the modulation of the average pulsar flux (integrated over the whole bandwidth). as at any given time.," That would lead to the decrease of the modulation of the average pulsar flux (integrated over the whole bandwidth), as at any given time,"
absorption.,absorption.
 For aand wwe obtain 0.52 keV fluxes o£ 12/10. P. 15.10+ and 1510HM erg em- respectively. consistent with those obtained with (Page.Mittaz 2000)..," For, and we obtain $0.5-2$ keV fluxes of $1.2\times 10^{-14}$ , $1.5 \times 10^{-14}$ and $1.8\times
10^{-14}$ erg $^{-2}$ $^{-1}$ respectively, consistent with those obtained with \citep{page00}. ."
 For wwe obtain a 0.5.2 keV Dux o£ 5«10.P ergem 7 +. approximately a quarter of its lux duringour survey. while for wwe obtain; a 0.52 keV Lux of 1.310η ere cn 22041c. approximately half the.Rosa’ Dux reported by Page.taz&Carrera (2000).," For we obtain a $0.5-2$ keV flux of $5\times 10^{-15}$ erg $^{-2}$ $^{-1}$, approximately a quarter of its flux duringour survey, while for we obtain a $0.5-2$ keV flux of $1.3\times 10^{-14}$ erg $^{-2}$ $^{-1}$, approximately half the flux reported by \citet{page00}."
. Simultaneous with the X-ray observations. the Optical Monitor (NMM-OM) took deep images in the UVAVIGiltert.. which has an elfective wavelength of2010A.," Simultaneous with the X-ray observations, the Optical Monitor (XMM-OM) took deep images in the UVW1, which has an effective wavelength of."
. These observations were obtained: primarily to provide photometric redshift’ constraints for objects surrounding the QSOs. and for the three highest. redshift objects the flux in this band is severely allected by. the Lyman break.," These observations were obtained primarily to provide photometric redshift constraints for objects surrounding the QSOs, and for the three highest redshift objects the flux in this band is severely affected by the Lyman break."
 Por aand hhowever. the Lyman break cuts in only at the extreme blue of the. UVNI transmission. anc will have a minor impact on the photometry.," For and however, the Lyman break cuts in only at the extreme blue of the UVW1 transmission, and will have a minor impact on the photometry."
 The data were reduced. using the NMM-OM| SAS version 6.5., The data were reduced using the XMM-OM SAS version 6.5.
 Phe UVMI magnitudes of aand ((in the NM-OM Vega system) are given in Table 1.., The UVW1 magnitudes of and (in the XM-OM Vega system) are given in Table \ref{tab:observations}.
 Droadband: optical spectra. of the five N-rav absorbed QSOs are shown in Fig. Ll., Broadband optical spectra of the five X-ray absorbed QSOs are shown in Fig. \ref{fig:optspecs}.
 Lt is notable that in all five objects. at least one absorption line is superimposed on the broad. UW emission line or on the continuum to the blue of this line.," It is notable that in all five objects, at least one absorption line is superimposed on the broad IV emission line or on the continuum to the blue of this line."
 Lo examine this more closely. we show the regions around the ΗΝ emission line in more detail in Fig. 2.. In 1tXJ005," To examine this more closely, we show the regions around the IV emission line in more detail in Fig. \ref{fig:CIV}."
734.. there are. two absorption lines apparent. with outflow velocities of 4800 and SLOO km assuming that they are CIIV.," In , there are two absorption lines apparent, with outflow velocities of 4800 and 8100 km $^{-1}$, assuming that they are IV."
 In the spectrum. ofΕΕ. at. least. one absorption line is present. apparently inllowing with a velocity of TOO km ‘assuming that it is LLY.," In the spectrum of, at least one absorption line is present, apparently inflowing with a velocity of 700 km $^{-1}$ assuming that it is IV."
 As this spectrum is relatively noisy. we are unable to confirm whether the tentative absorption features to the blue of ΗΝ are real or statistical Ductuations.," As this spectrum is relatively noisy, we are unable to confirm whether the tentative absorption features to the blue of IV are real or statistical fluctuations."
 There are two significant absorption features in1tNJ121803.. one inllowing at 1200 km s.l. and one outllowing at 1600 kms 1.," There are two significant absorption features in, one inflowing at 1200 km $^{-1}$ , and one outflowing at 1600 km $^{-1}$."
 LL absorption is detectedfrom the inllowing component., II absorption is detectedfrom the inflowing component.
 For wwe adopt an emission line redshift of z=2.236 (LlewittBurbidge. 1993).. although the reported. emission line redshift: of this source ranges [from z=2.22 (Doksenbergetal.LOTS) t0 z=2.244 (LLLPhompson&Elston.1993) depending on which emission lines the redshift is based on.," For we adopt an emission line redshift of $z=2.236$ \citep{hewitt93}, although the reported emission line redshift of this source ranges from $z=2.22$ \citep{boksenberg78} to $z=2.244$ \citep{hill93} depending on which emission lines the redshift is based on."
 Relative to this emission line redshift. the πl absorption line has a central velocity of -16700. km with a EFWILIM of 5700 kim + (Boksenbergetal..1978).," Relative to this emission line redshift, the IV broad absorption line has a central velocity of -16700 km $^{-1}$, with a FWHM of 5700 km $^{-1}$ \citep{boksenberg78}."
. 1n tthere are four absorption lines visible. but two of these are likely to be due to an intervening absorption line svstem with z=1.482. for which a number of other transitions are detected in the optical spectrum.," In there are four absorption lines visible, but two of these are likely to be due to an intervening absorption line system with $z=1.482$, for which a number of other transitions are detected in the optical spectrum."
 The remaining two lines have outllow velocities of SOO and 7700 kin, The remaining two lines have outflow velocities of 800 and 7700 km $^{-1}$.
 Both are accompanied by Lye absorption with consistent velocities. and absorption from HV. is detected in the 7700 km component.," Both are accompanied by $\alpha$ absorption with consistent velocities, and absorption from IV is detected in the 7700 km $^{-1}$ component."
 The CIV. absorption line properties of the five QSOs are listed in Table 2.., The IV absorption line properties of the five QSOs are listed in Table \ref{tab:uvlines}.
 The five QSOs have strong rest-frame ultraviolet continuum eniission., The five QSOs have strong rest-frame ultraviolet continuum emission.
 Ultraviolet spectral slopes were measurecl from the optical spectra. longward of Lvo. after masking emission and absorption lines.," Ultraviolet spectral slopes were measured from the optical spectra, longward of $\alpha$, after masking emission and absorption lines."
 The ultraviolet spectral slopes are Listed in Table 2.., The ultraviolet spectral slopes are listed in Table \ref{tab:uvlines}.
 With the exception of10NJ094144.. the ultraviolet continua of the fiveQSOs have spectralslopesin the range 0«ag< I. which is typical for optically-selectecl QSOs (Francisetal. LOO1).. indicating little or no dust. reclelening intrinsic to these objects.," With the exception of, the ultraviolet continua of the fiveQSOs have spectralslopesin the range $0<\alpha_{O}<1$ , which is typical for optically-selected QSOs \citep{francis91}, , indicating little or no dust reddening intrinsic to these objects."
 On the other hand. as can be seen in Fig.," On the other hand, as can be seen in Fig."
 1.the rest-frame ultraviolet continuum of, \ref{fig:optspecs} the rest-frame ultraviolet continuum of
the region of the parameter space occupied: by powerful unobseurecd AGNs (Stocke et al.,the region of the parameter space occupied by powerful unobscured AGNs (Stocke et al.
 1901)., 1991).
 The. optical Dux ratio is estimated from the relation The equation. above is erivecl from the X-raytooptical [lux ratio definition. of Stocke et al. (, The X-ray--to--optical flux ratio is estimated from the relation The equation above is derived from the X-ray--to--optical flux ratio definition of Stocke et al. (
1991) that involved kkeV. Dux. and. Y-band. magnitude.,1991) that involved keV flux and $V$ -band magnitude.
 These quantities are converted to. kkeV. [lux and. Ziband magnitude assuming a mean colour V—2=0.7 and a power-law X-ray spectral energy distribution with index P=1.7., These quantities are converted to keV flux and $R$ -band magnitude assuming a mean colour $V-R=0.7$ and a power-law X-ray spectral energy distribution with index $\Gamma=1.7$.
 In Figure 1 all the extragalactic hard X-ray. selected sources Lic in the AGN region of the parameter space (Le. between the logfx/f.icL diagonal lines)., In Figure \ref{fig_fxfo} all the extragalactic hard X-ray selected sources lie in the AGN region of the parameter space (i.e. between the $\log f_X/f_{opt}\pm1$ diagonal lines).
 Lard X-ray sources with radio counterparts have a range of X-raytooptical Dux ratios., Hard X-ray sources with radio counterparts have a range of X-ray–to–optical flux ratios.
 Optical unidentified sources are shown as upper limits in this figure., Optical unidentified sources are shown as upper limits in this figure.
 Some of them lie above the upper bound of the empirical AGN envelope. defined. by Stocke et. al. (, Some of them lie above the upper bound of the empirical AGN envelope defined by Stocke et al. (
1991) suggesting high redshift) and/or dust. obscuration (Alexander et al.,1991) suggesting high redshift and/or dust obscuration (Alexander et al.
 2001: Brusa οἱ al., 2001; Brusa et al.
 2003: Fiore et al., 2003; Fiore et al.
 2003: Gandhi et al., 2003; Gandhi et al.
 2004: Mignoli ct al., 2004; Mignoli et al.
 2004: Georgantopoulos et al., 2004; Georgantopoulos et al.
 2004)., 2004).
 Although none of these sources is detected in our relatively shallow A-band survey (CA.=18 mmag) they have. on average. hard. X-ray. spectral properties.," Although none of these sources is detected in our relatively shallow $K$ -band survey $K=18$ mag) they have, on average, hard X-ray spectral properties."
 This is garown in Figure 2. plotting hardness ratio (equation 1)) as vfunction of the N-ravtooptical (lux ratio (equation 2))., This is shown in Figure \ref{fig_hr_vs_fxfo} plotting hardness ratio (equation \ref{eq1}) ) as a function of the X-ray–to–optical flux ratio (equation \ref{eq2}) ).
" Optically unidentified sources with logfyων,z11 have Uk0.2 suggesting enhanced. observed: photoelectric absorption. (Nu.]=3⋅10721em Ll.—LT)-"," Optically unidentified sources with $\log 
f_X/f_{opt}\ga +1$ have $\rm HR>-0.2$ suggesting enhanced observed photoelectric absorption $\rm N_H>3\times10^{21}\, cm^{-2}$, $\Gamma=1.7$ )."
 Also. in Ligure 2. there is fair agreement between the X-rav and optical spectroscopic properties of our sources.," Also, in Figure \ref{fig_hr_vs_fxfo} there is fair agreement between the X-ray and optical spectroscopic properties of our sources."
 Spectroscopically confirmed. broad-line ACNs have soft. N-rav spectra. while narrow emiüssion-line. svstems have. on average. His suggesting observed. absorbing columns. in excess ofCapt 107em2qp (P=17).," Spectroscopically confirmed broad-line AGNs have soft X-ray spectra, while narrow emission-line systems have, on average, HRs suggesting observed absorbing columns in excess of $\rm 10^{21}\,cm^{-2}$ $\Gamma=1.7$ )."
- We further compare the N-ray and optical/NIR sroperties of the present sample in Figure 3. plotting the murdness ratio against 2A colours., We further compare the X-ray and optical/NIR properties of the present sample in Figure \ref{fig_hr_rk} plotting the hardness ratio against $R-K$ colours.
 Although. there is large scatter in this Figure. the obscured (high HI) X-ray. sources are. on average. redder than those with softer X-ray spectral »operties.," Although, there is large scatter in this Figure, the obscured (high HR) X-ray sources are, on average, redder than those with softer X-ray spectral properties."
 Εις suggests that the optical/NII light of X-ray aareler sources is dominated by the host galaxy rather than 16 obscured. central AGN(Barger ct al., This suggests that the optical/NIR light of X-ray harder sources is dominated by the host galaxy rather than the obscured central AGN(Barger et al.
 2002. 2003: Brusa ot al.," 2002, 2003; Brusa et al."
 2003: Fiore et al., 2003; Fiore et al.
 2003: Mignoli et al., 2003; Mignoli et al.
 2004: Gandhi et al., 2004; Gandhi et al.
 Y04: Crieorgantopoulos et al., 2004; Georgantopoulos et al.
 2004)., 2004).
 This is demonstrated in Figure 4. where we plot &dy and VF2 colours as a function of redshift., This is demonstrated in Figure \ref{fig_colour_vs_z} where we plot $R-K$ and $V-R$ colours as a function of redshift.
 Overlaid are the optical/NIU colours of a QSO spectrum (Cristiani Vio 1990: Cristiani et al., Overlaid are the optical/NIR colours of a QSO spectrum (Cristiani Vio 1990; Cristiani et al.
 2004: obtained from the template SEDs of the )) and the mean observed spectra of four cdilferent galaxy ἵνρος (I2/80. She. Sed. Lm) from Coleman. Wu Weeedman (1980).," 2004; obtained from the template SEDs of the ) and the mean observed spectra of four different galaxy types (E/S0, Sbc, Scd, Im) from Coleman, Wu Weedman (1980)."
 Broad line ACONs. most of which exhibit soft. X-ray spectra. have colours consistent. with the QSO template prediction. while the X-ray. harder sources follow the galaxy tracks in Figure 4..," Broad line AGNs, most of which exhibit soft X-ray spectra, have colours consistent with the QSO template prediction, while the X-ray harder sources follow the galaxy tracks in Figure \ref{fig_colour_vs_z}."
 Phe evidence above justifies the use of galaxy SEDs to estimate photometric redshifts for the X-ray. harder sources in section ??.., The evidence above justifies the use of galaxy SEDs to estimate photometric redshifts for the X-ray harder sources in section \ref{sample}.
 In Figures 2.. 3 there is evidence for a higher fraction of X-rav/radio matches within the harder (i.e. higher hardness ratio) X-ray population.," In Figures \ref{fig_hr_vs_fxfo}, \ref{fig_hr_rk} there is evidence for a higher fraction of X-ray/radio matches within the harder (i.e. higher hardness ratio) X-ray population."
 This is further explored in Figure 5.. where we plot the distribution of the LR and the column density. (ic. after correcting for the redshift) of both the hard X-ray selected sample and the X-rayradio matched population.," This is further explored in Figure \ref{fig_hr_nh_dist}, where we plot the distribution of the HR and the column density (i.e. after correcting for the redshift) of both the hard X-ray selected sample and the X-ray/radio matched population."
 The Ng at the is estimated from the X7. X-ray spectral Littings described in section ??.., The $\rm N_H$ at the is estimated from the $\chi^{2}$ X-ray spectral fittings described in section \ref{sample}.
 In the case of X-ray spectra with small number of counts we adopt the Ng values. estimated: by Ίο C-statistic method. assuming a spectral index EP=1.7., In the case of X-ray spectra with small number of counts we adopt the $\rm N_H$ values estimated by the C-statistic method assuming a spectral index $\Gamma=1.7$.
 The column density however. is lower than the one because the fA-cllect shifts. the bsorption turnover to lower energies.," The column density however, is lower than the one because the $k$ -effect shifts the absorption turnover to lower energies."
 The relation between 10 intrinsic rest-frame ancl the observed. column. density scales approximately as (1|aye (c.g. Barger et al., The relation between the intrinsic rest-frame and the observed column density scales approximately as $(1+z)^{2.65}$ (e.g. Barger et al.
 2002)., 2002).
 This correction is applied to all the sources in the sample before plotting the histogram in Figure 5.., This correction is applied to all the sources in the sample before plotting the histogram in Figure \ref{fig_hr_nh_dist}. .
 For sources without spectroscopic identilication we assume a mean redshift 2= 1. similar to the peak of the redshift distribution of the hard. X-ray population (c.g. Fiore ct al.," For sources without spectroscopic identification we assume a mean redshift $z=1$ , similar to the peak of the redshift distribution of the hard X-ray population (e.g. Fiore et al."
collision can occur within this svstem.,collision can occur within this system.
 Interesting cases of stellar interactions are not limited to BS formation alone., Interesting cases of stellar interactions are not limited to BS formation alone.
 Consider (he case of the primordial binary comprised of MS stars o£ 0.6 and 1.5M. with an eccentricitv οἱ 0.42 and an orbital period of ~270 vr that was part of the same GRAPE-G simulation mentioned above.," Consider the case of the primordial binary comprised of MS stars of 0.6 and $1.5 M_\odot$ with an eccentricity of 0.42 and an orbital period of $\sim 270\,$ yr that was part of the same GRAPE-6 simulation mentioned above."
 Residing in the core of the cluster this binary. suffered. a series of weak perturbations to its orbit which drove the eccentricity up to 0.95., Residing in the core of the cluster this binary suffered a series of weak perturbations to its orbit which drove the eccentricity up to 0.95.
 After the 1.5... star became a sub-giant it was involved in two exchange interactions. finally settling into a 33 vr orbit with eccentricity of 0.9 about a LAA. MS star alter 2120 Myr of evolution.," After the $1.5 M_\odot$ star became a sub-giant it was involved in two exchange interactions, finally settling into a $33\,$ yr orbit with eccentricity of 0.9 about a $1.4 M_\odot$ MS star after $2\,130\,$ Myr of evolution."
 The then evolved onto the giant. branch (GB) and by 7=2160 Myr tidal forces within the binary had cireularized the orbit resulüing in a separation of 250/2..," The sub-giant then evolved onto the giant branch (GB) and by $T = 2\,160\,$ Myr tidal forces within the binary had circularized the orbit resulting in a separation of $250 R_{\sun}$."
 While on the GB the 1.5. star filled its Roche-lobe ancl a phase of common-envelope evolution began., While on the GB the $1.5 M_\odot$ star filled its Roche-lobe and a phase of common-envelope evolution began.
 This stripped the envelope of the eiut. and left a helium-WD and a MS star separated by 522..., This stripped the envelope of the giant and left a helium-WD and a MS star separated by $52 R_{\sun}$.
" The MS star subsequently evolved to the GB. fillel its Roche-lobe. and another event ensued. resuliing in a pair of Q.4 and 0.3474. heliun-WDs with an orbital period of 0.7d. Owing to eravitational radiation this svstem would easily merge within 10!"" vr to possibly [orm a blue sub-dwarl star (Iben 1990). ie. a helium-burning object with a thin hydrogen envelope."," The MS star subsequently evolved to the GB, filled its Roche-lobe, and another common-envelope event ensued, resulting in a pair of 0.4 and $0.3 M_{\sun}$ helium-WDs with an orbital period of $0.7\,$ d. Owing to gravitational radiation this system would easily merge within $10^{10}\,$ yr to possibly form a blue sub-dwarf star (Iben 1990), i.e. a helium-burning object with a thin hydrogen envelope."
 The final case that we choose to highlight involves the formation of a Thorne-Zvyükow object (TZO. Thorne Zyvikow 1977).," The final case that we choose to highlight involves the formation of a Thorne-Żyytkow object (TZO, Thorne Żyytkow 1977)."
 Although TZOs have not been directly observed. they are thought (o result from stellar mergers involving either a neutron star ora black hole. where (he merger product is unstable and rapidly ejects all (he material involved other (han the neutron star or black hole. which remains.," Although TZOs have not been directly observed, they are thought to result from stellar mergers involving either a neutron star or a black hole, where the merger product is unstable and rapidly ejects all the material involved other than the neutron star or black hole, which remains."
 The svstem of interest began as a primordial binary with component masses 10.3 and 5.2... an eccentricity of 0.87 and a period of 1870d. After 20 Myr of evolution the orbital period had been reduced to 1350 cl owing to perturbations that hadhardened this already binary.," The system of interest began as a primordial binary with component masses $10.8$ and $5.3 M_\odot$, an eccentricity of 0.87 and a period of $1\,870\,$ d. After $20\,$ Myr of evolution the orbital period had been reduced to $1\,350\,$ d owing to perturbations that had this already binary."
 A few Myr later the more massive ol the two stars evolved onto the sub-giant branch and. as (he region of convection within its envelope grew. tidal forces began to circularize the orbit.," A few Myr later the more massive of the two stars evolved onto the sub-giant branch and, as the region of convection within its envelope grew, tidal forces began to circularize the orbit."
 AC 7=23 Myr the primary star filled its Roche-lobe and began transferring mass to the companion.," At $T = 23\,$ Myr the primary star filled its Roche-lobe and began transferring mass to the companion."
 When (he primary evolved onto the giant branch the rate of mass transler accelerated so Chat the giant quickly overlilled the Roche-lobes of both stars to leave the 2.42.4/. helium core of the giant and the 5.9144. MS star contained within a common-envelope., When the primary evolved onto the giant branch the rate of mass transfer accelerated so that the giant quickly overfilled the Roche-lobes of both stars to leave the $2.42 M_\odot$ helium core of the giant and the $5.31 M_\odot$ MS star contained within a common-envelope.
 Orbital friction then caused (hese two objects to spiral towards each other and the energy released was enough to drive off the envelope before (μον coalesced., Orbital friction then caused these two objects to spiral towards each other and the energy released was enough to drive off the envelope before they coalesced.
 This left a naked. helium star and a MS star in a circular, This left a naked helium star and a MS star in a circular
in (he virialization process.,in the virialization process.
 Taking into account the observation that we should only include a fraction 1—F of the dark energy potential energv. we can get (he equation determining .r For F=I. Eq. (15))," Taking into account the observation that we should only include a fraction $1-F$ of the dark energy potential energy, we can get the equation determining $x$ For $F=1$, Eq. \ref{gamma}) )"
 will reduce to Eq. (11)).," will reduce to Eq. \ref{main}) ),"
 while for F=0. it will reduce to the equation found by Mota&deBruck(2004).," while for $F=0$, it will reduce to the equation found by \citet{Mota}."
. Thus. our result Eq. (11))," Thus, our result Eq. \ref{main}) )"
 can be continuously connected to the case that dark energy. will also collapse with dark matter., can be continuously connected to the case that dark energy will also collapse with dark matter.
 This is physically salislving., This is physically satisfying.
 second. if we adopt the proposal of restoring energv. conservation by (hen when F= 1. the virialization equation is We showed the dependence of 2 on 4 trom Eq. (16))," Second, if we adopt the proposal of restoring energy conservation by \citet{Maor} then when $F=1$ , the virialization equation is We showed the dependence of $x$ on $q$ from Eq. \ref{1.1}) )"
 as the dashed-dotted line in Fig., as the dashed-dotted line in Fig.
 l., 1.
 lt can be seen that although the approach of restoring energy. conservation are different in Eqs. (16)), It can be seen that although the approach of restoring energy conservation are different in Eqs. \ref{1.1}) )
 and (11)). their predictions are rather close.," and \ref{main}) ), their predictions are rather close."
 This illustrates that although the underlving ideas are different. in practice. our approximation scheme is quantitatively close to the scheme of Maor&Lahay(2005).," This illustrates that although the underlying ideas are different, in practice, our approximation scheme is quantitatively close to the scheme of \citet{Maor}."
. In both cases. the difference from the old result (8)) is large when q is large.," In both cases, the difference from the old result \ref{old}) ) is large when $q$ is large."
 From Fig., From Fig.
 1: we can also see that for ¢107 or smaller. we get c=0.5 in all the four approaches.," 1 we can also see that for $q\sim10^{-2}$ or smaller, we get $x=0.5$ in all the four approaches."
 This is reasonable., This is reasonable.
 In (he virialization process. it is the sell-energyv. of matter that plavs thedominant role.," In the virialization process, it is the self-energy of matter that plays thedominant role."
" In fact. C09,Uo, and Tooμου ave both of the order since (“+wolc[670>99 and (4+))~Q.1. for. g<0.01 the above ratio is much smaller than 1. and thus we can expect that for small q. the problem of energy conservation will not influence (he virialization process greatly."," In fact, $U_{QQ.vir}/U_{mQ,vir}$ and $T_{QQ,vir}/T_{mQ,vir}$ are both of the order since $\left({a_{vir}\over a_{ta}}\right)^{-3(1+\omega_Q)}\simeq
1.6^{-3(1+\omega_Q)}$ and $\left({R_{vir}\over R_{ta}}\right)^3\sim
0.1$, for $q<0.01$ the above ratio is much smaller than $1$, and thus we can expect that for small $q$, the problem of energy conservation will not influence the virialization process greatly."
" Thus to estimate the elfects of dark energy on virialization. and especially the ambiguity of energv-nonconservalion. il is necessary to estimate the value of q lor the virialization redshift 2,4, that would beinteresting to observations."," Thus to estimate the effects of dark energy on virialization, and especially the ambiguity of energy-nonconservation, it is necessary to estimate the value of $q$ for the virialization redshift $z_{vir}$ that would beinteresting to observations."
" If for observationally interesting 2,;,. d will always be equite small. (hen we can conclude that the problem of energy non-conservation"," If for observationally interesting $z_{vir}$ , $q$ will always be quite small, then we can conclude that the problem of energy non-conservation"
is well cousisteut with recent 1ieasureiments ((5643) «105 photons loan 2) by CDS NIS-2 durimg the solar nuniuuu from 2006 to 2008 (DelZauna&Andretta and those (about GOX10* photons | cu? including the blended line) bx prototvpe-EVE rocket in April 2008 (DelZauua&Audretta2011) and bv SDO/EVE over AMay-December 2010 (κος Table 5)).,"is well consistent with recent measurements $\pm3$ $\times10^8$ photons $^{-1}$ $^{-2}$ ) by CDS NIS-2 during the solar minimum from 2006 to 2008 \citep{del11}, and those (about $\times10^8$ photons $^{-1}$ $^{-2}$ including the blended line) by prototype-EVE rocket in April 2008 \citep{del11} and by SDO/EVE over May-December 2010 (see Table \ref{tabhe}) )."
 These comparisons verity the good radiomoetric calibration for EUNIS-07., These comparisons verify the good radiometric calibration for EUNIS-07.
 Finally. we iav check the absolute intensity of the quiet-Sun lue from EUNIS-07. usine the theoretical line ratio and coordinated. cospatial EIS iieasuremenuts," Finally, we may check the absolute intensity of the quiet-Sun line from EUNIS-07 using the theoretical line ratio and coordinated, cospatial EIS measurements."
" The CTIITANTI (ver.6.0) shows that the 256 A//301 ratio in optically thin condition is somewhat deusitv sensitive. with a iminimuun value of 0.036 at Ιουν, = S.0. and a παπα value of 0.117 at Ίου, = 11.0. but a most likely value of 0.0512:0.011 for 9.0doeiV,. 10.0."," The CHIANTI (ver.6.0) shows that the 256 /304 ratio in optically thin condition is somewhat density sensitive, with a minimum value of 0.036 at $N_e$ = 8.0, and a maximum value of 0.117 at $N_e$ = 11.0, but a most likely value of $\pm$ 0.011 for $\leq$ $N_e$$\leq$ 10.0."
 Iu comparison. Jordan(1975) eave the observed ratio of this line pair to be 0.052. and Drosius.Thomas (1998b) measured the ratio of to to be 0.016-:0.008. for an active region.," In comparison, \citet{jor75} gave the observed ratio of this line pair to be 0.052, and \citet{bro98b} measured the ratio of to to be $\pm$ 0.008 for an active region."
 These uecasureiieuts agree with the predicted value within nucertainties., These measurements agree with the predicted value within uncertainties.
 Taking the theoretical ratio from CHIANTI and the measured EIS intensity of the 256 line (with calibration correction by EUNIS-07. ie.," Taking the theoretical ratio from CHIANTI and the measured EIS intensity of the 256 line (with calibration correction by EUNIS-07, ie."
 scaled wea factor of 1.2). we derived the tensity of to be LSLO+1OL0 for the EIS Ls:00 UT raster and 1630-1000 for the EIS 18:54 UT raster.," scaled by a factor of 1.2), we derived the intensity of to be $\pm$ 1040 for the EIS $-$ 18:00 UT raster and $\pm$ 1000 for the EIS $-$ 18:54 UT raster."
 Despite the lines being possibly optically thick. the quict-Sun 301 nuteusitv derivedi from EIS is well consistent with that directly measured by EUNIS-07. confriuus au agreenicnt between the EUNIS-07. and EIS cross-calibration.," Despite the lines being possibly optically thick, the quiet-Sun 304 intensity derived from EIS is well consistent with that directly measured by EUNIS-07, confirming an agreement between the EUNIS-07 and EIS cross-calibration."
 Iu the next flight (expected in 2011. November) EUNIS will focus ou the study of thermal structure of coronal loops and coordinated observations with SDO/AIA., In the next flight (expected in 2011 November) EUNIS will focus on the study of thermal structure of coronal loops and coordinated observations with SDO/AIA.
 Based ou SDO images. two slit locations and rotational aligunmieuts will be chosen before flight to sample both active regions and quieter areas.," Based on SDO images, two slit locations and rotational alignments will be chosen before flight to sample both active regions and quieter areas."
 EUNIS-11. will coutinne to provide the EIS crosscalibration as done with EUNIS-07 using the mseusitive line ratio techuique., EUNIS-11 will continue to provide the EIS cross-calibration as done with EUNIS-07 using the insensitive line ratio technique.
" Active region spectra will allow applications of more liue pairs such as from Pe wevitoprovideagoodeoverage forthe EISE band,", Active region spectra will allow applications of more line pairs such as from $-$ to provide a good coverage for the EIS LW band.
 Iun conclusion. EUNIS-07 las provided important underfüeht calibration updates for CDS/NIS aud Tinode/EIS.," In conclusion, EUNIS-07 has provided important underflight calibration updates for CDS/NIS and Hinode/EIS."
 The results bx EUNIS-07 well support the recent measurements of the long-term correction for the CDS and EIS iustruueut respousivities obtained by the inflight monitoring of the quict-Sun intensity of the chromospheric-transition region lines., The results by EUNIS-07 well support the recent measurements of the long-term correction for the CDS and EIS instrument responsivities obtained by the inflight monitoring of the quiet-Sun intensity of the chromospheric-transition region lines.
 The absolute value of the quict-Sun 301 iutensitv measured by EUNIS-07 is well consistent with the radiance measured by CDS NIS in quiet regions near the disk ceuter aud the solar mini irradiance obtained by CDS NIS aud SDO/EVE veceuth. but. it is about a factor of l.[1.6 smaller than the previous values fron SERTS-97 aud. Skylab. reflecting possible real variations with locations and tines.," The absolute value of the quiet-Sun 304 intensity measured by EUNIS-07 is well consistent with the radiance measured by CDS NIS in quiet regions near the disk center and the solar minimum irradiance obtained by CDS NIS and SDO/EVE recently, but it is about a factor of 1.4–1.6 smaller than the previous values from SERTS-97 and Skylab, reflecting possible real variations with locations and times."
 The EUNIS program is supported bv the NASA Ueliophysics Division through its Low Cost Access to Space Prograin in Solar aud Ueliospheric Physics., The EUNIS program is supported by the NASA Heliophysics Division through its Low Cost Access to Space Program in Solar and Heliospheric Physics.
 TW ds grateful to Drs., TW is grateful to Drs.
 William T. Thompson. Johu Abuiska and Vincenzo Andretta for their valuable cohunents.," William T. Thompson, John Mariska and Vincenzo Andretta for their valuable comments."
 The work of TW was supported by NASA erants NNNIOANTOG and NNNOSAELIC. The work of PRY was performed under contract with the Naval Research Laboratory aud was funded by NASA., The work of TW was supported by NASA grants NNX10AN10G and NNX08AE44G. The work of PRY was performed under contract with the Naval Research Laboratory and was funded by NASA.
 GDZ ackuowledecs support frou STFC (UR) via the Advanced Fellowship programune., GDZ acknowledges support from STFC (UK) via the Advanced Fellowship programme.
 Radiometric calibration of the EUNIS-06 instruineut was mace possible bv financial contributions aud technical support Boni both the Rutherford-Appletou Laboratory in England aud the Physikalisch-Technische Bundesanstalt in Germany. for which we are very grateful.," Radiometric calibration of the EUNIS-06 instrument was made possible by financial contributions and technical support from both the Rutherford-Appleton Laboratory in England and the Physikalisch-Technische Bundesanstalt in Germany, for which we are very grateful."
 CIILANTI is a collaborative project involving the Universities of Cambridge (UI). George Mason and Michigan (USA).," CHIANTI is a collaborative project involving the Universities of Cambridge (UK), George Mason and Michigan (USA)."
distribution function. of the redshift of an object in the photometric sample.,distribution function of the redshift of an object in the photometric sample.
 The angular size distance. D(z). and the comoving distance to redshift z. /(<). are determined from the basic cosmology.," The angular size distance, $D(z)$, and the comoving distance to redshift $z$, $l(z)$, are determined from the basic cosmology."
" We can see that since rospgm.. there is a degeneracy in the cross-ccorrelation signal between the redshift distribution and the intrinsic clustering of the two samples with each other (characterized by aandro.sp 2,,)."," We can see that since $\sim$, there is a degeneracy in the correlation signal between the redshift distribution and the intrinsic clustering of the two samples with each other (characterized by and )."
 We can estimate these cross-ccorrelation parameters from the autocorrelation measurements of each sample using the assumption of linear biasing. for which £am," We can estimate these correlation parameters from the autocorrelation measurements of each sample using the assumption of linear biasing, for which $\xi_{sp}=(\xi_{ss}\xi_{pp})^{1/2}$."
 We now Guy).outline the details of the particular. procedures which gave the best reconstruction of iin MNIO., We now outline the details of the particular procedures which gave the best reconstruction of in MN10.
 First. we need to calculate the autocorrelation parameters of each sample.," First, we need to calculate the autocorrelation parameters of each sample."
 To determine how eevolves with redshift we bin the spectroscopic objects in redshift and measure the two-point correlation function in each z-bin., To determine how evolves with redshift we bin the spectroscopic objects in redshift and measure the two-point correlation function in each $z$ -bin.
 We calculate uusing the as-observed redshifts from the simulation. which are affected by redshift space distortions in. the line-of-sight direction (?)..," We calculate using the as-observed redshifts from the simulation, which are affected by redshift space distortions in the line-of-sight direction \citep{1998ASSL..231..185H}."
" To minimize this effect it is common to calculate € as a function of the projected separation. r,. and the line-of-sight separation. 7. and then integrate along the line-of-sight to obtain the projected correlation function. where H(~) is defined following equation .."," To minimize this effect it is common to calculate $\xi$ as a function of the projected separation, $r_p$, and the line-of-sight separation, $\pi$, and then integrate along the line-of-sight to obtain the projected correlation function, where $H(\gamma)$ is defined following equation \ref{eq:wsp}. ."
 By measuring un multiple Lbins and fitting with equation 3.. we can determine Z) aandz (zi.," By measuring in multiple $z$ -bins and fitting with equation \ref{eq:wpa}, we can determine $(z)$ and $(z)$."
" Wefoundthatemplovingalinear fro and 5, as a function of resulted in a better recovery of fitoo5) than using each bin's valuez directly."," We found that employing a linear fit of $r_{0,ss}$ and $\gamma_{ss}$ as a function of $z$ resulted in a better recovery of $\phi_p(z)$ than using each bin's value directly."
" We then calculate the angular autocorrelation of the photometric sample. w,,(0).. and fit to obtain the parameters aandρε."," We then calculate the angular autocorrelation of the photometric sample, , and fit to obtain the parameters and."
" We use the autocorrelationA, parameters along with an initial guess of tto. calculate m-uusm)."," We use the autocorrelation parameters along with an initial guess of to calculate $r^{\gamma_{sp}}_{0,sp}=(r^{\gamma_{ss}}_{0,ss}r^{\gamma_{pp}}_{0,pp})^{1/2}$."
" We found that the best results were obtained by assuming the redshift dependence of the scale length is similar for each sample. Le. 5,2)x ross(z). withaninitial guessofro ppy(Z= FOSSCC)."," We found that the best results were obtained by assuming the redshift dependence of the scale length is similar for each sample, i.e. $(z)$ $\propto$ $(z)$, with an initial guess of $(z)$ $=$ $(z)$."
 For the angular cross-ccorrelation between the two samples. we bin the spectroscopic sample into small bins in Ws).redshift and. in each bin. measure the cross-ccorrelation between objects in that <-bin with all objects in the photometric sample.," For the angular correlation between the two samples, we bin the spectroscopic sample into small bins in redshift and, in each bin, measure the correlation between objects in that $z$ -bin with all objects in the photometric sample."
 We can then fit to obtain the parametersAsAspe and Cu.," We can then fit to obtain the parameters, and ."
 However. we found a significant degeneracy between these parameters when fitting.," However, we found a significant degeneracy between these parameters when fitting."
" To remove this degeneracy. we ΠΧ ντ(ss in each z-bin. and only fit for the amplitude and integral 25,)/2constraint."," To remove this degeneracy, we fix $\gamma_{sp}=(\gamma_{ss}+\gamma_{pp})/2$ in each $z$ -bin, and only fit for the amplitude and integral constraint."
 We choose this estimate for bbecause the clustering of the samples with each other is expected to be intermediate to the intrinsic clustering of each sample., We choose this estimate for because the clustering of the samples with each other is expected to be intermediate to the intrinsic clustering of each sample.
" Using the resulting values of aand5,,.. as well as the initial guess for Γον. we obtain an initial guess of the redshift distribution uusing equation |.."," Using the resulting values of and, as well as the initial guess for $r^{\gamma_{sp}}_{0,sp}$, we obtain an initial guess of the redshift distribution using equation \ref{eq:wsp}."
" Using this«,(<).. along with Aj, and pp. We can redetermine 7o, using Limber's equation (?).. which we use to redetermine 7;yp and thus o,0)."," Using this, along with $A_{pp}$ and $\gamma_{pp}$, we can redetermine $r_{0,pp}$ using Limber's equation \citep{1980lssu.book.....P}, which we use to redetermine $r^{\gamma_{sp}}_{0,sp}$ and thus $\phi_p(z)$."
 This process is repeated until convergence is reached., This process is repeated until convergence is reached.
 A more detailed description of this technique. including an error analysis for the resulting reconstructions. can be found in MN10.," A more detailed description of this technique, including an error analysis for the resulting reconstructions, can be found in MN10."
 We have implemented an additional step. in. the reconstruction of ffor this paper that was not employed by MNIO., We have implemented an additional step in the reconstruction of for this paper that was not employed by MN10.
 For each measurement. after fixing παπά fitting for aand iin each z-bin. we performed a smooth fit to the measured values of (Gase functiono Fredshi ftU," For each measurement, after fixing and fitting for and in each $z$ -bin, we performed a smooth fit to the measured values of $(z)$ as a function of redshift."
" singthesameo, bbut fixingC, aat the predicted values for each bin. we then fit forAg."," Using the same but fixing at the predicted values for each bin, we then fit for."
" We obtained the best results. from a Gaussian fit toC,.. although simply smoothing the measured CGOvalueswithaboxcaraveragealsoresultedinsigni Ficantgainsinreconst "," We obtained the best results from a Gaussian fit to, although simply smoothing the measured $(z)$ values with a boxcar average also resulted in significant gains in reconstruction accuracy."
binsmadethereconstructionworse.," We initially tested these techniques for MN10, but they did not improve the reconstruction, and in some $z$ -bins made the reconstruction worse."
However.afterincorporatingcovarianc likely because the determination of ffor each redshift bin is now more accurate.," However, after incorporating covariance information into our analyses, this additional step significantly reduced errors in the reconstruction of, likely because the determination of for each redshift bin is now more accurate."
Ον We have also made a change in the methods used to calculate average correlation measurements from multiple light cones., We have also made a change in the methods used to calculate average correlation measurements from multiple light cones.
 In MNIO this was done by summing the pair counts over all of the fields and using the total pair counts in the Landy Szalay estimator., In MN10 this was done by summing the pair counts over all of the fields and using the total pair counts in the Landy Szalay estimator.
 However. in the course of this paper we found that this method overestimates the mea correlation by more heavily weighting those light cones which are overdense at a particular redshift: they will both contai more pairs and. generally. exhibit stronger clustering tha a randomly-selected region of the universe.," However, in the course of this paper we found that this method overestimates the mean correlation by more heavily weighting those light cones which are overdense at a particular redshift: they will both contain more pairs and, generally, exhibit stronger clustering than a randomly-selected region of the universe."
 For this paper. we instead determine the average correlation by calculating the correlation function in each field individually and the performing an unweighted average of those measurements.," For this paper, we instead determine the average correlation by calculating the correlation function in each field individually and then performing an unweighted average of those measurements."
" This change had little effect on the autocorrelation functio of the photometric sample.,,(/).. mainly because the larger volume sampled meant that the density varies less from field to field."," This change had little effect on the autocorrelation function of the photometric sample, mainly because the larger volume sampled meant that the density varies less from field to field."
" The projected autocorrelation of the spectroscopic sample. and the cross-ccorrelation measurements.z).. were wW),(7),)..significantly affected by this change. however. with average decreases in the correlation strength of ~10— 20%."," The projected autocorrelation of the spectroscopic sample, and the correlation measurements, were significantly affected by this change, however, with average decreases in the correlation strength of $\sim10-20\%$ ."
 In MNIO we fit for the various correlation function parametersGos.Jee ete.)," In MN10 we fit for the various correlation function parameters, etc.)"
 assuming that there is no covariance between measurements in different bins., assuming that there is no covariance between measurements in different $r_p$ bins.
" We determined best-fit parameters by performingangular/r, a v minimization where the errors used were given by the standard deviation of the correlation function measurements in each of the 24 mock light-cones: 1.8. the fitting assumed that the relevant covariance matrices were all diagonal.", We determined best-fit parameters by performing a $\chi^2$ minimization where the errors used were given by the standard deviation of the correlation function measurements in each of the 24 mock light-cones; i.e. the fitting assumed that the relevant covariance matrices were all diagonal.
 However. analytical models as well as simulations have shown that the off-diagonal elements of the covariance matrix are non-negligible (222)..," However, analytical models as well as simulations have shown that the off-diagonal elements of the covariance matrix are non-negligible \citep{1994ApJ...424..569B,2005ApJ...630....1Z,2011MNRAS.414..329C}."
 We have confirmed this to be the case by calculating the full covariance matrices ofcorrelation function measurements in the 24fields., We have confirmed this to be the case by calculating the full covariance matrices ofcorrelation function measurements in the 24fields.
 Therefore. in MNIO we were not exploiting the full covariance information. when fitting for the correlation function parameters.," Therefore, in MN10 we were not exploiting the full covariance information when fitting for the correlation function parameters."
 By incorporating this information into. our fitting process. we should expect to obtain more accurate results.," By incorporating this information into our fitting process, we should expect to obtain more accurate results."
In Fig.,In Fig.
 3 we show the curve of phase coexistence. 7Z' versus n/ng. Lor various choices of 7...," 3 we show the curve of phase coexistence, $T$ versus $n/n_0$, for various choices of $T_c$."
 These are indicated by the solid curve., These are indicated by the solid curve.
 The dashed curve indicates the limit of isothermal metastabilit. or isothermal spinodal.," The dashed curve indicates the limit of isothermal metastability, or isothermal spinodal."
 When 7 is scaled by 7. the phase coexistence curves fall on top of one another. as do the spinodals. indicative of a special scaling feature of Chis parameterization.," When $T$ is scaled by $T_c$ the phase coexistence curves fall on top of one another, as do the spinodals, indicative of a special scaling feature of this parameterization."
Our observing technique aud analysis is essentially identical to our previous surveys of Hyacles (Cizis&Reid1995:Gigis1997b) aud field (Reid&Cizis1997a) M cdwarfs.,"Our observing technique and analysis is essentially identical to our previous surveys of Hyades \citep{hyades1,hyades2} and field \citep{fieldbin} M dwarfs."
 Companions with δημ of 0. 1. 3) and 2 magnitudes respectively can be resolved a 0.09. 0.11. 0.23. aud 0.32 arcsecouds respectively.," Companions with $\delta m_{850}$ of 0, 1, 3 and 5 magnitudes respectively can be resolved at 0.09, 0.14, 0.23, and 0.32 arcseconds respectively."
 However. we do not detecteig companions to our target stars.," However, we do not detect companions to our target stars."
 We estimate that our observations are sensitive O stars at the bottom of tlie halo main sequence for separatious of >10 A.U.. The Baalleetal.(1997) models predict hat eid of the metal-poor tain sequence lies at AM;zz11., We estimate that our observations are sensitive to stars at the bottom of the halo main sequence for separations of $>10$ A.U.. The \citet{bcah97} models predict that end of the metal-poor main sequence lies at $M_I \approx 14$.
 The ast 1.7 magniπο correspoud to Inasses between 0.083 ancl 0.09QO ALL.iuxl are predicted to have very re| colors but lie in a regime where the 1iocdels are very uncertain.," The last 1.7 magnitudes correspond to masses between 0.083 and 0.090 $M_\odot$, and are predicted to have very red colors but lie in a regime where the models are very uncertain."
 Tese subdwarfs a'e oesuumably ra'e. and they have not vet been detected.," These subdwarfs are presumably rare, and they have not yet been detected."
 Usine the Holtzmanetal.(1995). transfornuallons. we p‘eclict that these clhwarls have Masizz12.5. as illustrated in Fiet'e 3... but at present there is no eupirical verification of the validity ο‘the color transformations for subcdwarls of sicl extreme colors.," Using the \citet{hst} transformations, we predict that these dwarfs have $M_{850} \approx 12.5$, as illustrated in Figure \ref{fig-hstmi}, but at present there is no empirical verification of the validity of the color transformations for subdwarfs of such extreme colors."
" For Figure 3..) we have not allowec the Le: to FSSOLP correctio to exceed 1.5 1χαρητος,"," For Figure \ref{fig-hstmi}, we have not allowed the $_C$ to F850LP correction to exceed 1.5 magnitudes."
 We compare these values to coolest sdAl (LHS 377. observed Maso= 11.13) aud esdM (LHS 1712. tranformed Adgssy= 11.1) witi parallaxes.," We compare these values to coolest sdM (LHS 377, observed $M_{850} = 11.43$ ) and esdM (LHS 1742, tranformed $M_{850} = 11.1$ ) with parallaxes."
 (εἰς aud Schweitzeretal.(1999) have found extreme M subcwarfs tiat are slightly cooler that LHS 1712a. but 1o parallaxes are yet available.," \citet{gr97a} and \citet{apmpm2} have found extreme M subdwarfs that are slightly cooler than LHS 1742a, but no parallaxes are yet available."
 A multi-epoch HST study of NCC 6397 found LO €etected cluster members by A;zz12.2—12.7 (Ixiugetal.1998).. which would correspond to Algsgο12.0.," A multi-epoch HST study of NGC 6397 found no detected cluster members by $M_I \approx 12.2 - 12.7$ \citep{ngc6397}, which would correspond to $M_{850} \approx 11.5 - 12.0$."
 Wule the hydrogeu burning limit may be a or fainter than this poiut. it seems clear that the probability of detecting a subcdwarf iu this very siyall mass range is very low.," While the hydrogen burning limit may be at or fainter than this point, it seems clear that the probability of detecting a subdwarf in this very small mass range is very low."
 Most of OUI argets are classified sdM. aud therefore are more iuetal-ricl than NGC 6397. which may result inasightly redder. fainter hydrogeu burning limit.," Most of our targets are classified sdM, and therefore are more metal-rich than NGC 6397, which may result in a slightly redder, fainter hydrogen burning limit."
 We are seisitive to κους12 companions as close as 1-10. A.U. for all of the primary targets except LHS 171 (for which the limit is 15 A.U.). aud a distances of =12 A.U. we are typically sensitive to comyanious as faint as Masi=Li—16.," We are sensitive to $M_{850}=12$ companions as close as 4-10 A.U. for all of the primary targets except LHS 174 (for which the limit is 15 A.U.), and at distances of $\gtrsim 12$ A.U. we are typically sensitive to companions as faint as $M_{850} = 14 -16$."
 5ince we detect no companions but have οἱly niue nearby targets. the siguificance of our result is limited.," Since we detect no companions but have only nine nearby targets, the significance of our result is limited."
 I1 both the nearby Hyacles cluster (Cigis&Reid1995:Cizis1997b) and field {Reid&Gizis1997a).. we found that of ouw HST targets Owhich have similar mass but metalliCity) were resolved into «oubles. crespondiug to an overall companion rate of," In both the nearby Hyades cluster \citep{hyades1,hyades2} and field \citep{fieldbin}, we found that of our HST targets (which have similar mass but near-solar metallicity) were resolved into doubles, corresponding to an overall companion rate of."
 Thus we expect to observe 1.5 M subclwarl coiipauions rather than the none actually seen., Thus we expect to observe 1.8 M subdwarf companions rather than the none actually seen.
 Most ol our targes are actually closer thar the typic‘al objects in our previous programs. aud we reach the hydrogen buruit& limit. so if anythir& the fraction of observable compauious should be slightly Our Laiure {θεetect any Companis suggests that the binary fraction of M. subcdwarfs ts less," Most of our targets are actually closer than the typical objects in our previous programs, and we reach the hydrogen burning limit, so if anything the fraction of observable companions should be slightly Our failure to detect any companions suggests that the binary fraction of M subdwarfs is less"
in warm gas. with no indication that the positrons were born in a hot medium.,"in warm gas, with no indication that the positrons were born in a hot medium."
 We now proceed with calculating spectra expected. for annihilation of positrons in a cooling ISM., We now proceed with calculating spectra expected for annihilation of positrons in a cooling ISM.
 Ες implies solving a time dependent problem: for given initial eas temperature Zo and kinetic energy of positrons Ly find the annihilation spectrum emitted. while the gas cools down to a given final temperature 71., This implies solving a time dependent problem: for given initial gas temperature $T_0$ and kinetic energy of positrons $E_0$ find the annihilation spectrum emitted while the gas cools down to a given final temperature $T_1$.
 We solve this problem using a mocified version of our Monte Carlo code. which retains rom the original version the algorithms for description of slowing down. thermalization and annihilation of positrons (in à pure hydrogen plasma).," We solve this problem using a modified version of our Monte Carlo code, which retains from the original version the algorithms for description of slowing down, thermalization and annihilation of positrons (in a pure hydrogen plasma)."
" The outcome of this calculation crucially depends on the assumptions made about the ionization state of he ESAL during its cooling from =10"" to 10 k. In real astropivsical situations. à radiativelv cooling asma is expeced to be substantially overionizecl relative to collisional ionization equilibrium (CHE). since. the characteristic cooling time is shorter than the time scale of hydrogen recombination."," The outcome of this calculation crucially depends on the assumptions made about the ionization state of the ISM during its cooling from $\gtrsim 10^6$ to $\lesssim 10^4$ K. In real astrophysical situations, a radiatively cooling plasma is expected to be substantially overionized relative to collisional ionization equilibrium (CIE), since the characteristic cooling time is shorter than the time scale of hydrogen recombination."
 This will influence both the ISAL cooling rate ancl the fate of positrons., This will influence both the ISM cooling rate and the fate of positrons.
 We therefore aclopt the temperature dependencies for the non-equilibrium ionization state ancl cooling rate of an isochorically cooling eas [rom Schmutzler&Vscharnuter(19903). anc Guat& (2007).. which cover the temperature range from 10? Ντο 10 IX (ve assume that hvdrogen is Cully ionized at Tc510° IN).," We therefore adopt the temperature dependencies for the non-equilibrium ionization state and cooling rate of an isochorically cooling gas from \cite{1993A&A...273..318S} and \cite{2007ApJS..168..213G}, which cover the temperature range from $10^3$ K to $10^9$ K (we assume that hydrogen is fully ionized at $T>5~10^6$ K)."
 The temperature dependencies of the hvdrogen ionization fraction for the CLE and non-CLE cases are compared in the right panel of Fig. 11.., The temperature dependencies of the hydrogen ionization fraction for the CIE and non-CIE cases are compared in the right panel of Fig. \ref{fig:ism_fixed}. .
 We carried. out simulations covering a broad: range of parameter values: ο =10 keV10 MeV. 45=107 10* IX. A run was terminated when the LSM cooled down to 10* I: it turns out that the absolute majority of positrons annihilatebefore the gas reaches this temperature. except," We carried out simulations covering a broad range of parameter values: $E_0=$ 10 keV–10 MeV, $T_0=10^4$ $10^7$ K. A run was terminated when the ISM cooled down to $10^3$ K; it turns out that the absolute majority of positrons annihilatebefore the gas reaches this temperature, except"
routines inIRAF!.,routines in.
". We have also produced test fits using the PSF image built for the Spitzer Survey of Stellar Structure in Galaxies by combining stars in many Spitzer 3.6um images, which returned similar results."," We have also produced test fits using the PSF image built for the Spitzer Survey of Stellar Structure in Galaxies by combining stars in many Spitzer $\mu$ m images, which returned similar results."
" For reasons that will be clear shortly, we also produced fits including an exponential halo (model BDH) and a Sérrsic halo with Sérrsic index constrained to be larger than 2 (model BDH2)."," For reasons that will be clear shortly, we also produced fits including an exponential halo (model ) and a Sérrsic halo with Sérrsic index constrained to be larger than 2 (model )."
" The other free halo parameters are: effective radius, effective surface brightness and ellipticity (the position angle is the same as for the bulge)."," The other free halo parameters are: effective radius, effective surface brightness and ellipticity (the position angle is the same as for the bulge)."
" In addition, a fourth model was produced, with bulge and disc components only, but in which the bulge ellipticity varies with radius (model vEBD)."," In addition, a fourth model was produced, with bulge and disc components only, but in which the bulge ellipticity varies with radius (model )."
 The results from the fits are shown in Table 1 and Figs., The results from the fits are shown in Table \ref{tab:result} and Figs.
 2 to 7.., \ref{fig:profs_bd} to \ref{fig:imgs}.
 'The left panel in Fig., The left panel in Fig.
" 2 shows surface brightness radial profiles of NGC 4594 and modelBD, obtained through ellipse fits to the isophotes of both images, using theELLIPSE task inIRAF."," \ref{fig:profs_bd} shows surface brightness radial profiles of NGC 4594 and model, obtained through ellipse fits to the isophotes of both images, using the task in."
" If considered alone, it indicates that a good fit can be obtained with bulge and disc components only."," If considered alone, it indicates that a good fit can be obtained with bulge and disc components only."
" However, in the case of edge-on galaxies, using ellipse fits to study the light distribution in galaxies can be misleading."," However, in the case of edge-on galaxies, using ellipse fits to study the light distribution in galaxies can be misleading."
" In most galactocentric distances, the isophotes in an edge-on galaxy can result from more than one component."," In most galactocentric distances, the isophotes in an edge-on galaxy can result from more than one component."
" In the case of Sombrero, it is easy to see that, except from outermost isophotes, many isophotes are drawn from light coming from the disc, bulge and halo (see Fig. 1))"," In the case of Sombrero, it is easy to see that, except from outermost isophotes, many isophotes are drawn from light coming from the disc, bulge and halo (see Fig. \ref{fig:irac}) )."
" Thus, in this case, surface brightness radial profiles from ellipse fits are unsuitable to assess how light is distributed amongst different structural components, and hence to carefully judge the quality of a 2D fit, since at each given radius such profiles respond in a complex fashion to how the different components influence the isophotes."," Thus, in this case, surface brightness radial profiles from ellipse fits are unsuitable to assess how light is distributed amongst different structural components, and hence to carefully judge the quality of a 2D fit, since at each given radius such profiles respond in a complex fashion to how the different components influence the isophotes."
" Note that in the case of face-on or less inclined galaxies, although at any given isophote there is likely a contribution from more than one structural component only, such components are usually strongly dominant at specific radii intervals, which overcomes this difficulty, and render surface brightness radial profiles from ellipse fits to isophotes suitable."," Note that in the case of face-on or less inclined galaxies, although at any given isophote there is likely a contribution from more than one structural component only, such components are usually strongly dominant at specific radii intervals, which overcomes this difficulty, and render surface brightness radial profiles from ellipse fits to isophotes suitable."
" 'Thus, in order to more properly evaluate how light is distributed amongst the different structural components in the case of Sombrero, we made cuts along the major and minor axes of the disc to produce another set of surface brightness radial profiles (see right panel of Fig."," Thus, in order to more properly evaluate how light is distributed amongst the different structural components in the case of Sombrero, we made cuts along the major and minor axes of the disc to produce another set of surface brightness radial profiles (see right panel of Fig."
 2 — the minor axis cuts are discussed in Sect. 2.2))., \ref{fig:profs_bd} – the minor axis cuts are discussed in Sect. \ref{sec:minor}) ).
" In contrast to profiles built via isophotes, in this second set of profiles, each radius correspond essentially to a unique galactocentric radius."," In contrast to profiles built via isophotes, in this second set of profiles, each radius correspond essentially to a unique galactocentric radius."
" Thus, in this case, each component dominates over the others at different radii intervals."," Thus, in this case, each component dominates over the others at different radii intervals."
 Now one can see that modelBD is a relatively poor fit to the outer parts of NGC 4594., Now one can see that model is a relatively poor fit to the outer parts of NGC 4594.
" In the right panel of Fig. 2,,"," In the right panel of Fig. \ref{fig:profs_bd},"
" the galaxy profile exhibits two important breaks (indicated by circles): the first, at re 28"", marks the limit inward to which the bulge dominates over the disc, while the second at rz215”, marks the limit outward to which the outer spheroid dominates over the"," the galaxy profile exhibits two important breaks (indicated by circles): the first, at $r\approx28""$ , marks the limit inward to which the bulge dominates over the disc, while the second at $r\approx215""$, marks the limit outward to which the outer spheroid dominates over the"
While Ro and. A could have. been. merged into oue single operator. there are intentionally kept distinct.,"While $\mathbf{R}$ and $\mathbf{A}$ could have been merged into one single operator, there are intentionally kept distinct."
 The rationale for this choice so is that the left hand side of Eq. 2..," The rationale for this choice so is that the left hand side of Eq. \ref{eq:all},"
 i.e. the measurements. can be acquired by reading directlv the imaginary part of the complex visibility.," i.e. the measurements, can be acquired by reading directly the imaginary part of the complex visibility."
 Given that the next (quadratic) term in the Tavlor expansion of e being real. this makes the approximation valid to the third order in phase.," Given that the next (quadratic) term in the Taylor expansion of $e^{i\varphi}$ being real, this makes the approximation valid to the third order in phase."
" This also makes A of striking aspect as it is then exclusively filled with values 0, 1 or -]"," This also makes $\mathbf{A}$ of striking aspect as it is then exclusively filled with values 0, 1 or -1."
 If the matrix A were iuvertible. then the analysis of one unique focal plaue iuage of a suele star (case correspouding to Eq. 1))," If the matrix $\mathbf{A}$ were invertible, then the analysis of one unique focal plane image of a single star (case corresponding to Eq. \ref{eq:transfer}) )"
 would be sufficient to determine the iustrunental pliase y as seen from the detector. aud dive an AO system and/or delay lines.," would be sufficient to determine the instrumental phase $\varphi$ as seen from the detector, and drive an AO system and/or delay lines."
 Except for the special case of a uou-redundant aperture. the problem is however kuown to be degenerate. despite the larger muuber of measures than unknowns (Af>N1)? As demoustrated by the successes of =NRALinterferometiy. a complete characterization of the wavefront is not esseutial if oue can determine observable quantities that are pupil-phase independent.," Except for the special case of a non-redundant aperture, the problem is however known to be degenerate, despite the larger number of measures than unknowns $M > N-1$ As demonstrated by the successes of NRM-interferometry, a complete characterization of the wavefront is not essential if one can determine observable quantities that are pupil-phase independent."
 The closure relations used dn interferometry- can be related to the operator A: these relations are simply linear colmbinations Guocdelized by an operator KC) of rows of A that produce 0. forming something known as the left null space of A: For a non-redundant array. each closure relation will fill a row of Ko with mostly zeroes. except in three positions corresponding to the baselines forming a closing triangle. hat will contain 1 or -l.," The closure relations used in interferometry can be related to the operator $\mathbf{A}$: these relations are simply linear combinations (modelized by an operator $\mathbf{K}$ ) of rows of $\mathbf{A}$ that produce 0, forming something known as the left null space of A: For a non-redundant array, each closure relation will fill a row of $\mathbf{K}$ with mostly zeroes, except in three positions corresponding to the baselines forming a closing triangle, that will contain 1 or -1."
 These relations are however rot the only possible oues. aud less trivial combinations. involving amore than three rows at a time. can be constructed.," These relations are however not the only possible ones, and less trivial combinations, involving more than three rows at a time, can be constructed."
 The total wmmber of independent relations jowever remains uuchaused aud is only inposed by the econetry of the array., The total number of independent relations however remains unchanged and is only imposed by the geometry of the array.
" Although not impossible. finding the operator K ""by mand” (d.e. fiudiug a basis for the left null-space of A) or a redundant aperture is a tedious task. as the matrix A can ect quite larec."," Although not impossible, finding the operator $\mathbf{K}$ “by hand” (i.e. finding a basis for the left null-space of $\mathbf{A}$ ) for a redundant aperture is a tedious task, as the matrix $\mathbf{A}$ can get quite large."
 A very efficient way to do this is to caleutate the singular value decomposition (SVD) of AT., A very efficient way to do this is to calcutate the singular value decomposition (SVD) of $\mathbf{A}^T$.
 The SVD aleorithin (Pressetal.2002).. allows to decompose the now (NL)«Af matrix AJ as the product ofa CN13«M cohuun-orthogoual matrix U. a AL«M diagonal iiatrix W with positive or zero clemeuts (the so-called singular values) aud the transpose of au AL<Af orthogonal matrix V: Oue relevant property of the SVD is that it explicitly constructs orthonormal bases for both the uull-space and the range of the matrix AT.," The SVD algorithm \citep{2002nreb.book.....V}, allows to decompose the now $(N-1) \times M$ matrix $\mathbf{A}^T$ as the product of a $(N-1)
\times M$ column-orthogonal matrix $\mathbf{U}$, a $M \times M$ diagonal matrix $\mathbf{W}$ with positive or zero elements (the so-called singular values) and the transpose of an $M \times M$ orthogonal matrix $\mathbf{V}$: One relevant property of the SVD is that it explicitly constructs orthonormal bases for both the null-space and the range of the matrix $\mathbf{A}^T$."
 Of particular interest here. are the cohunus of V. that correspond to singular values equal to zero: these vectors form an orthouormal base for the uullspace. also refered to as Kernel of AT. that is exactly what is needed to fll iu the rows of K.," Of particular interest here, are the columns of $\mathbf{V}$ that correspond to singular values equal to zero: these vectors form an orthonormal base for the null-space, also refered to as Kernel of $\mathbf{A}^T$, that is exactly what is needed to fill in the rows of $\mathbf{K}$."
 If the observed target is not perfectly svnunetriic. and exhibits actual phase imforination (i6. δο+0. see for instance Mounier(2000})). Eq.," If the observed target is not perfectly symmetric, and exhibits actual phase information (i.e. $\Phi_O \neq 0$, see for instance \citet{2000plbs.conf..203M}) ), Eq."
 5 is required., \ref{eq:all} is required.
 Miltiplvine it with the left side operator K leads to a new series of new phlase-like quautitics that are nof contanunated by imstrinental phase. ecucralizing the notion of closure-pliase (Baldwinctal.1986). on which NRALiuterterometry from the eround 2000) aud from space (Sivaramalavishuanetal.2009) rely entirely.," Multiplying it with the left side operator $\mathbf{K}$ leads to a new series of new phase-like quantities that are not contaminated by instrumental phase, generalizing the notion of closure-phase \citep{1986Natur.320..595B} on which NRM-interferometry from the ground \citep{2000PASP..112..555T} and from space \citep{2009SPIE.7440E..30S} rely entirely."
 While not as inmnecdiately tangible as the notion of closurc-phDase. this proposed ecueralization. hereafter refered to as keruclphase (or IKer-phliase) since it relates to the kernel of the matrix AT. exhibits a unique advantage over the classical closure-phase: it is not restricted to non-redundant apertures and makes it possible to extract plasc-residual iuuuune information fron mages acquired from telescopes of arbitrary pupil ecometry.," While not as immediately tangible as the notion of closure-phase, this proposed generalization, hereafter refered to as kernel-phase (or Ker-phase) since it relates to the kernel of the matrix $\mathbf{A}^T$, exhibits a unique advantage over the classical closure-phase: it is not restricted to non-redundant apertures and makes it possible to extract phase-residual immune information from images acquired from telescopes of arbitrary pupil geometry."
 This has some obvious advantages over the restrictive non-redundant case:, This has some obvious advantages over the restrictive non-redundant case:
densities by using the rotational diagram method ?2).,densities by using the rotational diagram method .
". Briefly. for an optically thin line. the column density in the upper level (N,) can be written as V,=3KW/(ScVS pr). where k is the Boltzmann constant. W is the integrated intensity of a line cfType V). v the frequency. S the line strength. µ the dipole moment."," Briefly, for an optically thin line, the column density in the upper level $N_u$ ) can be written as $N_u = 3kW/(8\pi^3 \nu S \mu^2)$ , where $k$ is the Boltzmann constant, $W$ is the integrated intensity of a line $\int T_{\rm {MB}} d$ V), $\nu$ the frequency, $S$ the line strength, $\mu$ the dipole moment."
" Under LTE conditions. the population of each level follows a Boltzmann law at the gas temperature 7 by N,=(N/QigueE, where N is the total column density. ο the partition function. and g,, and E, are the statistical weight and theenergy of the upper level. respectively."," Under LTE conditions, the population of each level follows a Boltzmann law at the gas temperature $T$ by $N_u = (N/Q)g_u e^{-E_u/kT}$, where $N$ is the total column density, $Q$ the partition function, and $g_u$ and $E_u$ are the statistical weight and theenergy of the upper level, respectively."
 We then obtain Using Eq. 4..," We then obtain Using Eq. \ref{erot},"
" we plot log(Ny/gu) versus E,/K (see Fig. 6))", we plot $\rm{log} (N_u/g_u)$ versus $E_u/k$ (see Fig. \ref{Frot}) )
" and make a least-squares fit for T anc N taking into accountboth CH;OH 3,-» |, and 3,—[4, bands.", and make a least-squares fit for $T$ and $N$ taking into accountboth $_3$ OH $_{k} \rightarrow$ $_{k}$ and $5_{k} \rightarrow 4_{k}$ bands.
 The partition function of CH;OH is οaemeJ!(9. where fi is the Planck constant and A. B. and C are the rotation constants?," The partition function of $_3$ OH is $Q = 2[\frac{\pi~(kT)^3}{h^3ABC}]^{1/2}$, where $h$ is the Planck constant and $A$, $B$, and $C$ are the rotation constants."
?).A ο=1.23T? was used in the calculations.,A $Q = 1.23~T^{1.5}$ was used in the calculations.
" The CH:OH 5,—4; data were smoothed to the resolution of the 2,—I, data.", The $_3$ OH $5_{k} \rightarrow 4_{k}$ data were smoothed to the resolution of the $2_{k} \rightarrow 1_{k}$ data.
 CH3OH transition lines that were used in this fit are listed in Table 4.., $_3$ OH transition lines that were used in this fit are listed in Table \ref{Ttrans}.
" To estimate the CH;OH fractional abundance (relative to H3). Χσμιοη. we calculate thebeam-averaged H> column density. Ny,. following the expression where 7!“ is the peak intensity in Jy/beam. py,= 2.8 is the molecular weight per hydrogen molecule. and Q=(TAninGna)/(4In2) is the beam solid angle of an elliptical Gaussian beam with minor and major axes @yiy and C. respectively."," To estimate the $_3$ OH fractional abundance (relative to $_2$ ), $X_{\rm CH_3OH}$, we calculate thebeam-averaged $_2$ column density, $N_{\rm H_2}$, following the expression where $I_{\nu}^{\rm peak}$ is the peak intensity in Jy/beam, $\mu_{\rm H_2} =$ 2.8 is the molecular weight per hydrogen molecule, and $\Omega = (\pi \theta_{\rm min} \theta_{\rm maj})/(4 \rm{ln2}) $ is the beam solid angle of an elliptical Gaussian beam with minor and major axes $\theta_{\rm min}$ and $\theta_{\rm maj}$, respectively."
" We obtained a rotational temperature of 15 K and à CH:OH column density. Neg.ou. of 1.2x10° towards the (1755.00"")) peak position."," We obtained a rotational temperature of 15 K and a $_3$ OH column density, $N_{\rm CH_3OH}$, of $1.2 \times 10^{15}$ towards the ) peak position."
" Since the lines are likely sub- excited. we take a dust temperature Ty= 60 K (see LVG analysis) andobtain à Ny,=4.6x10-7(from our | mm continuum data convolved tothe 3 mm data) and à Xcy.on of 2.6 x 107°. At the ("," Since the lines are likely sub-thermally excited, we take a dust temperature $T_{\rm d} =$ 60 K (see LVG analysis) andobtain a $N_{\rm H_2} = 4.6~\times 10^{22}$(from our 1 mm continuum data convolved tothe 3 mm data) and a $X_{\rm CH_3OH}$ of 2.6 $\times$ $^{-8}$ ."
"13711.00"")) position. we get à Χσομοη = 3.7 x 107°. when using Ncu.og = 2.9 x 107 and Nu, = 7.7 x |07 em7.."," At the ) position, we get a $X_{\rm CH_3OH}$ = 3.7 $\times$ $^{-9}$ , when using $N_{\rm CH_3OH}$ = 2.9 $\times$ $^{14}$ and $N_{\rm{H_2}}$ = 7.7 $\times$ $^{22}$ ."
 A rotational temperature of 13 K was calculated., A rotational temperature of 13 K was calculated.
" At the (—9755. 22722) position. the values for the Xenon. Newson. and Ny, are: 5.6 x 1077. 3.8 x 10/7 e"," At the $-$ 2) position, the values for the $X_{\rm CH_3OH}$ , $N_{\rm CH_3OH}$ , and $N_{\rm{H_2}}$ are: 5.6 $\times$ $^{-9}$ , 3.8 $\times$ $^{14}$ ,"
" At the (—9755. 22722) position. the values for the Xenon. Newson. and Ny, are: 5.6 x 1077. 3.8 x 10/7 em"," At the $-$ 2) position, the values for the $X_{\rm CH_3OH}$ , $N_{\rm CH_3OH}$ , and $N_{\rm{H_2}}$ are: 5.6 $\times$ $^{-9}$ , 3.8 $\times$ $^{14}$ ,"
" At the (—9755. 22722) position. the values for the Xenon. Newson. and Ny, are: 5.6 x 1077. 3.8 x 10/7 em."," At the $-$ 2) position, the values for the $X_{\rm CH_3OH}$ , $N_{\rm CH_3OH}$ , and $N_{\rm{H_2}}$ are: 5.6 $\times$ $^{-9}$ , 3.8 $\times$ $^{14}$ ,"
roughly one quarter of the entire sky.,roughly one quarter of the entire sky.
 As the latitude distribution of NEOs ts not uniform (see figure 2)). a search program similar to the one described above could cover the ecliptic to roughly + 20° in ecliptic latitude each month. a region in which > of NEOs are found.," As the latitude distribution of NEOs is not uniform (see figure \ref{fig:s2}) ), a search program similar to the one described above could cover the ecliptic to roughly $\pm$ $^{\circ}$ in ecliptic latitude each month, a region in which $\gtrsim$ of NEOs are found."
 Alternatively. a two month strategy could reach ecliptic latitudes of + 407. and = of NEOs.," Alternatively, a two month strategy could reach ecliptic latitudes of $\pm$ $^{\circ}$, and $\gtrsim$ of NEOs."
" This nplies that SDSS. operating in 343 binned mode. would be roughly equivalent to à Vso, = 21.5 survey from Jedicke et al. ("," This implies that SDSS, operating in $\times$ 3 binned mode, would be roughly equivalent to a $_{50\%}$ = 21.5 survey from Jedicke et al. ("
2003). and would be able to detect of NEOs larger than | km by about the year 2010 if such a program were implemented starting in 2002.,"2003), and would be able to detect of NEOs larger than 1 km by about the year 2010 if such a program were implemented starting in 2002."
 However. this is a very indirect argument.," However, this is a very indirect argument."
 In the following section we present the simulated results of 10 year NEO surveys which include a realistic pre-detected population., In the following section we present the simulated results of 10 year NEO surveys which include a realistic pre-detected population.
 To better evaluate the performance of an SDSS NEO survey. we have performed long-term. 10 year simulations of NEO discovery using the different modes of operation discussed in the previous sections.," To better evaluate the performance of an SDSS NEO survey, we have performed long-term, 10 year simulations of NEO discovery using the different modes of operation discussed in the previous sections."
" We have included a realistic pre-detected population of NEOs by running a ""pseudo-LINEAR"" simulation of NEO detection as in Jedicke et al. (", We have included a realistic pre-detected population of NEOs by running a “pseudo-LINEAR” simulation of NEO detection as in Jedicke et al. (
2003) on our sample of 4668 NEOs with H < 20.,2003) on our sample of 4668 NEOs with H $\leq$ 20.
 The pre-detection simulation was run until it matched the 628 NEOs with H < 18 known as of Jan 1. 2003.," The pre-detection simulation was run until it matched the 628 NEOs with H $\leq$ 18 known as of Jan 1, 2003."
 At the end of this simulation the total number of pre-detected NEOs was 1424. slightly more than the 1333 H < 20 NEOs known as of 1/1/2003 (data from the Minor Planet Center).," At the end of this simulation the total number of pre-detected NEOs was 1424, slightly more than the 1333 H $\leq$ 20 NEOs known as of 1/1/2003 (data from the Minor Planet Center)."
 The distributions of the known and pre-detected populations are shown in Fig 9. and match up remarkably well. giving us confidence that our pre-detected population ts realistic.," The distributions of the known and pre-detected populations are shown in Fig \ref{fig:predet} and match up remarkably well, giving us confidence that our pre-detected population is realistic."
 The results of four 10 year simulations are shown in Figures 10 and 11... including NEOs with 2 or more detections in a span of 10 days.," The results of four 10 year simulations are shown in Figures \ref{fig:comp}
 and \ref{fig:comp1k}, including NEOs with 2 or more detections in a span of 10 days."
 An unbinned survey. described in Sections 5 and 6. detects the most NEOs in 10 years.," An unbinned survey, described in Sections 5 and 6, detects the most NEOs in 10 years."
 The completeness of the pre-detected population is30%.. and reaches after a 10 year survey in unbinned mode.," The completeness of the pre-detected population is, and reaches after a 10 year survey in unbinned mode."
 Completenesses are calculated assuming the Bottke et al. (, Completenesses are calculated assuming the Bottke et al. (
2003) model as an underlying NEO population. as described in Section 3.,"2003) model as an underlying NEO population, as described in Section 3."
 If the goal of an NEO survey ts to achieve the Spaceguard goal of detecting of NEOs with H < 18. then Figure 11 shows that the «3(1) binned survey. described in Sections 5 and 6. is most effective.," If the goal of an NEO survey is to achieve the Spaceguard goal of detecting of NEOs with H $\leq$ 18, then Figure \ref{fig:comp1k} shows that the $\times$ 3(ii) binned survey, described in Sections 5 and 6, is most effective."
 The completeness of the pre-detected population is60%.. and reaches by the end of a 10 year survey in 261) binned mode.," The completeness of the pre-detected population is, and reaches by the end of a 10 year survey in $\times$ 3(ii) binned mode."
 The mark is reached after seven years. in January 2010.," The mark is reached after seven years, in January 2010."
 Note that this is almost exactly the time predicted by Jedicke et al. (, Note that this is almost exactly the time predicted by Jedicke et al. (
2003) for a survey with limiting magnitude of V50G- = 21.5. and determined independently.,"2003) for a survey with limiting magnitude of ${50\%}$ = 21.5, and determined independently."
 It is interesting that the optimal survey strategy depends on the goal of the survey., It is interesting that the optimal survey strategy depends on the goal of the survey.
 The balance between magnitude limit and sky coverage is such that a «3(1) binned survey is able to achieve the Spaceguard goal the fastest. while an unbinned survey detects a significantly larger fraction of the total NEO population.," The balance between magnitude limit and sky coverage is such that a $\times$ 3(ii) binned survey is able to achieve the Spaceguard goal the fastest, while an unbinned survey detects a significantly larger fraction of the total NEO population."
 A «2 binned survey does moderately well in both regimes. detecting a total of of NEOs after 10 years.," A $\times$ 2 binned survey does moderately well in both regimes, detecting a total of of NEOs after 10 years."
 One can imagine a long-term NEO survey which begins operation in « 361) binned mode. and transitions to unbinned mode after the completion of the Spaceguard goal.," One can imagine a long-term NEO survey which begins operation in $\times$ 3(ii) binned mode, and transitions to unbinned mode after the completion of the Spaceguard goal."
 Such a hybrid survey would provide the appropriate balance between survey depth and sky coverage. and adapt to the current scientific need.," Such a hybrid survey would provide the appropriate balance between survey depth and sky coverage, and adapt to the current scientific need."
 The detection of km-sized potentially hazardous asteroids 15 a high priority., The detection of km-sized potentially hazardous asteroids is a high priority.
 We have demonstrated that the SDSS telescope and camera system has the ability to detect and characterize the orbits of NEOs at a fast rate., We have demonstrated that the SDSS telescope and camera system has the ability to detect and characterize the orbits of NEOs at a fast rate.
 We have detailed four different cadences. which depend on the binning of the CCDs. the spatial distribution of NEOs. and observational restrictions.," We have detailed four different cadences, which depend on the binning of the CCDs, the spatial distribution of NEOs, and observational restrictions."
 In «3 binned mode. the 5o detection limit corresponds to V ~ 21.4.," In $\times$ 3 binned mode, the $\sigma$ detection limit corresponds to V $\sim$ 21.4."
" The <3 areal coverage rate implies that an SDSS NEO survey in that mode would be roughly equivalent to a Vso, = 21.5 NEO survey from Jedicke et al (2003).", The $\times$ 3 areal coverage rate implies that an SDSS NEO survey in that mode would be roughly equivalent to a $_{50\%}$ = 21.5 NEO survey from Jedicke et al (2003).
 Their results. in turn. imply that such a survey could reach the Spaceguard goal of detecting of NEOs with H < 18 by the year 2010. had such a survey begun in early 2002.," Their results, in turn, imply that such a survey could reach the Spaceguard goal of detecting of NEOs with H $\leq$ 18 by the year 2010, had such a survey begun in early 2002."
 We have performed long term. 10 year simulations of SDSS NEO surveys with each of our four cadences.," We have performed long term, 10 year simulations of SDSS NEO surveys with each of our four cadences."
 We find that an unbinned survey detects the largest number of NEOs. of NEOs with H < 20 in 10 years.," We find that an unbinned survey detects the largest number of NEOs, of NEOs with H $\leq$ 20 in 10 years."
 Alternatively. the « 3(11) binned survey reaches the Spaceguard Goal most quickly. in 2010 for a survey beginning in January. 2003.," Alternatively, the $\times$ 3(ii) binned survey reaches the Spaceguard Goal most quickly, in 2010 for a survey beginning in January, 2003."
 This 15 very close to the prediction of Jedicke et al. (, This is very close to the prediction of Jedicke et al. (
2003).,2003).
 The accurate. five-band photometry of the SDSS system would also be a huge benefit to NEO science. through the composition and albedo (and therefore potential hazard) determination of NEOs.," The accurate, five-band photometry of the SDSS system would also be a huge benefit to NEO science, through the composition and albedo (and therefore potential hazard) determination of NEOs."
 A large side benefit to Solar System science would be the serendipitous discovery and compositional determination of a large number of small solar system bodies. main belt asteroids and. Kuiper belt objects.," A large side benefit to Solar System science would be the serendipitous discovery and compositional determination of a large number of small solar system bodies, main belt asteroids and Kuiper belt objects."
 An unbinned survey would be most beneficial in this regard. due to its deeper exposures and frequent scanning of the ecliptic.," An unbinned survey would be most beneficial in this regard, due to its deeper exposures and frequent scanning of the ecliptic."
 We gratefully acknowledge extensive discussions with our colleagues in the SDSS/APO community., We gratefully acknowledge extensive discussions with our colleagues in the SDSS/APO community.
 Our thanks to the SDSS Advisory Council and Management Committee for supporting this effort to investigate an NEO survey. to Bill Bottke for generating our NEO sample population. and to Ted Bowell and Al Harris for helpful discussions.," Our thanks to the SDSS Advisory Council and Management Committee for supporting this effort to investigate an NEO survey, to Bill Bottke for generating our NEO sample population, and to Ted Bowell and Al Harris for helpful discussions."
 CH thanks NSF grant AST-0098557 at the University of Washington for support., CH thanks NSF grant AST-0098557 at the University of Washington for support.
 SR and TQ are grateful to the NASA Astrobiology Institute for support., SR and TQ are grateful to the NASA Astrobiology Institute for support.
The two expressions of the thermal energv. (Eq.,The two expressions of the thermal energy (Eq.
 38) and the conductive cooling rate (Eq., 38) and the conductive cooling rate (Eq.
" 35) allow us to define the cooling time 7. by thermal conduction. If we express (his relation in dimensionless units in terms of (he reference values 7,=10' lx and Ly=25 Mm we obtain the following scaling law. In Fig."," 35) allow us to define the cooling time $\tau_c$ by thermal conduction, If we express this relation in dimensionless units in terms of the reference values $T_0=10^7$ K and $L_0=25$ Mm we obtain the following scaling law, In Fig."
" 6 (top left panel) we plot this theoretically estimated cooling time 7,(7).L) calculated from the observed values of the flare peak temperature 7,, and fare length scale L as a function of the observed flare duration times τε,"," 6 (top left panel) we plot this theoretically estimated cooling time $\tau_c(T_p, L)$ calculated from the observed values of the flare peak temperature $T_p$ and flare length scale $L$ as a function of the observed flare duration times $\tau_f$."
 We find that the theoretically estimated conductive cooling tme 7. of most flares is comparable or shorter than the flare duration 7;., We find that the theoretically estimated conductive cooling time $\tau_c$ of most flares is comparable or shorter than the flare duration $\tau_f$.
" The radiative loss rate is generally expressed as a product of (he electron density à». ion density 2;. and the radiative loss function A(7). which in the coronal approximation (with full ionization. i.e.. n,2 n;) is where (he radiative loss function can be approximated by piece-wise powerlaws (Rosner el al."," The radiative loss rate is generally expressed as a product of the electron density $n_e$, ion density $n_i$, and the radiative loss function $\Lambda (T)$, which in the coronal approximation (with full ionization, i.e., $n_e \approx n_i$ ) is where the radiative loss function can be approximated by piece-wise powerlaws (Rosner et al."
 1978: Mewe et al., 1978; Mewe et al.
 1985). The radiative cooling time can then be defined as the ratio of the thermal energy (Eq.," 1985), The radiative cooling time can then be defined as the ratio of the thermal energy (Eq."
 39) and the racliative loss rate (Eq., 39) and the radiative loss rate (Eq.
 41). where we can eliminate the unknown density by inserting the RIV law (Eq.," 41), where we can eliminate the unknown density by inserting the RTV law (Eq."
 21).," 21),"
Alaser emission from the (6.7-GlIz) transition of methanol was first. detected: by Menten (1991).. who found it to be common towards star formation regions.,"Maser emission from the (6.7-GHz) transition of methanol was first detected by Menten \shortcite{Me1991b}, who found it to be common towards star formation regions."
 Subsequent observations have confirmed this. ancl there are presently more than 250 published sites of 6.7-Gllz methanol emission within the Galaxy (MacLeod&vanderWaltetal.1995:Ellingsen 1995)..," Subsequent observations have confirmed this, and there are presently more than 250 published sites of 6.7-GHz methanol emission within the Galaxy \cite{Ma1992b,Ma1992a,Sc1993,Ca1995a,Ho1995,Va1995b,El1995a}."
 Currently all 6.7-Gllz methanol masers are thought to be associated with regions of massive star formation. although the untargeted survey of Ellingsen (1995) etected a number of sources with no known associations.," Currently all 6.7-GHz methanol masers are thought to be associated with regions of massive star formation, although the untargeted survey of Ellingsen \shortcite{El1995a} detected a number of sources with no known associations."
 The 6.7-Gllz transition of methanol produces. the second strongest. Galactic masers of any molecule., The 6.7-GHz transition of methanol produces the second strongest Galactic masers of any molecule.
 “Phis makes it ideal [for interferometric observations. as the accuracy with which we can determine the spatial distribution of maser spots is largely dependent on the signal-to-noise ratio.," This makes it ideal for interferometric observations, as the accuracy with which we can determine the spatial distribution of maser spots is largely dependent on the signal-to-noise ratio."
 The first high-resolution spatial images of the 12.2-Cllz methanol masers (Norrisetal.LOSS) showed. that. unlike OLD orH2O0.. the methanol masers often exhibit a simple spatial morphology.," The first high-resolution spatial images of the 12.2-GHz methanol masers \cite{No1988} showed that, unlike OH or, the methanol masers often exhibit a simple spatial morphology."
 Subsequent observations of the 6.7-Gllz methanol masers in many of the same sources (Norrisetal.1993). revealed that. they also frequently have a curved or linear spatial structure., Subsequent observations of the 6.7-GHz methanol masers in many of the same sources \cite{No1993} revealed that they also frequently have a curved or linear spatial structure.
 Interferometric observations of the 12.2- and 6.7-Cillz methanol masers show that the methanol masers often emanate from the same region as the Ol] masers (A\lentcnetal.1988:Alenten1992:Caswell 1995)..," Interferometric observations of the 12.2- and 6.7-GHz methanol masers show that the methanol masers often emanate from the same region as the OH masers \cite{Me1988,Me1992,Ca1995e}."
 The similarity in the spectra of many 6.7- ancl 12.2-Cllz methanol masers was first noted by Alenten (1991).., The similarity in the spectra of many 6.7- and 12.2-GHz methanol masers was first noted by Menten \shortcite{Me1991b}.
. The observations of Menten (1092) and Norris (1993) show that when there is à correspondence between one or more 12.2- and 6.7-Gllz spectral features. the maser emission at the two frequencies appears to originate from the same location.," The observations of Menten \shortcite{Me1992} and Norris \shortcite{No1993} show that when there is a correspondence between one or more 12.2- and 6.7-GHz spectral features, the maser emission at the two frequencies appears to originate from the same location."
 Lt has been suggested that 6.7- and 12.2-Gllz methanol masers occur in the circumstellar dise whieh surrouncls massive stars during their formation (Norrisetal.1993:Nor-risetal. 1995).," It has been suggested that 6.7- and 12.2-GHz methanol masers occur in the circumstellar disc which surrounds massive stars during their formation \cite{No1993,No1995}."
.. Lowe are observing these disces nearly edge- then this provides an explanation for the curved. and linear structures observed in many methanol masers.," If we are observing these discs nearly edge-on, then this provides an explanation for the curved and linear structures observed in many methanol masers."
 One of the predictions of this model is that the masers should show a simple velocity structure. and Norris (1995) have presented evidence for this.," One of the predictions of this model is that the masers should show a simple velocity structure, and Norris \shortcite{No1995} have presented evidence for this."
 Another prediction is that the. masers should. be approximately coincident with the peak of the continuum emission., Another prediction is that the masers should be approximately coincident with the peak of the continuum emission.
 This is in contrast to OLL masers. which are typically found near," This is in contrast to OH masers, which are typically found near"
"Carrying out the integration over rm in J leads to from which we can derive Eq. 19,","Carrying out the integration over $m_2$ in $I_1$ leads to from which we can derive Eq. \ref{eq:distri:makino_convergence1},"
", the first convergence criterion of ?..", the first convergence criterion of \citet{Makino:1998p8778}.
" We consider the case where this condition does not hold, i.e., Then, the term in brackets dominates over the other term."," We consider the case where this condition does not hold, i.e., Then, the term in brackets dominates over the other term."
" Thus, the term in brackets is constant and carrying out the integration yields Now, if the second condition, Eq."," Thus, the term in brackets is constant and carrying out the integration yields Now, if the second condition, Eq."
" 20 holds, using mp«m, we derive We rewrite [2 using the dimensionless variables x,=m,/m and Xx»=mz/m which yields By integrating over x2, we derive The term in square brackets can be split into a sum of integrals, the first of which is straight-forward to evaluate Cl.."," \ref{eq:distri:makino_convergence2} holds, using $m_0 \ll m$, we derive We rewrite $I_2$ using the dimensionless variables $x_1 = m_1/m$ and $x_2 = m_2/m$ which yields By integrating over $x_2$, we derive The term in square brackets can be split into a sum of integrals, the first of which is straight-forward to evaluate \ref{fig:distri:I2}."
 C11 , \ref{eq:distri:new_condition1} 
of the irregular galaxies with the SAIC being an example of a normal inregular an the LMC being a barred irregular galaxy.,of the irregular galaxies with the SMC being an example of a normal irregular an the LMC being a barred irregular galaxy.
 Furthermore (see for example Sandage 1975) lenticular ealaxies were also found to exhibit either normal (S0) or barred (SBO) morphology., Furthermore (see for example Sandage 1975) lenticular galaxies were also found to exhibit either normal (S0) or barred (SB0) morphology.
 Saudage (1975) and Sandage Tanunann (1981) assign the overwhelming majority of spiral galaxies to either the normal or barred (wpe. with few intermediate objects.," Sandage (1975) and Sandage Tammann (1981) assign the overwhelming majority of spiral galaxies to either the normal or barred type, with few intermediate objects."
 On the other hand de Vaucouleurs (1959) advocated a classification svstem in which bar strength varied continuouslv from pure spirals of type SA. through intermediate objects of type ΑΟ. to pure bars assigned (o tvpe SB.," On the other hand de Vaucouleurs (1959) advocated a classification system in which bar strength varied continuously from pure spirals of type SA, through intermediate objects of type SAB, to pure bars assigned to type SB."
 Galaxies that Sandage Toanmunnann classilied as being edee-on were excluded from the sample because it is often difficult (or impossible) to distinguish normal and barred spirals that are viewed edge-on., Galaxies that Sandage Tammann classified as being edge-on were excluded from the sample because it is often difficult (or impossible) to distinguish normal and barred spirals that are viewed edge-on.
. Also excluded were those ealaxies which Sandage Tanunann classified as being peculiar., Also excluded were those galaxies which Sandage Tammann classified as being 'peculiar'.
 Some of such peculiar ealaxies (turned oul to be unusually blue. indicating that (heir apparent peculiarity is due lo (or associated with) a recent burst of star formation.," Some of such peculiar galaxies turned out to be unusually blue, indicating that their apparent peculiarity is due to (or associated with) a recent burst of star formation."
 The adopted luminosities of galaxies are (he MS. values of Sandage Tamamann (1981).," The adopted luminosities of galaxies are the $M^{o,i}_{B_T}$ values of Sandage Tammann (1981)."
 In the subsequent discussion (hese magnitudes will. for the sake of simplicity. be relerred (to as Mp.," In the subsequent discussion these magnitudes will, for the sake of simplicity, be referred to as $M_{B}$."
 For the majority of the galaxies in the Shaplev-Ames catalog total (asvmptotie) colors on the Johnson B-V svstem. that have been corrected for Galactic and internal extinction. and for the effects of redshift. are available from theGalaxies (=RC3) by de Vaucouleurs οἱ al. (," For the majority of the galaxies in the Shapley-Ames catalog total (asymptotic) colors on the Johnson B-V system, that have been corrected for Galactic and internal extinction, and for the effects of redshift, are available from the (=RC3) by de Vaucouleurs et al. ("
1991).,1991).
" These intrinsic colors will subsequently be designated (2—V),.", These intrinsic colors will subsequently be designated $(B-V)_{o}$.
" The following discussion is based on all those galaxies in the Revised Shapleyv-Ames Catalog which are not classified as ""edge-on' or as ‘peculiar’. and for which the RCS catalog gives (2B—V), colors. ["," The following discussion is based on all those galaxies in the Revised Shapley-Ames Catalog which are not classified as `edge-on' or as `peculiar', and for which the RC3 catalog gives $(B-V)_o$ colors. ["
For both normal spirals and for barred spirals the fraction of objects classified as being peculiar by Sandage Tammann lies between and 656].,For both normal spirals and for barred spirals the fraction of objects classified as being peculiar by Sandage Tammann lies between and ].
 Iis not clear, It is not clear
The most prominent difference with Bochum 9 is the presence of a clump of stars in the bright end of the ALS.,The most prominent difference with Bochum 9 is the presence of a clump of stars in the bright end of the MS.
 All the stars having CDV. photometry have been plotted in the two color digram in Fig., All the stars having $UBV$ photometry have been plotted in the two color digram in Fig.
 9., 9.
 Most of them exhibit basically no redcdening. like the bulk of stars in Bochum 9.," Most of them exhibit basically no reddening, like the bulk of stars in Bochum 9."
 llowever the clump of stars at. (2B1) = 041 and (Uο) = 07 has a larger reddening E(BV) = 0.4. and is identified by an empirical ZAAIS shifted by. this amount (dotted. line).," However the clump of stars at $(B-V)$ = 0.1 and $(U-B)$ = $-$ 0.7 has a larger reddening $(B-V)$ = 0.47, and is identified by an empirical ZAMS shifted by this amount (dotted line)."
 Since these stars have a common extinction. which is significantly larger than that undergone by the bulls of the stars. it is reasonable to see whether they define a distinct sequence in the color magnitude For this purpose we selected all the stars having 0.42 < E(BOV) x 0.52 (IS stars in total).," Since these stars have a common extinction, which is significantly larger than that undergone by the bulk of the stars, it is reasonable to see whether they define a distinct sequence in the color magnitude For this purpose we selected all the stars having 0.42 $\leq$ $(B-V)$ $\leq$ 0.52 (18 stars in total)."
 These are plotted in Fig., These are plotted in Fig.
 10. and seem to actually define a clear sequence.," 10, and seem to actually define a clear sequence."
 There are 6 stars which lie olf the MS. and they are plotted. with open circles.," There are 6 stars which lie off the MS, and they are plotted with open circles."
" Phe ZAMS has been over-imposed by adopting (inAJ), = 12.20. which implies a distance of 2.7 kpc rom the Sun."," The ZAMS has been over-imposed by adopting $(m-M)_o$ = 12.20, which implies a distance of 2.7 kpc from the Sun."
 The dashed line in Fig., The dashed line in Fig.
 10 represents the same ZAMS 0.75 mag brighter. and it defines the ZAMS of unresolved binaries.," 10 represents the same ZAMS 0.75 mag brighter, and it defines the ZAMS of unresolved binaries."
 Accordingly the two stars at Vuzz12.3. (D.V)ozc0.8 may be binaries.," Accordingly the two stars at $V_0 \approx 12.3$, $(B-V)_0 \approx -0.8$ may be binaries."
 We looked for the relative position of these stars within he cluster. and. found that. with the exception of the two," We looked for the relative position of these stars within the cluster, and found that, with the exception of the two"
heu computed the effective area function at the position of for cach observation.,then computed the effective area function at the position of for each observation.
 This was corrected to account for he fraction of the PSF enclosed by the extraction region., This was corrected to account for the fraction of the PSF enclosed by the extraction region.
 Finally. we estimated the detector response for the source iu each observation using positiou-dependent response files that accounted for the corrections we made to undo xwtiallv the charec-transter iucfficieucy. (Townsleyctal. 2002a).," Finally, we estimated the detector response for the source in each observation using position-dependent response files that accounted for the corrections we made to undo partially the charge-transfer inefficiency \citep{tow02a}."
. The mean &ux did not change between the two observations on 2001 July 57. so we stummed the source spectra. and computed the average effective area and response functions weighted bv the nuuber of counts from the two observations.," The mean flux did not change between the two observations on 2004 July 5–7, so we summed the source spectra, and computed the average effective area and response functions weighted by the number of counts from the two observations."
 We obtained enough photons to model the spectra from the observations on 2001 July 57 (1710 total counts) and 2001 August 28 (306 total counts)., We obtained enough photons to model the spectra from the observations on 2004 July 5–7 (1740 total counts) and 2004 August 28 (306 total counts).
 We subtracted the same background spectrum frou the 2001 July aud Aueust spectra., We subtracted the same background spectrum from the 2004 July and August spectra.
 The background contributed <3% to the total flux., The background contributed $<$ to the total flux.
 We erouped the source spectra so that each euergv bin had at least 20 counts;, We grouped the source spectra so that each energy bin had at least 20 counts.
 The spectra are displaved in Figure L., The spectra are displayed in Figure \ref{fig:spectra}.
 We modeled the spectra using NSPEC version 11.3.1 (Arnaudetal.1996)., We modeled the spectra using XSPEC version 11.3.1 \citep{arn96}.
.. We initially modeled the spectimm a power-law absorbed by interstellar eas aud dust., We initially modeled the spectrum a power-law absorbed by interstellar gas and dust.
 However. we found that for the longer observation. this model did not re-produce the 0.5.2.0 keV. part of the spectzuii and left residuals near the phloto-clectric edge of Fe at 7 keV. Therefore. we added a second absorption compoucut that only affected a fraction of the cmitting region.," However, we found that for the longer observation, this model did not re-produce the 0.5–2.0 keV part of the spectrum and left residuals near the photo-electric edge of Fe at 7 keV. Therefore, we added a second absorption component that only affected a fraction of the emitting region."
 The free parameters im this model were the column of interstellar eas CVpqs). the coluun of the partiabeoveriug absorber (NVppe) and the fraction of the cmitting region covered by this absorber (foe). the photon iudex (D) aud nonnalization (Nr) of the power law.," The free parameters in this model were the column of interstellar gas $N_{\rm H,ISM}$ ), the column of the partial-covering absorber $N_{\rm H,pc}$ ) and the fraction of the emitting region covered by this absorber $f_{\rm pc}$ ), the photon index $\Gamma$ ) and normalization $N_\Gamma$ ) of the power law."
 The optical depth of dust was set to 7—0.185-Nyτοσα7). and the halo area to LOO times that of the PSF (Baganofetal.2003).," The optical depth of dust was set to $\tau = 0.485 \cdot N_{\rm H}/(10^{22} {\rm cm}^{-2})$, and the halo area to 100 times that of the PSF \citep{bag03}."
. The best-fit spectral parameters for the two epochs are listed in Table 2.., The best-fit spectral parameters for the two epochs are listed in Table \ref{tab:spectra}.
 We found that the interstellar absorption in the 2001 July spectrum is consistent with the value towardA... δις10°? 7.," We found that the interstellar absorption in the 2004 July spectrum is consistent with the value toward, $6\times10^{22}$ $^{-2}$."
 There was uot cuonels signal in the 2001 August observation to constrain all of the parameters. so we fixed the iterstellar absorption to this value.," There was not enough signal in the 2004 August observation to constrain all of the parameters, so we fixed the interstellar absorption to this value."
 The change in the spectrum in Figure lis the result of an order-ofanaguitude decrease in the column deptl of the partial-coveriug absorber between 2001 July aud August., The change in the spectrum in Figure \ref{fig:spectra} is the result of an order-of-magnitude decrease in the column depth of the partial-covering absorber between 2004 July and August.
 Iu. contrast. the values of the photon indices from the two observations are consistent withiu their 260 nucertaimtics. so the intrinsic spectrum appears to chauge very little.," In contrast, the values of the photon indices from the two observations are consistent within their $\sigma$ uncertainties, so the intrinsic spectrum appears to change very little."
 Likewise. after accounting for the imterstellar and partial-covering absorption. the inferred. Ihuuinosity of290031... changes by only between 2001 July aud August.," Likewise, after accounting for the interstellar and partial-covering absorption, the inferred luminosity of, changes by only between 2004 July and August."
 Finally. in order to determine the quiesceu nunositv of290031... we extractec he comnts from the oobservatious during 19992003. and during February 2005.," Finally, in order to determine the quiescent luminosity of, we extracted the counts from the observations during 1999–2003, and during February 2005."
" During 199920023. the region contained 185 total counts, of which the expected backeround coutribution was 371 counts."," During 1999–2003, the region contained 485 total counts, of which the expected background contribution was 371 counts."
 Although this excess flux could represcut the quiescent cussion from290031. two voung. cluission-lue stars also lie within the cextraction region (IRS 33N aud IRS 33E). aud. these may be X-ray sources.," Although this excess flux could represent the quiescent emission from, two young, emission-line stars also lie within the extraction region (IRS 33N and IRS 33E), and these may be X-ray sources."
 [f we assume a a D—1.5 power law spectrum (typical for a quiescent LNMXD: e.g. Nong 22002) absorbed by 6«1072 cin? of eas and dust. we can place a rough upper linut to the quiescent Iuninosity," If we assume a a $\Gamma = 1.5$ power law spectrum (typical for a quiescent LMXB; e.g., Kong 2002) absorbed by $6\times10^{22}$ $^{-2}$ of gas and dust, we can place a rough upper limit to the quiescent luminosity"
"the balance between coagulationunderstood. and fragmentation, which remains poorly ","the balance between coagulation and fragmentation, which remains poorly understood."
"We also neglect stellar irradiation, which will become important in the late stages of the disk evolution."," We also neglect stellar irradiation, which will become important in the late stages of the disk evolution."
" Irradiation will maintain high temperatures in the inner disk (22:100 KK; Chambers 2009)), gap formation for "," Irradiation will maintain high temperatures in the inner disk $\approx$ K; \citealp{Chambers}) ), preventing gap formation for planets."
"On the otherpreventing hand, irradiation should lead to planets.hole-forming photoevaporating wind (Clarkeetal.dula001;Alexandcretal.20 006)), which quickly depletes the thus possibly shouldbringing sclf-migration to an even earlier halt."," On the other hand, irradiation should lead to a hole-forming photoevaporating wind \citealp{Clarke,Alexander}) ), which quickly depletes the disk, thus possibly bringing migration to an even earlier halt."
 Future work -consistentlv address these issucs., Future work should self-consistently address these issues.
" As aconsequence of the independence of equilibrium radi on mass, all planets migrateplanets to these planetlocations."," As a consequence of the independence of equilibrium radii on planet mass, all planets migrate to these equilibrium locations."
 Ensembles of reachingbody them may equilibriumbecome violently unstable duc to N- interactions., Ensembles of planets reaching them may become violently unstable due to $N$ -body interactions.
" Nevertheless, even if scattered away, these will drive the plancts back toward migrationradii."," Nevertheless, even if scattered away, migration will invariably drive the planets back toward these radii."
" The final invariablyoutcome maywell be collisions driving further planet growth, aiding rapid giant planct formation or planets in 1:1 resonance."," The final outcome may well be collisions driving further planet growth, aiding rapid giant planet formation or forming planets in 1:1 resonance."
" If this is the case, forminghowever, it raises the question of the solar has a set of spaced planets as whyopposed to only systemtwo, as the two neatlyequilibrium radii of the model (and naively "," If this is the case, however, it raises the question of why the solar system has a set of neatly spaced planets as opposed to only two, as the two equilibrium radii of the model might naively suggest."
One possible solution is that Γ mightthus suggest. racius) shows a dependence on the planet-to-starany cquilibriummass ratio q at the of when gzI? (Massetetal. 2006))., One possible solution is that $\Gamma$ (and thus any equilibrium radius) shows a dependence on the planet-to-star mass ratio $q$ at the verge of gap opening when $q\approx{h^3}$ \citealp{Masset}) ).
" vergeAnother is gapthat we opening consider the fully unsaturated whereas saturationonly depends on the width of the horseshoetorque, region and therefore on the planet's mass."," Another is that we only consider the fully unsaturated torque, whereas saturation depends on the width of the horseshoe region and therefore on the planet's mass."
" However, the level of saturation in radiative disks is not fully understood at present, and we cannot easily add it to our study."," However, the level of saturation in radiative disks is not fully understood at present, and we cannot easily add it to our study."
 Future models should include effects of saturation to study possible masstimescales segregation., Future models should include effects of saturation to study possible mass segregation.
"for Finally, in view of the long migration Ms01to, such planets may just not have the time vanishesmigrate back to the equilibrium location before the disk if scattered. far enough."," Finally, in view of the long migration timescales for $M\lesssim{0.1}$, such planets may just not have the time to migrate back to the equilibrium location before the disk vanishes if scattered far enough."
 This scattered. population of small planets could provide the initial conditions for the terrestrial planets of our own solar system., This scattered population of small planets could provide the initial conditions for the terrestrial planets of our own solar system.
" Our results provide qualitative. and quantitative justification for the reduction of Tvpesynthesis I migration rates assumed in planetary population models Alibertctal.2004;Ida&Lin2008;Mordasinict(c.g,al.2009))."," Our results provide qualitative and quantitative justification for the reduction of Type I migration rates assumed in planetary population synthesis models \citealp[e.g.,][]{Alibert,Ida,Mordasini}) )."
" Instead of on the fast, mass- timescale finig,migrating we find that planets spend their first Myr near equilibrium radii that change onlv on the slow acerction timescale f£..."," Instead of migrating on the fast, mass-dependent, timescale $t_{\rm mig}$, we find that planets spend their first Myr near equilibrium radii that change only on the slow accretion timescale $t_{\nu}$."
 We show in that fagf.~OL fora planet during most of the evolution/ of the disk., We show in that $t_{\rm mig}/t_{\nu}\sim0.1$ for a planet during most of the evolution of the disk.
" —dependence the same figure for different masses showsExamining a lincar on mass, fnig0.10M/M...), consistent with the population synthesis/fi7 assumptions."," Examining the same figure for different masses shows a linear dependence on mass, $t_{\rm mig} /
t_{\nu} \sim 0.1 (M / \mbox{\mearth})$, consistent with the population synthesis assumptions."
 W.L. is partly by a Kalbfleisch Research Fellowship from.supported the. AMNH., W.L. is partly supported by a Kalbfleisch Research Fellowship from the AMNH.
" M.-M.M.L. is partly supported by NSF07AI74G. CDI grant AST-0835734, and NASA OSS ellow.grant NNX S-].P.useful is an STFC Cal "," M.-M.M.L. is partly supported by NSF CDI grant AST-0835734, and NASA OSS grant NNX07AI74G. S.-J.P. is an STFC postdoctoral fellow."
We acknowledge discussionspostdoctor with Aordasini and T. Birnsticl., We acknowledge useful discussions with C. Mordasini and T. Birnstiel.
that SiS molecules are less likely to be depleted onto dust grains than SiO molecules.,that SiS molecules are less likely to be depleted onto dust grains than SiO molecules.
 Therefore. flreeze-out. should not be the reason for the depletion of Sis in since no depletion of SiO is found for this object.," Therefore, freeze-out should not be the reason for the depletion of SiS in since no depletion of SiO is found for this object."
" On the other hand. with a high efficiency. Sis can be photodissociated into . which iniüiates. cireumstellar SiC,, chemistry Charnlev1999)."," On the other hand, with a high efficiency, SiS can be photodissociated into $^+$, which initiates circumstellar $_n$ chemistry \citep{mackay99}."
. IIence. we inler (hat ellicient photodissociation in has clestroved Sis. and silicon chemistry has been ongoing in this evolved C-star envelope.," Hence, we infer that efficient photodissociation in has destroyed SiS, and silicon chemistry has been ongoing in this evolved C-star envelope."
 Interferometric observations of these Si-bearing molecules are obviously needed to verily the conjecture., Interferometric observations of these Si-bearing molecules are obviously needed to verify the conjecture.
 ]sotopic ratios of various elements provide substantial tests for uucleosvuthesis of and intermecliate-mass stars (LIMS)., Isotopic ratios of various elements provide substantial tests for nucleosynthesis of low- and intermediate-mass stars (LIMS).
 When a LIAIS evolves into the AGB stage. the iucleosvnthesized products svuthesized through the CNO evele inside (he star are dredged up to the surface and then are ejected into the circumstellar envelope.," When a LIMS evolves into the AGB stage, the nucleosynthesized products synthesized through the CNO cycle inside the star are dredged up to the surface and then are ejected into the circumstellar envelope."
 Consequently. 1 isotopic composition in the cireumstellar shell can be markedly changed.," Consequently, the isotopic composition in the circumstellar shell can be markedly changed."
 Dased on the yaclional abundances proposed in Table 3.. we deduce (he isotopic ratios (or their lower imiis) of carbon. oxvgen. silicon. and sulfur in6... The results are listed in Table 4..," Based on the fractional abundances proposed in Table \ref{col_cit6}, we deduce the isotopic ratios (or their lower limits) of carbon, oxygen, silicon, and sulfur in The results are listed in Table \ref{isoto_cit6}."
 The errors estimated from (he measurement aud calibration are given., The errors estimated from the measurement and calibration are given.
 For comparison. we also ist the isotopic ratios for (Cernicharoetal.2000). ancl the Sun (Locdders," For comparison, we also list the isotopic ratios for \citep{cernicharo00} and the Sun \citep{lodders}."
2003).. The PC/@C abundance ratio is the most studied isotopic abundance in LIMS., The $^{12}$ $^{13}$ C abundance ratio is the most studied isotopic abundance in LIMS.
 Standard stellar models predict that the C/C abundance ratio can be significantly increased during {he nucleosvuthesis and dredge-p processes in the AGB stage., Standard stellar models predict that the $^{12}$ $^{13}$ C abundance ratio can be significantly increased during the nucleosynthesis and dredge-up processes in the AGB stage.
" However. extensive observations have shown that the PC/""C abundance ratios in LIMSs are considerably lower than those expected by standard stellar models (e.g.Charbonnel&doN"," However, extensive observations have shown that the $^{12}$ $^{13}$ C abundance ratios in LIMSs are considerably lower than those expected by standard stellar models \citep[e.g.][]{charbonnel98}."
ascimento19983).. (1995) proposed an extra mixing process to account for the low C/C. In low-mass AGB stars. the nonstandard mixing called cool bottom processing nay decrease the PC/!*C ratio to ~4 (Sackmann&Boothrovd1999:Sackmann1999).," \citet{charbonnel95} proposed an extra mixing process to account for the low $^{12}$ $^{13}$ C. In low-mass AGB stars, the nonstandard mixing called cool bottom processing may decrease the $^{12}$ $^{13}$ C ratio to $\sim4$ \citep{sackmann99,boothroyd99}."
. For AGB stars more massive than eΕΛ... the hot bottom burning may take place and induce ο ΠΟ to further decrease to ils equilibrium value of ~3.5 (Frostetal. 1998).," For AGB stars more massive than $\sim4 M_\sun$, the hot bottom burning may take place and induce $^{12}$ $^{13}$ C to further decrease to its equilibrium value of $\sim3.5$ \citep{frost98}."
.Current observations of the CO isolopologues in PNs (Balseretal.2002:Josselin&Bachiller2003) suggest that the," .Current observations of the CO isotopologues in PNs \citep{balser02,josselin03}
 suggest that the"
Es»ectrum with a template donor star spectrum. and finding 16 combination of template star ancl donor velocity at which the cross-correlation peak is strongest.,"spectrum with a template donor star spectrum, and finding the combination of template star and donor velocity at which the cross-correlation peak is strongest."
" This process is equivalent to. producing a traileck “cross-correlation spectrum"". and then back-projecting this trail into velocity space. producing à cross-correlation map in velocitv-space (the skew map) which should show a peak at the velocity of the donor star."," This process is equivalent to producing a trailed “cross-correlation spectrum”, and then back-projecting this trail into velocity space, producing a cross-correlation map in velocity-space (the skew map) which should show a peak at the velocity of the donor star."
 The normalized spectra of the template AL cwarls and UUMa were continuum subtracted. anc were Caussian smoothed with ENLIM of 2.5 pixels to increase S/N without losing any spectral information.," The normalized spectra of the template M dwarfs and UMa were continuum subtracted, and were Gaussian smoothed with FWHM of 2.5 pixels to increase S/N without losing any spectral information."
" Each UUMa. spectrum. L(A). was cross correlated. with the template spectrum. ZA). for a range of velocity shifts. ο. using correlation cocllicient ἐς defined as where 727,(À)=-)."," Each UMa spectrum, $F(\lambda)$, was cross correlated with the template spectrum, ${T}(\lambda)$, for a range of velocity shifts, $v$, using correlation coefficient $C_v$ defined as where ${T'}_v(\lambda)=T(\frac{\lambda}{1+v/c})$."
" Εις definition of T'(X2 simplv has the effect. of ""uured-shifting: the template spectrum bv velocity e before cross-correlating.", This definition of ${T'}_v(\lambda)$ simply has the effect of red-shifting the template spectrum by velocity $v$ before cross-correlating.
 The denominator of ος is chosen so that if the template and donor spectra are identical. the value of €. at the peak will be 1. independent of any simple scaling of the Εαν of either spectrum.," The denominator of $C_v$ is chosen so that if the template and donor spectra are identical, the value of $C_v$ at the peak will be 1, independent of any simple scaling of the flux of either spectrum."
 The correlation trails thus. produced. were then. transformed o velocitv-space using the Fourier-Lilterecl back-projection echnique as implemented in “Tom Alarsh’s software., The correlation trails thus produced were then transformed to velocity-space using the Fourier-filtered back-projection technique as implemented in Tom Marsh's software.
 The strength of the skew map at à given velocity therefore garows how well the object spectra match a star of the emplate's spectral type orbiting at that velocity., The strength of the skew map at a given velocity therefore shows how well the object spectra match a star of the template's spectral type orbiting at that velocity.
 Only the doublet wavelength range was used in de Cross-Correlation. since this is the only sharp donor tbsorption feature detected. and will therefore provide all 10 velocity. information.," Only the doublet wavelength range was used in the cross-correlation, since this is the only sharp donor absorption feature detected, and will therefore provide all the velocity information."
 Skew maps were also produced using the spectral range A= (with the and lines masked out) which uses all re detected. donor star features. but. this simply. smears out the donor star in the skew map. probably a result. of," Skew maps were also produced using the spectral range $\lambda=$ (with the and lines masked out) which uses all the detected donor star features, but this simply smears out the donor star in the skew map, probably a result of"
Observations of the Cosmic Microwave Background (CAIB) provide some of the most compelling support for the currently [avored ACDAL. orconcordance. cosmological model.,"Observations of the Cosmic Microwave Background (CMB) provide some of the most compelling support for the currently favored $\Lambda$ CDM, or, cosmological model."
 Phe concordance framework. predicts that the CALB should. posses temperature fluctuations which are both statistically isotropic (i.e. stationary over the celestial sphere) and Gaussian (CGuthSteinhardt&Turner 1983).," The concordance framework predicts that the CMB should posses temperature fluctuations which are both statistically isotropic (i.e. stationary over the celestial sphere) and Gaussian \citep{Guth1982,Starobinskij1982,Bardeen1983}."
. Measurements by the Wilkinson Microwave Anisotropy Probe (WALAP) (Bennettetal.2003:Linshawct2009). have undergone extensive statistical analysis. much of which has confirmed the concordance model but with some indications of departures that may be significant: see for example (2008).," Measurements by the Wilkinson Microwave Anisotropy Probe (WMAP) \citep{Bennett2003,Hinshaw2009} have undergone extensive statistical analysis, much of which has confirmed the concordance model but with some indications of departures that may be significant; see for example \cite{Yadav2008}."
. More specifically. there is some evidence for hemispherical power asymmetry (I5riksen2007:Lloftultctal.2009:Hansenet2009) and also a Cold Spot has been identified 2005).," More specifically, there is some evidence for hemispherical power asymmetry \citep{Eriksen2004a,Park2004,Eriksen2007,Hoftuft2009,Hansen2009} and also a Cold Spot has been identified \citep{Vielva2004,Cruz2005}."
. In other words there is some evidence of an anisotropic universe. i.e. one in which the backerounc cosmology may not be described by the standard. EFriedman-lItobertson-Malker (PFRAV) metrice.," In other words there is some evidence of an anisotropic universe, i.e. one in which the background cosmology may not be described by the standard Friedman-Robertson-Walker (FRW) metric."
 Of course the background cosmology [or a non-Isotropic universe may still be described by the EV metric. but this would require a non-standard topology which we do not consider in this analysis.," Of course the background cosmology for a non-isotropic universe may still be described by the FRW metric, but this would require a non-standard topology which we do not consider in this analysis."
 The Bianchi classification provides a complete characterization of all the known homogeneous but. anisotropic exact solutions to Gencral Relativity., The Bianchi classification provides a complete characterization of all the known homogeneous but anisotropic exact solutions to General Relativity.
 The classification was first proposed by Bianchi and later applied to General Relativity 1969)., The classification was first proposed by Bianchi and later applied to General Relativity \citep{Ellis1969}.
. Initial studies used the lack of large-scale asymmetry inthe CMD temperature to put strong constraints on the possible Bianchi models (Barrow.Juszkiewicz&Sonoda1985: 1997).," Initial studies used the lack of large-scale asymmetry inthe CMB temperature to put strong constraints on the possible Bianchi models \citep{Barrow1985, Bunn1996, Kogut1997}."
". However. simulations of the CIB from Bianchi universes not only show a preferred direction. but mocels with negative spatial curvature (such as the types V and. VlL,) can produce localized features (Barrow.Juszkiewicz&Sonoda 1985).."," However, simulations of the CMB from Bianchi universes not only show a preferred direction, but models with negative spatial curvature (such as the types V and $_h$ ) can produce localized features \citep{Barrow1985}. ."
 So, So
To infer the metallicity from the observed. emission-line spectra. we carried out model calculations by using the photoionization code Cloudy version 07.02 (Ferland et al.,"To infer the metallicity from the observed emission-line spectra, we carried out model calculations by using the photoionization code Cloudy version 07.02 (Ferland et al."
 1998)., 1998).
 Here we assume that the clouds in the NLR of HzRGs are mainly phototonized and not significantly affected by shocks., Here we assume that the clouds in the NLR of HzRGs are mainly photoionized and not significantly affected by shocks.
 Although Nagao et al. (, Although Nagao et al. (
2006a) demonstrated that this assumption is appropriate when focusing oniv. and Cm]. we will examine how this assumption is valid in section. 5.1.,"2006a) demonstrated that this assumption is appropriate when focusing on, and ], we will examine how this assumption is valid in section 5.1."
 The parameters for the calculations are (1) the spectral energy distribution (SED) of the photoionizing continuum radiation: (2) the hydrogen density of a cloud (14): (3) the ionization parameter (U). 1.e.. the ratio of the ionizing photo density to the hydrogen density at the irradiated surface of a cloud: (4) the column density of a cloud (Ny): and (5) the elemetal composition of the gas.," The parameters for the calculations are (1) the spectral energy distribution (SED) of the photoionizing continuum radiation; (2) the hydrogen density of a cloud $n_\mathrm{H}$ ); (3) the ionization parameter $U$ ), i.e., the ratio of the ionizing photon density to the hydrogen density at the irradiated surface of a cloud; (4) the column density of a cloud $N_\mathrm{H}$ ); and (5) the elemental composition of the gas."
" For the SED of the tonizing photons. we used the ""table AGN” command. that roughly reproduces the typical SED of ionizing photons in AGNs (Mathews Ferland 1987)."," For the SED of the ionizing photons, we used the ""table AGN"" command, that roughly reproduces the typical SED of ionizing photons in AGNs (Mathews Ferland 1987)."
 We do not examine the dependences of the calculations on the SED but adopt only this SED. because Nagao et al. (," We do not examine the dependences of the calculations on the SED but adopt only this SED, because Nagao et al. ("
20062) already investigated the dependences in HzRGs and concludec that the SED effects do not affect the discussion of the NLR metallicity evolution in HzRGs.,2006a) already investigated the dependences in HzRGs and concluded that the SED effects do not affect the discussion of the NLR metallicity evolution in HzRGs.
 We adopted gas clouds with thehydrogen density jj=107 and 107em? and the io1Zatlol parameters U=10777—107'7., We adopted gas clouds with thehydrogen density $n_\mathrm{H}=10^2$ and $10^4 \ \mathrm{cm}^{-3}$ and the ionization parameters $U = 10^{-2.4} - 10^{-1.2}$.
 Here we assumed dust-free gas clouds. since dusty models are inconsistent with observations when high-tonization emission lines of HzRGs are cocernec (Nagao et al.," Here we assumed dust-free gas clouds, since dusty models are inconsistent with observations when high-ionization emission lines of HzRGs are concerned (Nagao et al."
 20062)., 2006a).
 ote that this is suggested also by rest- optical or near-infrared emission lines (e.g.. Marconi et al.," Note that this is suggested also by rest-frame optical or near-infrared emission lines (e.g., Marconi et al."
 1994; Ferguson et al., 1994; Ferguson et al.
 1997b; Nagao et al., 1997b; Nagao et al.
 2003)., 2003).
 For the chemical composition of gas. we assumed that the all metals scale by keeping solar ratios except for He and N. For helium. we assumed a primary nucleosynthesis component in additio to the primordial value.," For the chemical composition of gas, we assumed that the all metals scale by keeping solar ratios except for He and N. For helium, we assumed a primary nucleosynthesis component in addition to the primordial value."
 Nitrogen scales as the square power of other metal abundances because it is à secondary element., Nitrogen scales as the square power of other metal abundances because it is a secondary element.
 We adopted the analytical expressions for the heltum and nitroge relative abundances as functions of the metallicity given 1 Dopita et al. (, We adopted the analytical expressions for the helium and nitrogen relative abundances as functions of the metallicity given in Dopita et al. (
2000).,2000).
 Another free parameter in our calculatio is the cloud column density., Another free parameter in our calculation is the cloud column density.
 Since we are now focusing o relatively high-ionization emission linesv.iv.Hen. anc ir. we stop our calculations when the hydrogen tonizatio fraction drops below159c.," Since we are now focusing on relatively high-ionization emission lines, and ]), we stop our calculations when the hydrogen ionization fraction drops below."
. This requirements ensures that the line fluxes of interest will not depend on the choice of a particular column density., This requirements ensures that the line fluxes of interest will not depend on the choice of a particular column density.
 In Figure 2 we show the dependence of the emission-line luminosity on the NLR metallicity. for models with ay=10°em? and 10em. and Uo=1078 and 10772.," In Figure 2 we show the dependence of the emission-line luminosity on the NLR metallicity, for models with $n_\mathrm{H} = 10^2 \ \mathrm{cm}^{-3}$ and $10^4 \ \mathrm{cm}^{-3}$, and $U = 10^{-1.6}$ and $10^{-2.0}$."
 The line luminosity is normalized by the number of H-ionizing photons in the input continuum emission., The line luminosity is normalized by the number of H-ionizing photons in the input continuum emission.
 The model behavior is completely different between and the other emission lines: the ts a recombination line and its luminosity is proportional to the rate of He-1onizing photons. while the other emission lines are collisionally excited and their emissivity strongly depends on the gas temperature.," The model behavior is completely different between and the other emission lines: the is a recombination line and its luminosity is proportional to the rate of $\mathrm{He}^+$ -ionizing photons, while the other emission lines are collisionally excited and their emissivity strongly depends on the gas temperature."
 The equilibrium temperature of ionized gas clouds i8 sensitive to metallicity because of the radiative cooling by metal emission lines., The equilibrium temperature of ionized gas clouds is sensitive to metallicity because of the radiative cooling by metal emission lines.
 Therefore the luminosity of collisionally excited emission lines decreases at high metallicity., Therefore the luminosity of collisionally excited emission lines decreases at high metallicity.
 Note that the luminosity decreases at much higher metallicity than the and Cin] luminosity., Note that the luminosity decreases at much higher metallicity than the and ] luminosity.
 This is because the nitrogen abundance increases at high metallicity. i.e.. N/H « (O/H).," This is because the nitrogen abundance increases at high metallicity, i.e., N/H $\propto$ $\mathrm{(O/H)}^2$."
 All of the above results are insensitive to the adopted gas density and ionization parameter., All of the above results are insensitive to the adopted gas density and ionization parameter.
 Figure 2 suggests that the flux ratio is possibly good metallicity diagnostic., Figure 2 suggests that the flux ratio is possibly good metallicity diagnostic.
 However. this flux ratio. also depends on other parameters such as the tonization parameter.," However, this flux ratio also depends on other parameters such as the ionization parameter."
 This degeneracy can be solved by combining it with the ratio which 15 primarily sensitive to the ionization parameter., This degeneracy can be solved by combining it with the ratio which is primarily sensitive to the ionization parameter.
 Therefore a diagram involving both the and ratios is expected to be a powerful metallicity diagnostic. as originally proposed by Nagao et al. (," Therefore a diagram involving both the and ratios is expected to be a powerful metallicity diagnostic, as originally proposed by Nagao et al. ("
20062).,2006a).
 In Figure 3. the results of our phototonization model calculations are plotted on this diagnostic diagram.," In Figure 3, the results of our photoionization model calculations are plotted on this diagnostic diagram."
 The model grids indicate that this diagram is quite useful to investigate the NLR metallicity., The model grids indicate that this diagram is quite useful to investigate the NLR metallicity.
 Note that. as shown in Figure 3. the flux ratio depends also on the gas density and thus the gas metallicity is not uniquely determined through this diagram.," Note that, as shown in Figure 3, the flux ratio depends also on the gas density and thus the gas metallicity is not uniquely determined through this diagram."
 However. it can be useful to investigate differences in metallicity and to assess the possible redshift evolution of the NLR metallicity.," However, it can be useful to investigate differences in metallicity and to assess the possible redshift evolution of the NLR metallicity."
 In the rest of the paper we only consider models with ay=LOtem™ (a typical NLR density: see. e.g.. Nagao et al.," In the rest of the paper we only consider models with $n_\mathrm{H} = 10^4 \mathrm{cm}^{-3}$ (a typical NLR density; see, e.g., Nagao et al."
 2001a. 20024).," 2001a, 2002a)."
 By comparing the observed flux ratios of HzRGs with the prediction of the photoionization models. we investigate the gas metallicity.," By comparing the observed flux ratios of HzRGs with the prediction of the photoionization models, we investigate the gas metallicity."
 In Figure 4. we plot the flux ratios of HZRGs on the diagnostic diagram with the calculated model grids.," In Figure 4, we plot the flux ratios of HzRGs on the diagnostic diagram with the calculated model grids."
 We also plot the flux ratios of the composite spectrum of HzRGs on this diagram., We also plot the flux ratios of the composite spectrum of HzRGs on this diagram.
 Though new 9 data are at higher redshift than the data in Nagao et al. (, Though new 9 data are at higher redshift than the data in Nagao et al. (
2006a) on average. there is no systematic difference in the data distribution between our new observations and the data of Nagao et al. (,"2006a) on average, there is no systematic difference in the data distribution between our new observations and the data of Nagao et al. ("
20062).,2006a).
 This result naively suggests that there is no significant chemical evolution in NLRs of HzRGs. even up to z-4.," This result naively suggests that there is no significant chemical evolution in NLRs of HzRGs, even up to $z \sim 4$."
 We now investigate whether shock models can explain the observed flux ratios of HzRGs., We now investigate whether shock models can explain the observed flux ratios of HzRGs.
 In Figure + we overplot the shock models and shock plus precursor models presented by Allen et al. (, In Figure 4 we overplot the shock models and shock plus precursor models presented by Allen et al. (
2008).,2008).
" Specifically. we plot shock models with shock velocities of 200 km s!«v,900 km s. magnetic parameters of B/n'= 0. 1. 2. and 4 μΟ en, and solar abundance. and shock plus precursor models with shock velocities of 200 km s!<v,«400km s7! .à magnetic"," Specifically, we plot shock models with shock velocities of 200 km $\mathrm{s}^{-1} < v_s < 900$ km $\mathrm{s}^{-1}$, magnetic parameters of $B/n^{1/2}=0$ , 1, 2, and 4 $\mu$ G $\mathrm{cm}^{3/2}$ , and solar abundance, and shock plus precursor models with shock velocities of 200 km $\mathrm{s}^{-1} < v_s < 400$km $\mathrm{s}^{-1}$ , a magnetic"
 3c(a)-level (dashed line) to show that the detected peak exceeds it significantly.,$3\sigma(a)$ -level (dashed line) to show that the detected peak exceeds it significantly.
 Another method for 1c-level of amplitude calculation was proposed for use by R.A. Fisher (see Fisher 1935;; Fisher 1936)) and often called as Fisher Randomization Test.," Another method for $\sigma$ -level of amplitude calculation was proposed for use by R.A. Fisher (see \citeauthor{fisher}
 \citeyear{fisher}; \citeauthor{fisher2} \citeyear{fisher2}) ) and often called as Fisher Randomization Test."
" The idea is to take the original light curve and preserving the time column, shuffle the corresponding intensities around."," The idea is to take the original light curve and preserving the time column, shuffle the corresponding intensities around."
 That destroys any coherent signal in the light curve while keeping the time sampling intact., That destroys any coherent signal in the light curve while keeping the time sampling intact.
 We are left with a shuffled light curve of pure white noise., We are left with a shuffled light curve of pure white noise.
 The next step is to compute a DFT of this light curve which will look really noisy., The next step is to compute a DFT of this light curve which will look really noisy.
 The standard deviation of the average amplitude of such a DFT is close to the 1o limit., The standard deviation of the average amplitude of such a DFT is close to the $\sigma$ limit.
" We iterated this 25 times, therefore we use the average of 25 standard deviation values to determine lo-level."," We iterated this 25 times, therefore we use the average of 25 standard deviation values to determine $\sigma$ -level."
" This pipeline gave us the value of c(a)=0.0028, which is slightly less than o(a) from 'analytical' and ‘least-squares error matrix’ calculations, hence we plotted the bigger value on our periodogram to be confident."," This pipeline gave us the value of $\sigma(a) = 0.0028$, which is slightly less than $\sigma(a)$ from 'analytical' and 'least-squares error matrix' calculations, hence we plotted the bigger value on our periodogram to be confident."
In Fig.,In Fig.
 3 we show μοι as a function of the comoving energy density (° according to the application of this model to all sources. the sources analyzed in this paper plus those considered in G98 for consistency.," 3 we show $\gamma_{\rm peak}$ as a function of the comoving energy density $U$ according to the application of this model to $all$ sources, the sources analyzed in this paper plus those considered in G98 for consistency."
" As expected. for powerful blazars (large C. small 5,4: We do not find significant differences with respect to the results of the previous model (compare the branches at high  of Fig."," As expected, for powerful blazars (large $U$, small $\gamma_{\rm peak}$ ) we do not find significant differences with respect to the results of the previous model (compare the branches at high $U$ of Fig."
 2 and Fig., 2 and Fig.
" 3). sincefor these sources το-ii. and therefore 2,41ii In both scenarios."," 3), sincefor these sources $\gamma_{\rm c} \ll \gamma_{\rm min}$, and therefore $\gamma_{\rm peak}\sim \gamma_{\rm min}$ in both scenarios."
"However. for small values of . 5,41 coincides with e>μήν and this automatically ensures that 2,4xUFl except when , results to be so large to exceed >... (in this case. of course. ,ak= ua).","However, for small values of $U$, $\gamma_{\rm peak}$ coincides with $\gamma_{\rm c} >\gamma_{\rm min}$ and this automatically ensures that $\gamma_{\rm peak}\propto U^{-1}$, except when $\gamma_{\rm c}$ results to be so large to exceed $\gamma_{\rm max}$ (in this case, of course, $\gamma_{\rm peak}=\gamma_{\rm max}$ )."
" In the finite injection model. in fact. the relation ,XCU.! is built-in. and translates into a SpeakMUlo when .>45."," In the finite injection model, in fact, the relation $\gamma_{\rm c}\propto U^{-1}$ is built–in, and translates into a $\gamma_{\rm peak} \propto U^{-1}$ when $\gamma_{\rm c}>\gamma_{\rm min}$."
 What we have verified is that this model fits the SEDs of all blazars. including the powerful ones.," What we have verified is that this model fits the SEDs of all blazars, including the powerful ones."
" For the latter Ce. large ( and small 7,4: we find the same correlation as found using the steady state model.", For the latter (i.e. large $U$ and small $\gamma_{\rm peak}$ ) we find the same correlation as found using the steady state model.
 We conclude that also this more consistent scenario confirms the existence of the two branches., We conclude that also this more consistent scenario confirms the existence of the two branches.
" These connect. as before. for values of (~ a few erg em."" and ipoak300."," These connect, as before, for values of $U\sim$ a few erg $^{-3}$ and $\gamma_{\rm peak}\sim 300$."
" This is a consequence of 5. becoming smaller than 7,5, caused by the increased radiative cooling in powerful blazars.", This is a consequence of $\gamma_{\rm c}$ becoming smaller than $\gamma_{\rm min}$ caused by the increased radiative cooling in powerful blazars.
 By studying blazars of very high and very small observed power we have confirmed that different flavors of blazars form à spectral and power sequence. where the peak frequency position and the relative intensity of the low and high energy spectral components decrease with increasing source power.," By studying blazars of very high and very small observed power we have confirmed that different flavors of blazars form a spectral and power sequence, where the peak frequency position and the relative intensity of the low and high energy spectral components decrease with increasing source power."
 This phenomenological behavior 15 plausibly the manifestation of a physical trend., This phenomenological behavior is plausibly the manifestation of a physical trend.
 By (necessarily) adopting an emission model for the production of the radiation. it 15 then possible to infer the physical parameters and look for the process(es) responsible for it.," By (necessarily) adopting an emission model for the production of the radiation, it is then possible to infer the physical parameters and look for the process(es) responsible for it."
 In particular we considered the emission. via synchrotron and inverse Compton scattering by a homogeneous region containing a tangled magnetic field and relativistic electrons., In particular we considered the emission via synchrotron and inverse Compton scattering by a homogeneous region containing a tangled magnetic field and relativistic electrons.
" Already in a previous study (G98) this resulted in the finding of a clear relationship between the energy of the particles emitting at the peaks of the spectrum ,(c? and the total energy density.", Already in a previous study (G98) this resulted in the finding of a clear relationship between the energy of the particles emitting at the peaks of the spectrum $\gamma_{\rm peak} m_e c^2$ and the total energy density.
 Here we extended the range of parameters by including sources with more extreme values of μον , Here we extended the range of parameters by including sources with more extreme values of $\gamma_{\rm peak}$.
The physical conditions found for low power BL Lacs imply a radiative cooling timescale long compared with the source light crossing time. and led us to consider the effects of a finite time tinj for the injection of the relativistic particles.," The physical conditions found for low power BL Lacs imply a radiative cooling timescale long compared with the source light crossing time, and led us to consider the effects of a finite time $t_{\rm inj}$ for the injection of the relativistic particles."
 The modeling of the blazar SED including à finite injection timescale (e.g. plausibly resembling what expected in the internal shock scenario) confirms the existence of a new branch of the correlation at high speak. with speakxU Ἰ. Ας the injection of particles above an energy μμμος lasts for fij we obtain two behaviors: in the fast cooling regime," The modeling of the blazar SED including a finite injection timescale (e.g. plausibly resembling what expected in the internal shock scenario) confirms the existence of a new branch of the correlation at high $\gamma_{\rm peak}$ , with $\gamma_{\rm peak}\propto U^{-1}$ As the injection of particles above an energy $\gamma_{\rm min} m_{\rm e} c^2$ lasts for $t_{\rm inj}$ we obtain two behaviors: in the fast cooling regime"
sopulations aud cau be highly attenuated by the diffuse dust in the ISM.,populations and can be highly attenuated by the diffuse dust in the ISM.
 Most of the photous absorbed by the dust. iu our models. originated as short waveleugth UV Cluission.," Most of the photons absorbed by the dust, in our models, originated as short wavelength UV emission."
 This ca1 be seeu in Figure 10. as the difference vetween the itysic stellar cuission (long dashed line) aud the observed enission (solid line) once the photons lave propagated. hrough the dusty ISM., This can be seen in Figure \ref{7321_sed} as the difference between the intrinsic stellar emission (long dashed line) and the observed emission (solid line) once the photons have propagated through the dusty ISM.
 The amount of absorption tends ο decrease wit1 jucreasing wavelength as the dust opaciv decreases aud the photons are able o travel througi the ISM. wih a lower probability of interaction., The amount of absorption tends to decrease with increasing wavelength as the dust opacity decreases and the photons are able to travel through the ISM with a lower probability of interaction.
 O1r models can reproduce the observed optical and NIR fiuxes well but srow slight diserepaucies in the FUV cussion., Our models can reproduce the observed optical and NIR fluxes well but show slight discrepancies in the FUV emission.
 The iuclels are also unable to reproduce the + xuxl flux. (0.8% )4un)., The models are also unable to reproduce the $z$ band flux $0.893 \mu$ m).
 We believe this may be due to tlιο lower S/N i the 2 hand combined with the intrinsic low surface brightness of the galaxies. leading to galaxy flux being lost durius removal of the sky backeround.," We believe this may be due to the lower S/N in the $z$ band combined with the intrinsic low surface brightness of the galaxies, leading to galaxy flux being lost during removal of the sky background."
 The 5.8 and 8.0721. TRAC bands trace eimissiou. from ΡΑΠ molecules while the MIPS μιαν cinission is produced primarily by the wari VSGs, The $5.8$ and $8.0\mu$ m IRAC bands trace emission from PAH molecules while the MIPS $24 \mu$ m emission is produced primarily by the warm VSGs.
 Rh1 all three cases the 8.07211 cussion is over-predicted by οur models., In all three cases the $8.0\mu$ m emission is over-predicted by our models.
 The 2 [jin flux is over-precdicted by the mode of UGC 7321. unuder-predieted for IC 2233.," The $24\mu$ m flux is over-predicted by the model of UGC 7321, under-predicted for IC 2233."
 This behavior in the MIR is likely a result of our treatiment of he PAII/VSC Cluission which is based on Milky. Wav abundances iud ilunünatiug radiatiou field shape (see ??))., This behavior in the MIR is likely a result of our treatment of the PAH/VSG emission which is based on Milky Way abundances and illuminating radiation field shape (see \ref{dustmodel}) ).
 Both the relative abundances of PATI molecules aux VSCs in LSBs and the shape of the ISRF in LSBs are likely differcut causing the discrepancies observed in the MIR., Both the relative abundances of PAH molecules and VSGs in LSBs and the shape of the ISRF in LSBs are likely different causing the discrepancies observed in the MIR.
 The larecr. cooler dust grains are responsible for the peak of the FIR. cinission bracketed by the MIPS observations at TO and 160522. Iu all three cases we have been able to reproduce the FIR 70 and 160411: ciission. withiu the quoted photometry errors. using our models.," The larger, cooler dust grains are responsible for the peak of the FIR emission bracketed by the MIPS observations at $70$ and $160\mu$ m. In all three cases we have been able to reproduce the FIR $70$ and $160\mu$ m emission, within the quoted photometry errors, using our models."
Alultiple components contribute to each peak visible in the full fit.,Multiple components contribute to each peak visible in the full fit.
 For example. using the elobal spectrum of 555 (Figure 5: highest S/N) as a guide. the 7.7 san PAIL complex has contributions from components at 7.6 jm and 7.8 jan. Similarly. the minor contribution of the 8.3 yan PAIL feature is evident between the 8.6 jan and 7.7 jm complexes. and the 11.3 jan complex separates into (svo features αἱ 11.2 and 11.3. jan. respectively.," For example, using the global spectrum of 55 (Figure \ref{pahfit55}; highest S/N) as a guide, the 7.7 $\mu$ m PAH complex has contributions from components at 7.6 $\mu$ m and 7.8 $\mu$ m. Similarly, the minor contribution of the 8.3 $\mu$ m PAH feature is evident between the 8.6 $\mu$ m and 7.7 $\mu$ m complexes, and the 11.3 $\mu$ m complex separates into two features at 11.2 and 11.3 $\mu$ m, respectively."
 We remind the reader (hat the PAIIFIT. Moin Power Feature (see discussion in 2)) explicitly ealeulates raciances across these blended complexes., We remind the reader that the PAHFIT Main Power Feature (see discussion in \ref{S2}) ) explicitly calculates radiances across these blended complexes.
 Figures 5.. 6.. and 7 show that the monochromatic specific intensity al all Irequencies is hiehest in 555.," Figures \ref{pahfit55}, \ref{pahfit3109}, and \ref{pahfit5152} show that the monochromatic specific intensity at all frequencies is highest in 55."
 It is interesting to note that the stellar continuum is weaker compared io the dust continuum in 555 than in the other two svstems: we attribute this to both a larger dust content and a higher star formation rate in 555 (han in 33109 or 1C:55152., It is interesting to note that the stellar continuum is weaker compared to the dust continuum in 55 than in the other two systems; we attribute this to both a larger dust content and a higher star formation rate in 55 than in 3109 or 5152.
 We also note with interest that the fit lor 33109 shows contributions from 11. 5(5) and [Ar IH] at 6.56 jm and 6.94 jm respectively (though the errorbars are appreciable). features that are largely absent [rom the other (wo galaxies.," We also note with interest that the fit for 3109 shows contributions from $_{\rm 2}$ S(5) and [Ar II] at 6.86 $\mu$ m and 6.94 $\mu$ m respectively (though the errorbars are appreciable), features that are largely absent from the other two galaxies."
 The absolute values for the extracted radiances (units of καν |) of the PAIL features and ionized atomic lines are given in Table 2.., The absolute values for the extracted radiances (units of $^{-2}$ $^{-1}$ ) of the PAH features and ionized atomic lines are given in Table \ref{globalpahline}.
 As noted above. 555 has the laveest PAIL luminosity in our sample: it has = 5 and & 10 times higher radiances in each PAI feature than 1€555152 or 33109. respectively.," As noted above, 55 has the largest PAH luminosity in our sample; it has $\gsim$ 5 and $\gsim$ 10 times higher radiances in each PAH feature than 5152 or 3109, respectively."
 555 also has the highest ionized atomic line radiances (compare the [Ne II]. 12.8 san values)., 55 also has the highest ionized atomic line radiances (compare the [Ne II] 12.8 $\mu$ m values).
 Given these properties. the appearance of the modest ionization potential [Ar II] line (15.76 eV: 2000)) in only 33109 is not surprising.," Given these properties, the appearance of the modest ionization potential [Ar II] line (15.76 eV; \nocite{Cox00}) ) in only 3109 is not surprising."
 The other (wo systems have stronger radiation fields: the [8 IV] 10.5 yan feature in 555 has an ionization potential of 34.79 eV. and the [Ne IH] 12.5 jm Tine in both 555 and 1055152 has an ionization potential of 21.56 eV. The PAIT features overwhelm the [Ar IH] line in these svstenis.," The other two systems have stronger radiation fields: the [S IV] 10.5 $\mu$ m feature in 55 has an ionization potential of 34.79 eV, and the [Ne II] 12.8 $\mu$ m line in both 55 and 5152 has an ionization potential of 21.56 eV. The PAH features overwhelm the [Ar II] line in these systems."
 We compare the ratios of the radiances of the four prominent PAIL features in a elobal sense for each galaxy in Table 3.., We compare the ratios of the radiances of the four prominent PAH features in a global sense for each galaxy in Table \ref{globalcomp}.
 The global (8.6 jm)/(11.3 yam) ratio is the same £00.19) for all three galaxies within the measurement uncertainties., The global (8.6 $\mu$ m)/(11.3 $\mu$ m) ratio is the same $\pm$ 0.19) for all three galaxies within the measurement uncertainties.
 The (6.2 jmm)/(11.3 jam). Cc. pa)/(6.2 jum). and (7.7 pom)/(11.8 pom) ratios have more significant scatter (factors as large as 3-4).," The (6.2 $\mu$ m)/(11.3 $\mu$ m), (7.7 $\mu$ m)/(6.2 $\mu$ m), and (7.7 $\mu$ m)/(11.3 $\mu$ m) ratios have more significant scatter (factors as large as 3-4)."
 It is not immediately clear why the (8.6 fam)/(11.8 san) ratio is the most stable across all (11ος galaxies., It is not immediately clear why the (8.6 $\mu$ m)/(11.3 $\mu$ m) ratio is the most stable across all three galaxies.
 Considering the small sample size. it is possible that. the small dispersion is a coincidence.," Considering the small sample size, it is possible that the small dispersion is a coincidence."
 Since the 8.6 jii and 11.3 pan PAIL features are postulated to have contributions from CII bending modes (though the CII contribution to the 8.6 jam feature is weak when the PAI] carriers are ionized: see 1.1)). the small dispersion in those bands could be due to the ionization state of the PAIIs.," Since the 8.6 $\mu$ m and 11.3 $\mu$ m PAH features are postulated to have contributions from CH bending modes (though the CH contribution to the 8.6 $\mu$ m feature is weak when the PAH carriers are ionized; see \ref{S1.1}) ), the small dispersion in those bands could be due to the ionization state of the PAHs."
 However. as mentioned above. the hardness of the radiation field in these svstems varies considerably on both the global and the local level.," However, as mentioned above, the hardness of the radiation field in these systems varies considerably on both the global and the local level."
 Further. differences in ionization state do not explain why statistically significant," Further, differences in ionization state do not explain why statistically significant"
Lt ds resolved. in all bands. with the only exception. of D band. likely due to the lower spatial resolution achieved.,"It is resolved in all bands with the only exception of B band, likely due to the lower spatial resolution achieved."
 Component SL is resolved in all NIIt/optical bands. showing a tail extending towards 52.," Component S1 is resolved in all NIR/optical bands, showing a tail extending towards S2."
" Its radio-to-optical spectral index is a, —0.954:0.10.", Its radio-to-optical spectral index is $\alpha_{r-o}=$ $\pm$ 0.10.
 On the other hand. 52 appears unresolved. in all bands. with the exception of Ix. and. 11 bands. i.e. those with the highest. resolution achieved.," On the other hand, S2 appears unresolved in all bands, with the exception of K and H bands, i.e. those with the highest resolution achieved."
 In these NIIt bands 52 is extended in the southern direction. resembling what is observed. in radio.," In these NIR bands S2 is extended in the southern direction, resembling what is observed in radio."
" Lts racio-to-optical spectral index is a, —1.05-0.10. Dilluse emission connecting the main hotspot components and extending το the southwestern part of the hotspot complex is detected in most of the NLR and optical In the A-ray band. S1 is the brightest. component. whereas the emission. from S3 is very weak (formally"," Its radio-to-optical spectral index is $\alpha_{r-o}=$ $\pm$ Diffuse emission connecting the main hotspot components and extending to the southwestern part of the hotspot complex is detected in most of the NIR and optical In the X-ray band, S1 is the brightest component, whereas the emission from S3 is very weak (formally"
being ejected by the binary. becoming free-floating planets while stable systems remained near or at the Here. we are interested m an earlier stage of evolution during which the giant planet is still. forming through the growth of a solid core.,"being ejected by the binary, becoming free-floating planets while stable systems remained near or at the Here, we are interested in an earlier stage of evolution during which the giant planet is still forming through the growth of a solid core."
 To address this issue. we have performed hydrodynamical simulations of low mass protoplanets evolving in a cireumbinary disk.," To address this issue, we have performed hydrodynamical simulations of low mass protoplanets evolving in a circumbinary disk."
 We begin by simulating the evolution of a binary-cireumbinary disk system., We begin by simulating the evolution of a binary–circumbinary disk system.
 These simulations are run for ~10° binary orbits until we get à quasi-stationary state. within which the disk structure and the binary eccentricity remain unchanged.," These simulations are run for $\sim 10^5$ binary orbits until we get a quasi-stationary state, within which the disk structure and the binary eccentricity remain unchanged."
 We then use this equilibrium state as the mitial conditions for the disk and the binary in subsequent simulations of protoplanets embedded in circumbinary disks., We then use this equilibrium state as the initial conditions for the disk and the binary in subsequent simulations of protoplanets embedded in circumbinary disks.
 This paper is organized as follows., This paper is organized as follows.
 In section 2 we describe the physical model and the numerical setup., In section 2 we describe the physical model and the numerical setup.
 In section 3 we present the results of the simulations., In section 3 we present the results of the simulations.
 We first describe the results dealing with binary-disk interactions. and discuss these results mm the context of previous theoretical and numerical work on binary-disk interactions.," We first describe the results dealing with binary-disk interactions, and discuss these results in the context of previous theoretical and numerical work on binary–disk interactions."
 We then focus on the evolution of planets in circumbinary disks., We then focus on the evolution of planets in circumbinary disks.
 We find that a low-mass protoplanet is trapped at the edge of the cavity created by the binary and we show that this effect arises when the corotation and Lindblad torques cancel each other., We find that a low-mass protoplanet is trapped at the edge of the cavity created by the binary and we show that this effect arises when the corotation and Lindblad torques cancel each other.
 We finally discuss our results in section 4 and present our conclusions., We finally discuss our results in section 4 and present our conclusions.
 Assuming that the disk aspect ratio is small. we can consider vertically averaged quantities when writing the equations of motion.," Assuming that the disk aspect ratio is small, we can consider vertically averaged quantities when writing the equations of motion."
 The problem ts therefore reduced to a two-dimensional one., The problem is therefore reduced to a two-dimensional one.
 In polar coordinates (0.Φ) and in a frame with the origin located at the centre of mass of the binary. the continuity equation reads: where X=[pds is the disk surface density.," In polar coordinates $(r,\phi)$ and in a frame with the origin located at the centre of mass of the binary, the continuity equation reads: where $\Sigma = \int^{\infty}_{-\infty} \rho dz$ is the disk surface density."
" The equations for the radial and azimuthal components of the disk velocity v=(7.v4) are respectively given by: Xv In the above equations. p is the vertically integrated pressure. f, and f, are respectively the radial and azimuthal components of the vertically averaged viscous force per unit volume."," The equations for the radial and azimuthal components of the disk velocity ${\bf v}=(v_r,v_\phi)$ are respectively given by: and In the above equations, $p$ is the vertically integrated pressure, $f_r$ and $f_\phi$ are respectively the radial and azimuthal components of the vertically averaged viscous force per unit volume."
" Expressions for f, and f; can be found for example in Nelson et al. (", Expressions for $f_r$ and $f_\phi$ can be found for example in Nelson et al. (
2000).,2000).
" @ is the gravitational potential and can be written as: where @, is the potential of the / member of the binary with mass M: and 6,r-ri;l is the potential of the planet with mass 51: In the previous equation. € is a softening parameter and is chosen to be e=0.6H/r. where H/r is the disk aspect ratio."," $\Phi$ is the gravitational potential and can be written as: where $\Phi_{si}$ is the potential of the $i^{\rm th}$ member of the binary with mass $M_{si}$ : and $\Phi_p$ is the potential of the planet with mass $m_p$: In the previous equation, $\epsilon$ is a softening parameter and is chosen to be $\epsilon=0.6 H/r$, where $H/r$ is the disk aspect ratio."
 Pg Is an indirect term which comes from the fact that the frame centered on the binary centre of mass is not inertial., $\Phi_{ind}$ is an indirect term which comes from the fact that the frame centered on the binary centre of mass is not inertial.
 This term reads: where M. is the total mass of the binary and the integral is performed over the surface area of the disk., This term reads: where $M_*$ is the total mass of the binary and the integral is performed over the surface area of the disk.
 In this work each body can experience the gravitational force due to every other one., In this work each body can experience the gravitational force due to every other one.
 In other words. we allow the planet to gravitationally interact with both the disk and the binary. while each member of the binary can interact with the other star and also with the disk and the planet.," In other words, we allow the planet to gravitationally interact with both the disk and the binary, while each member of the binary can interact with the other star and also with the disk and the planet."
" The equation of motion for the protoplanet is therefore given by: and the equation of motion for the i"" member of the binary IS: In the previous equations. fy; is the force due to the disk and is defined by: Note that 1f this force is applied to the binary the softening parameter € is set to 0. and if this force is applied to the planet we exclude the material located inside the Roche lobe of the planet Ry=a),(n,/3M:)."," The equation of motion for the protoplanet is therefore given by: and the equation of motion for the $i^{\rm th}$ member of the binary is: In the previous equations, ${\bf f}_{di}$ is the force due to the disk and is defined by: Note that if this force is applied to the binary the softening parameter $\epsilon$ is set to 0, and if this force is applied to the planet we exclude the material located inside the Roche lobe of the planet $R_H=a_p(m_p/3M_\odot)^{1/3}$."
 Previous simulations have demonstrated that 2D simulations of protoplanets embedded in disks give migration rates in good agreement with 3D results if €=0.6H (Nelson Papaloizou 2004). which is why we adopt this value for the softening.," Previous simulations have demonstrated that 2D simulations of protoplanets embedded in disks give migration rates in good agreement with 3D results if $\epsilon = 0.6H$ (Nelson Papaloizou 2004), which is why we adopt this value for the softening."
 As already mentioned. the last term νι arises because the frame centrered on the binary centre of mass is not inertial.," As already mentioned, the last term $-\nabla \Phi_{ind}$ arises because the frame centrered on the binary centre of mass is not inertial."
 The Navier-Stokes equations are solved using the hydrodynamic code GENESIS. which is basically a 2D ZEUS-like code.," The Navier-Stokes equations are solved using the hydrodynamic code GENESIS, which is basically a 2D ZEUS-like code."
 It uses a staggered mesh and solvesthe equations of motion for the disk by means of finite differences., It uses a staggered mesh and solvesthe equations of motion for the disk by means of finite differences.
often chosen for a given galaxw.,often chosen for a given galaxy.
 Iu cases where the Inspectors were evenly split. the ealaxy was assigned the more disturbed interpretation.," In cases where the inspectors were evenly split, the galaxy was assigned the more disturbed interpretation."
 For example. a galaxy flageed as an aud as by au equal uunber of inspectors would be assigned the class.," For example, a galaxy flagged as an and as by an equal number of inspectors would be assigned the class."
 These combined classifications were then used to calculate the fraction of ACN aud control galaxies with a given morphology or disturbance class., These combined classifications were then used to calculate the fraction of AGN and control galaxies with a given morphology or disturbance class.
 Further details on the CANDELS visual classification system. including low well the visual morplologics conrpare against quantitative morphology iieasures. can © found in Nartaltepe et al. (," Further details on the CANDELS visual classification system, including how well the visual morphologies compare against quantitative morphology measures, can be found in Kartaltepe et al. ("
in preparation).,in preparation).
 A xwtieulur concern for the AGN host galaxies is the »ossibilitv that unclear poiut source emission may mninic a central bulge component., A particular concern for the AGN host galaxies is the possibility that nuclear point source emission may mimic a central bulge component.
 We tested for this using xuanetrie Serie (1968) fits to the surface brightucss xofiles of the ACN hosts (van der Wel et al.," We tested for this using parametric Sersic (1968) fits to the surface brightness profiles of the AGN hosts (van der Wel et al.,"
 iu reparation)., in preparation).
 The fits were done using the GALFIT vackage (Penge et al., The fits were done using the GALFIT package (Peng et al.
 2002) aud the GALAPACGOS wrapper., 2002) and the GALAPAGOS wrapper.
 In general we fiud broad agreement between he resulting best-fit Sersic indices. s. auc the visual norphologics.," In general we find broad agreement between the resulting best-fit Sersic indices, $n$, and the visual morphologies."
 Ouly a handful of sources show sigus of oo)naf source contaunuuatiou. as evidenced bv best-fit Sersic profiles that are steeper than a de Vaucouleurs xofile (£9>E: de Vaucouleurs 1918).," Only a handful of sources show signs of point source contamination, as evidenced by best-fit Sersic profiles that are steeper than a de Vaucouleurs profile $n>4$; de Vaucouleurs 1948)."
 These sources were xedominautlv the most huuinous ACN iu our sample and were easilv identified visually as extended spheroids. despite the added nuclear emission.," These sources were predominantly the most luminous AGN in our sample and were easily identified visually as extended spheroids, despite the added nuclear emission."
 For these reasous we do not believe that point source contamination las biased or stronely affecting the visual classification of the bulk of the ACN host sample., For these reasons we do not believe that point source contamination has biased or strongly affecting the visual classification of the bulk of the AGN host sample.
 Sample WFC3 H-baud images of AGN host galaxies that exhibit a range of morphologies and disturbances are shown in Figure 3.. while the combined results of the visual analysis of the ACN hosts and control galaxies are shown in Figure | and listed in Table 1.," Sample WFC3 -band images of AGN host galaxies that exhibit a range of morphologies and disturbances are shown in Figure \ref{fig-montage}, while the combined results of the visual analysis of the AGN hosts and control galaxies are shown in Figure 4 and listed in Table 1."
 In the following sections we first present the breakdown of these ealaxies and later discuss the morphologicalfrequency of disturbances observed among then., In the following sections we first present the morphological breakdown of these galaxies and later discuss the frequency of disturbances observed among them.
 A brief note regarding nomenclature: in the following sections the term (or disks)) vefers to all ealaxies with a visible disk. oeincluding those with aud without a discernible central bulee.," A brief note regarding nomenclature: in the following sections the term (or ) refers to all galaxies with a visible disk, including those with and without a discernible central bulge."
 We will use the teri to refer to disk-like galaxies where uo bulge is discernible., We will use the term to refer to disk-like galaxies where no bulge is discernible.
 Ou the other haud. (or spherotds)) veters to spheroidal galaxies with no discernible disk component.," On the other hand, (or ) refers to spheroidal galaxies with no discernible disk component."
 At times we will use the teri to veter to both pure spleroids aud the bulge component of galaxies with a visible disk., At times we will use the term to refer to both pure spheroids and the bulge component of galaxies with a visible disk.
 Shown on the left side of Figure [| is the fraction of AGN hosts and coutrol ealaxies that were classified ax having disk. spheroid. point-like. or ireeular morplologics.," Shown on the left side of Figure 4 is the fraction of AGN hosts and control galaxies that were classified as having disk, spheroid, point-like, or irregular morphologies."
 The error bars on cach fraction reflect the πιο coufidence Bits given the nuuber of sources im cach αἱcategory. calculated usine the method of Cameron et al. (," The error bars on each fraction reflect the binomial confidence limits given the number of sources in each category, calculated using the method of Cameron et al. ("
2010).,2010).
 For the disk fraction. we show both the fraction of ACN foundin pure disks(i.c.. those with no discerniblebulge) aud the fraction hosted by any disky ealaxy (1.c.. disks with and without a discernible bulge).," For the disk fraction, we show both the fraction of AGN found in pure disks (i.e., those with no discernible bulge) and the fraction hosted by any disky galaxy (i.e., disks with and without a discernible bulge)."
 If AGN activity at 2~ is trigecred predominantly by niajor merecrs. we mieht expect au increased incidence of irregular morphologies amoug the AGN hosts.," If AGN activity at $z\sim2$ is triggered predominantly by major mergers, we might expect an increased incidence of irregular morphologies among the AGN hosts."
 Iustead. we find the nereeular fraction to be relatively low (16.7ee ) and consistent with the fraction observed amone the control sample (18.217found2200 ," Instead, we find the irregular fraction to be relatively low $16.7^{+5.3}_{-3.5}\%$ ) and consistent with the fraction observed among the control sample $18.2^{+2.9}_{-2.3}\%$ )."
This is the first indication that ACN are not in substantially disturbed galaxies more often than their non-active counterparts at this redshift., This is the first indication that AGN are not found in substantially disturbed galaxies more often than their non-active counterparts at this redshift.
 In fact. a high fraction of the AGN are found in galaxies with a visible disk. a conrponeut which is uulikelv to lave survived a major iiereor in the recent past.," In fact, a high fraction of the AGN are found in galaxies with a visible disk, a component which is unlikely to have survived a major merger in the recent past."
 We find disks to be the most conunionu single morphology assigned to the AGN hosts. making up 51.1!25% ofthe cutive saniple.," We find disks to be the most common single morphology assigned to the AGN hosts, making up $51.4^{+5.8}_{-5.9}\%$ of the entire sample."
 Two-thirds of these galaxies j) also exhibit a prominent bulec component. while of the disk galaxies show uo discernible central bulec.," Two-thirds of these galaxies ) also exhibit a prominent bulge component, while of the disk galaxies show no discernible central bulge."
 Of the remaining hosts. pure splieroids comprise 27.877 of the entire sample. while point-like sources constitute 9.7!12," Of the remaining hosts, pure spheroids comprise $27.8^{+5.8}_{-4.6}\%$ of the entire sample, while point-like sources constitute $9.7^{+4.7}_{-2.5}\%$."
 Despite the prevaleuce of disks amoug the ACN hosts. we find that the active galaxies ire more often associated with spheroid morplologics thau their nouactive ," Despite the prevalence of disks among the AGN hosts, we find that the active galaxies are more often associated with spheroid morphologies than their non-active counterparts."
"Pure spheroids make up 2T805Dsthe of theconuterparts, AGN hosts versus only 16.97 of massive control galaxies.", Pure spheroids make up $27.8^{+5.8}_{-4.6}\%$ of the AGN hosts versus only $16.9^{+2.8}_{-2.2}\%$ of the massive control galaxies.
 Disks. on the other haud. aremore conmmon among the control sample. 69.01the294 of the noi-active galaxies. but onlycomprising 51.1ο.ENZ of ACN hosts.," Disks, on the other hand, aremore common among the control sample, comprising $69.0^{+2.9}_{-3.3}\%$ of the non-active galaxies, but only $51.4^{+5.8}_{-5.9}\%$ of the AGN hosts."
 The smaller disk fraction the active galaxies compared to the coutrol galaxies is sienificaut at thelevel. assume a binomial error distribution.," The smaller disk fraction among the active galaxies compared to the control galaxies is significant at thelevel, assuming a binomial error distribution."
 The fact that the AGN tend to favor more splieroid-dominated hosts is further illustrated in Figure 5. where we show the fraction. of active aud control galaxies classified as pure clisks. disks with central bulges and pure spheroids.," The fact that the AGN tend to favor more spheroid-dominated hosts is further illustrated in Figure 5, where we show the fraction of active and control galaxies classified as pure disks, disks with central bulges and pure spheroids."
 The AGN host morphologies are skewed toward more spheroid-donunated svstenis as they show an excess of pure spheroid morphologies relative to the control sample aud a deficit of pure disk morphologics., The AGN host morphologies are skewed toward more spheroid-dominated systems as they show an excess of pure spheroid morphologies relative to the control sample and a deficit of pure disk morphologies.
 We find that bulecless. pure disks constitute 30.1a!:1 he control population while making up only 14.A ot AGN host eulaxies.," We find that bulgeless, pure disks constitute $30.1^{+3.3}_{-2.9}\%$ of the control population while making up only $16.7^{+5.3}_{-3.5}\%$ of the AGN host galaxies."
 These findines sugge that the rend observed at lower redshifts. that ACN hosts are nore spleroid-domunatecd relative to similarly massive ji0n-active galaxies (c.e.. Cuogin et al.," These findings suggests that the trend observed at lower redshifts, that AGN hosts are more spheroid-dominated relative to similarly massive non-active galaxies (e.g., Grogin et al."
 2005: Pierce ot al., 2005; Pierce et al.
" 2007). continues to some extent out tc ~2,"," 2007), continues to some extent out to $z\sim2$."
 Lastly. we have considered the triggeringpossibility that host uorphologv. and. heuce niechandsnis. Vary systematically with N-rav Iuninosityv.," Lastly, we have considered the possibility that host morphology, and hence triggering mechanisms, vary systematically with X-ray luminosity."
 To investigate this. we have examined the morphologics of active galaxies with N-ray dhunduosities above and below Lx=107 ere D.," To investigate this, we have examined the morphologies of active galaxies with X-ray luminosities above and below $L_{\rm X} = 10^{43}$ erg $^{-1}$."
 These subsunples includes 32 aud {0 AGN respectively. out of the full sample of 72 at 2~2.," These subsamples includes 32 and 40 AGN, respectively, out of the full sample of 72 at $z\sim2$."
 The morphological breakdown of these subsamples is listed in Table 1., The morphological breakdown of these subsamples is listed in Table 1.
 We find no increase in the imegular fraction none the more luninous ACN. but we do observe a dramatic reversal iu spheroid and disk fractious: spheroids constitute 10.6theAGN20d of the galaxies hostiug the more X- ]Iumiuous _. while the disk fraction drops to 311!ray: .," We find no increase in the irregular fraction among the more luminous AGN, but we do observe a dramatic reversal in the spheroid and disk fractions: spheroids constitute $40.6^{+9.0}_{-7.9}\%$ of the galaxies hosting the more X-ray luminous AGN, while the disk fraction drops to $34.4^{+9.1}_{-7.3}\%$ ."
" Thisis compared to a spheroid aud disk. fraction of 18.1!T and 68.112"" respectively."," This is compared to a spheroid and disk fraction of $18.4^{+7.9}_{-4.7}\%$ and $68.4^{+6.5}_{-8.3}\%$ , respectively,"
which ts the equation for the phase-shift method. suited for 3D migration (Yilmaz2001)..,"which is the equation for the phase-shift method, suited for $3D$ migration \citep{yilmaz}."
 The involvement of w can be eliminated from this equation. by making use of Eq. (10)).," The involvement of $\omega$ can be eliminated from this equation, by making use of Eq. \ref{kayzed}) ),"
" under the constraint that ο is constant. and &, and &,, are to be kept unchanged (Yilmaz2001).."," under the constraint that $v$ is constant, and $k_x$ and $k_y$ are to be kept unchanged \citep{yilmaz}."
 This will first deliver the relation leading ultimately to which is the equation for constant velocity 3D Stolt migration (Yilmaz2001).., This will first deliver the relation leading ultimately to which is the equation for constant velocity $3D$ Stolt migration \citep{yilmaz}.
 The derivation of the result in Eq. (22)), The derivation of the result in Eq. \ref{stolt}) )
 is certainly consistent with what has been forwarded as a mathematical definition of migration in Section 3.., is certainly consistent with what has been forwarded as a mathematical definition of migration in Section \ref{sec3}. .
 However. short of resorting to an involved numerical treatment. the full 3D problem does not lend itself very easily to deriving any pedagogical insight out of it.," However, short of resorting to an involved numerical treatment, the full $3D$ problem does not lend itself very easily to deriving any pedagogical insight out of it."
 Hence it should be instructive to consider a very special case of this migration method. for a wavefield that has a spatial dependence on the : coordinate only. and so will actually be a vertically propagating planar wavefield.," Hence it should be instructive to consider a very special case of this migration method, for a wavefield that has a spatial dependence on the $z$ coordinate only, and so will actually be a vertically propagating planar wavefield."
 For such a wavefield. with no dependence on the .c and y coordinates. and propagating in a planar front along the : axis only. one can set down the wavefield as P=P(:.f).," For such a wavefield, with no dependence on the $x$ and $y$ coordinates, and propagating in a planar front along the $z$ axis only, one can set down the wavefield as $P \equiv P(z,t)$."
 In terms of the Fourier inverse transform it can be expressed as Now it is already known that Eq. (11)), In terms of the Fourier inverse transform it can be expressed as Now it is already known that Eq. \ref{solinteg}) )
 will give an extrapolation relation going as for the special case that is being studied here., will give an extrapolation relation going as for the special case that is being studied here.
 From Eq. (10)), From Eq. \ref{kayzed}) )
 one also gets À;.=w/t. since there Is no involvement of the .c and 4 coordinates.," one also gets $k_z = \omega/v$, since there is no involvement of the $x$ and $y$ coordinates."
 Use of all these conditions in Eq. (23)).," Use of all these conditions in Eq. \ref{b1}) ),"
 will result in which. for £=0. will give But it is also known that ¢ and wv are conjugate variables for the Fourier transform.," will result in which, for $t=0$, will give But it is also known that $t$ and $\omega$ are conjugate variables for the Fourier transform."
 Their mathematical connection is givenby which can then be compared with the result given in Eq. (26))., Their mathematical connection is givenby which can then be compared with the result given in Eq. \ref{b4}) ).
 This will immediately allow for setting down, This will immediately allow for setting down
"how well an ideal 10,000 deg? survey can constrain the dark energy equation of state (EOS) with weak lensing (WL), baryon acoustic oscillations (BAOs), and type Ia supernova (SNe) luminosity distances.","how well an ideal 10,000 $^2$ survey can constrain the dark energy equation of state (EOS) with weak lensing (WL), baryon acoustic oscillations (BAOs), and type Ia supernova (SNe) luminosity distances."
" These dark energy probes have different sensitivities to the cosmic expansion and structure growth as well as various systematic uncertainties in the observations, and hence are highly complementary to each other for constraining dark energy properties (e.g.,Knoxetal.2005;Zhan2006;Zhanetal."," These dark energy probes have different sensitivities to the cosmic expansion and structure growth as well as various systematic uncertainties in the observations, and hence are highly complementary to each other for constraining dark energy properties \citep[e.g.,][]{knox05,zhan06d,zhan09}."
" The SNe technique2009).. relies on the standardizable candle of the SNe intrinsic luminosity (Phillips1993) to measure the luminosity distance, Dy(z)."," The SNe technique relies on the standardizable candle of the SNe intrinsic luminosity \citep{phillips93} to measure the luminosity distance, $D_{\rm L}(z)$."
 Dark energy properties can then be inferred from the distance-redshift relation., Dark energy properties can then be inferred from the distance--redshift relation.
" The BAO technique utilizes the standard ruler of the baryon imprint on the matter (and hence power spectrum (Peebles&Yu1970;Bond&Efstathiougalaxy) to measure the angular diameter distance, Da(z), 1984)and, if the redshifts are sufficiently accurate, the Hubble parameter, H(z) (Eisensteinetal."," The BAO technique utilizes the standard ruler of the baryon imprint on the matter (and hence galaxy) power spectrum \citep{peebles70, bond84} to measure the angular diameter distance, $D_{\rm A}(z)$, and, if the redshifts are sufficiently accurate, the Hubble parameter, $H(z)$ \citep{eisenstein98, cooray01b, blake03, hu03b, linder03, seo03}."
 The WL technique has the advantage that it can measure2003).. both Da(z) from the lensing kernel and the growth factor of the large-scale structure G(z) (Hu&Tegmark1999;etal.2006a;Zhan 2009).," The WL technique has the advantage that it can measure both $D_{\rm A}(z)$ from the lensing kernel and the growth factor of the large-scale structure $G(z)$ \citep{hu99,huterer02b,refregier03,takada04,knox06b,zhan09}."
". Because of the excellent seeing condition and infrared accessibility at Dome A, KDUST has a number of advantages for the commonly used cosmological probes."," Because of the excellent seeing condition and infrared accessibility at Dome A, KDUST has a number of advantages for the commonly used cosmological probes."
" For example, the signal-to-noise ratio for point sources is inversely proportional to the seeing."," For example, the signal-to-noise ratio for point sources is inversely proportional to the seeing."
" Thus, a 6 meter telescope at Dome A (e0"".3 median seeing in the optical) would be equivalent to a 14 meter telescope at a temperate site (~0"".7 seeing) for point-source observations with the same sky background level."," Thus, a 6 meter telescope at Dome A $\sim 0''.3$ median seeing in the optical) would be equivalent to a 14 meter telescope at a temperate site $\sim 0''.7$ seeing) for point-source observations with the same sky background level."
" An 8m KDUST could detect SNe out to redshift 3 in the Kaark (2.27-2.45um, redward of K) band (Kimetal. 2010)."," An 8m KDUST could detect SNe out to redshift 3 in the $K_{\rm dark}$ $2.27$ $2.45\mu$ m, redward of $K$ ) band \citep{kim2010}."
". Although high-z distances are not sensitive to conventional dark energy, they can be used to determine the mean curvature accurately, which, in turn, helps constrain dark energy EOS (Linder2005;Knoxetal. 2006b)."," Although high-z distances are not sensitive to conventional dark energy, they can be used to determine the mean curvature accurately, which, in turn, helps constrain dark energy EOS \citep{linder05b,knox06c}."
". Moreover, even though dark energy is thought to be sub-dominant at high redshift, there is no direct evidence to prove one way or another."," Moreover, even though dark energy is thought to be sub-dominant at high redshift, there is no direct evidence to prove one way or another."
 Measurements of SNe at z>2 will provide crucial data for tests of early dark energy., Measurements of SNe at $z > 2$ will provide crucial data for tests of early dark energy.
 Small and stable seeing is particularly helpful for WL., Small and stable seeing is particularly helpful for WL.
" One could resolve more galaxies at the same surface brightness limit, which reduces the shape noise for shear measurements."," One could resolve more galaxies at the same surface brightness limit, which reduces the shape noise for shear measurements."
 Fine resolution helps measure the shape accurately and reduce the shear measurement systematic errors., Fine resolution helps measure the shape accurately and reduce the shear measurement systematic errors.
" In addition, deep photometry can track the break of an elliptical galaxy to z~3 and improve photometric redshifts (photo-zss) as well as systematic uncertainties in the error distribution (Abdallaetal.2008),, which has a large impact on WL constraints on the dark energy EOS (Hutereretal.2006;MaZhan2006).."," In addition, deep photometry can track the break of an elliptical galaxy to $z \sim 3$ and improve photometric redshifts s) as well as systematic uncertainties in the error distribution \citep{abdalla08}, which has a large impact on WL constraints on the dark energy EOS \citep{huterer06,ma06,zhan06d}."
" Adding or Kgark band will certainly improve galaxy photo-zss, especially at z=3."," Adding or $K_{\rm dark}$ band will certainly improve galaxy s, especially at $z \gtrsim 3$."
" However, currently planned multiband dark energy surveys use galaxies at z S38, and their concern is the confusion between zS;0.5 ellipticals and 2Sz3.5 star-forming galaxies, which is greatly mitigated by u and JH bands (Abdallaetal.2008)."," However, currently planned multiband dark energy surveys use galaxies at $z \lesssim 3$ , and their concern is the confusion between $z\lesssim 0.5$ ellipticals and $2 \lesssim z \lesssim 3.5$ star-forming galaxies, which is greatly mitigated by $u$ and $JH$ bands \citep{abdalla08}."
". Another consideration is that Dome A is far more advantageous at Kgark band than at K band because of the low thermal background there, so Kgarx is likely to be chosen over K."," Another consideration is that Dome A is far more advantageous at $K_{\rm dark}$ band than at $K$ band because of the low thermal background there, so $K_{\rm dark}$ is likely to be chosen over $K$."
 This would leave a considerable gap in the wavelength coverage and reduce the already-small gain on photo-zss in the useful redshift range for dark energy investigations., This would leave a considerable gap in the wavelength coverage and reduce the already-small gain on s in the useful redshift range for dark energy investigations.
" Therefore, we do not discuss utilities of wavebands beyond H in this paper."," Therefore, we do not discuss utilities of wavebands beyond $H$ in this paper."
" Nevertheless, the Kaark band is crucial for a broad range of other sciences and will be an important aspect of the KDUST survey."," Nevertheless, the $K_{\rm dark}$ band is crucial for a broad range of other sciences and will be an important aspect of the KDUST survey."
 This paper is organized as follows., This paper is organized as follows.
 Section 2 discusses the survey plan of KDUST including that of its pathfinder in context of the LSST survey.," Section \ref{sec:survey}
 discusses the survey plan of KDUST including that of its pathfinder in context of the LSST survey."
" We then consider a joint KDUST and LSST survey in for constraining the dark energy EOS with BAO, WL, and type Ia SN techniques."," We then consider a joint KDUST and LSST survey in for constraining the dark energy EOS with BAO, WL, and type Ia SN techniques."
 The results are presented in both two-parameter space where the dark energy EOS is parameterized as w(z)=wo-4-waz(14-z)-! and in model-independent principle component space., The results are presented in both two-parameter space where the dark energy EOS is parameterized as $w(z)=w_0+w_az(1+z)^{-1}$ and in model-independent principle component space.
 T'he conclusion is drawn in4., The conclusion is drawn in.
". Dome A has a great potential for cosmology, but, given other ambitious projects that will be concurrent with KDUST, one must carefully plan the KDUST survey to make the best use of the Dome A site."," Dome A has a great potential for cosmology, but, given other ambitious projects that will be concurrent with KDUST, one must carefully plan the KDUST survey to make the best use of the Dome A site."
" As we discuss, below, a potentially efficient strategy for KDUST is to focus on the near infrared (NIR) bands and incorporate optical data from LSST or other surveys."," As we discuss, below, a potentially efficient strategy for KDUST is to focus on the near infrared (NIR) bands and incorporate optical data from LSST or other surveys."
" In the optical bands, a 6m KDUST is about twice as fast as LSST for surveying sky-dominated point sources at the same sky level, in which case the survey speed is proportional to the aperture and field of view and inversely proportional to the seeing disk area."," In the optical bands, a 6m KDUST is about twice as fast as LSST for surveying sky-dominated point sources at the same sky level, in which case the survey speed is proportional to the aperture and field of view and inversely proportional to the seeing disk area."
" In reality, aurorae increase the sky brightness in short wavelengths."," In reality, aurorae increase the sky brightness in short wavelengths."
" It is estimated that the sky brightness at Dome A would be twice as bright as that at the best temperate site in B and brighter in V (Saundersetal.2009);; measurements have shown that the median i-band sky brightness at Dome A in was 19.81 mag arcsec~? and 20.46 mag arcsec? during dark time, better than that at other good sites (Zouetal."," It is estimated that the sky brightness at Dome A would be twice as bright as that at the best temperate site in $B$ and brighter in $V$ \citep{saunders09}; measurements have shown that the median $i$ -band sky brightness at Dome A in was $19.81$ mag $^{-2}$ and $20.46$ mag $^{-2}$ during dark time, better than that at other good sites \citep{zou10}. ."
" With the above considerations, the 6m KDUST could 2010)..survey 10,000 deg? to LSST depths in griz and much deeper in y (~26 mag, 50 point sources) in 2.5 years."," With the above considerations, the 6m KDUST could survey 10,000 $^2$ to LSST depths in $griz$ and much deeper in $y$ $\sim 26$ mag, $5\sigma$ point sources) in 2.5 years."
 The NIR camera of KDUST would have a much smaller field of view., The NIR camera of KDUST would have a much smaller field of view.
 It could reach J=25 mag and H—24.6 mag over the same area in 3.5 years., It could reach $J = 25$ mag and $H = 24.6$ mag over the same area in 3.5 years.
" Since LSST plans to survey the southern sky in ugrizy, it is not absolutely necessary for KDUST to survey in the optical again except in the y band."," Since LSST plans to survey the southern sky in $ugrizy$, it is not absolutely necessary for KDUST to survey in the optical again except in the $y$ band."
" LSST would spend of its time in y band to achieve a 5-c limiting magnitude of 24.4 for point sources, which is 2.8 magnitudes shallower than itsr band limit."," LSST would spend of its time in $y$ band to achieve a $\sigma$ limiting magnitude of 24.4 for point sources, which is 2.8 magnitudes shallower than its$r$ band limit."
" From consideration, it is desirable to have the y band limit not too much shallower than thelimits in shorter wavebands."," From consideration, it is desirable to have the $y$ band limit not too much shallower than thelimits in shorter wavebands."
" KDUST could improve the situation in its 10,000 deg? survey area, which would be covered by LSST as well."," KDUST could improve the situation in its 10,000 $^2$ survey area, which would be covered by LSST as well."
 A joint effort of KDUST in yJH and LSST, A joint effort of KDUST in $yJH$ and LSST
(hese trends.,these trends.
 Given that /;+0.02 and Dz23x10.7 [or model 200-0.1. values that are [actors of ~20 and  100 times higher than in the standard shock front model (Boss 2010). respectively. 1 is clear (hat injection efficiencies and dilution factors depend sensitively on the assumed shock wave parameters. all other things being equal.," Given that $f_i \approx 0.02$ and $D \approx 3 \times 10^{-3}$ for model 200-0.1, values that are factors of $\sim 20$ and $\sim$ 100 times higher than in the standard shock front model (Boss 2010), respectively, it is clear that injection efficiencies and dilution factors depend sensitively on the assumed shock wave parameters, all other things being equal."
 We now tum to the question of whether any of the injecüon efficiencies and dilution factors shown in Table 1 are able to mateh the demands of the meteoritical record for the SLHIs. ancl in particular. whether anv such desirable shock waves might exist in reality.," We now turn to the question of whether any of the injection efficiencies and dilution factors shown in Table 1 are able to match the demands of the meteoritical record for the SLRIs, and in particular, whether any such desirable shock waves might exist in reality."
 The desired dilution [actors for a supernova trigger range from D=1.3x10! to 1.9x10.? (Takigawa οἱ al., The desired dilution factors for a supernova trigger range from $D = 1.3 \times 10^{-4}$ to $1.9 \times 10^{-3}$ (Takigawa et al.
 2008) to D=3x107 (Gaidos et al., 2008) to $D = 3 \times 10^{-3}$ (Gaidos et al.
 2009)., 2009).
 Table 1 shows that four collapse models had D values in this broad range: models 100-0.1. 200-0.1. 400-0.1. and 10-1.," Table 1 shows that four collapse models had $D$ values in this broad range: models 100-0.1, 200-0.1, 400-0.1, and 10-1."
 HLowever. (hese are not (he appropriate D values lor comparison will a supernova source. because a supernova shock launched at  1000 kin/sec must snowplow ~ 25 Umes ils own mass in order to slow down to ~ 40 km/sec (Boss et al.," However, these are not the appropriate $D$ values for comparison with a supernova source, because a supernova shock launched at $\sim$ 1000 km/sec must snowplow $\sim$ 25 times its own mass in order to slow down to $\sim$ 40 km/sec (Boss et al."
 2010)., 2010).
 The model dilution factorsin Table 1 must then be decreased by this same factor. dropping D to ~1.2x10.! for model 200-0.1 and ~4x10.+ for model 400-0.1.," The model dilution factorsin Table 1 must then be decreased by this same factor, dropping $D$ to $\sim 1.2 \times 10^{-4}$ for model 200-0.1 and $\sim 4 \times 10^{-4}$ for model 400-0.1."
 These values are close to those proposed by Takigawa οἱ al. (, These values are close to those proposed by Takigawa et al. (
2008). but about LO (times smaller than that [avored by Gaidos et al. (,"2008), but about 10 times smaller than that favored by Gaidos et al. ("
2009).,2009).
 As noted by Boss et al. (, As noted by Boss et al. (
2010). other factors ean result in higher values of D for the models. such as incomplete accretion of the target cloud (e.g.. Fieure 4. which would raise D [or model 200-0.1 by a factor of 2). preferential addition of the late arriving SLHIs to the solar nebula. rather than the protosun. aud lower target cloud densities (and consequently larger initial cloud. diameters).,"2010), other factors can result in higher values of $D$ for the models, such as incomplete accretion of the target cloud (e.g., Figure 4, which would raise $D$ for model 200-0.1 by a factor of 2), preferential addition of the late arriving SLRIs to the solar nebula, rather than the protosun, and lower target cloud densities (and consequently larger initial cloud diameters)."
 Given that all of these factors work in the direction of increasing D. the fact that both models 200-0.1 ancl 400-0.1 produce D estimates nich closer to the desired range than the standard shock models (Boss et al.," Given that all of these factors work in the direction of increasing $D$, the fact that both models 200-0.1 and 400-0.1 produce $D$ estimates much closer to the desired range than the standard shock models (Boss et al."
 2010) must be viewed as a positive outcome [or a supernova (rigger., 2010) must be viewed as a positive outcome for a supernova trigger.
" llowever. a successIul outcome demands (hat supernova shock waves in their radiative phase have properties similar to those of the shocks assumed in models 200-0.1 ancl 400-0.1. where the shock thickness was LOY em and the shock number densities were 2xLO""  and 4x109 7. respectively."," However, a successful outcome demands that supernova shock waves in their radiative phase have properties similar to those of the shocks assumed in models 200-0.1 and 400-0.1, where the shock thickness was $10^{15}$ cm and the shock number densities were $2 \times 10^6$ $^{-3}$ and $4 \times 10^6$ $^{-3}$ , respectively."
 The Cvenus Loop. the ~ 10/-vi-old remnant of a core collapse," The Cygnus Loop, the $\sim 10^4$ -yr-old remnant of a core collapse"
models listed in Table 2 it is found that the computed bolometric BL Iuminosity is larger (han the disk luminosity.,models listed in Table 2 it is found that the computed bolometric BL luminosity is larger than the disk luminosity.
 The discrepaney is even larger for the model with M-—1x10?M. /NT., The discrepancy is even larger for the model with $\dot{M} = 1 \times 10^{-9}M_{\odot}$ /yr.
" The only models for which the BL bolometric luminosity is smaller than the disk luminosity (eq.G) is for an extended BL ((6wo-ring model) with a temperature as low as 10000018. For that model the bolometric BL Iuminositv is of the disk huninosity. implying a rotational velocity (eq.G) of less than its Neplerian value or about 135km/s. With an inclination /=10°+3 and a projected rotational velocity of 200+450km /s (as derived in the low state). the (non-projected) rotational velocity should be in the range ó6rkm/s«V, «2050km/s. or 0.18«O,/O,0.54 (the lower limit is for a velocity of 150km/s and 7=127. while the upper limit is for 250km/s and ;/=7°)."," The only models for which the BL bolometric luminosity is smaller than the disk luminosity (eq.6) is for an extended BL (two-ring model) with a temperature as low as 100,000K. For that model the bolometric BL luminosity is of the disk luminosity, implying a rotational velocity (eq.6) of less than its Keplerian value or about 135km/s. With an inclination $i=10^{\circ}\pm 3^{\circ}$ and a projected rotational velocity of $200\pm 50$ km/s (as derived in the low state), the (non-projected) rotational velocity should be in the range $< V_{rot}<$ 2050km/s, or $0.18 < \Omega_*/\Omega_K < 0.54$ (the lower limit is for a velocity of 150km/s and $i=13^{\circ}$, while the upper limit is for 250km/s and $i=7^{\circ}$ )."
 This produces a BL Iuninosity in (he range 0.68>Lay/Lau20.21., This produces a BL luminosity in the range $ 0.68 > L_{BL}/L_{disk} > 0.21$.
 For the BL model to agree with the upper limit. one could reduce the BL temperature (by. 10.000Ix) or increase the mass accretion rate (bv 1/3. such a model is listed at the end of Table 2) or both.," For the BL model to agree with the upper limit, one could reduce the BL temperature (by 10,000K) or increase the mass accretion rate (by 1/3, such a model is listed at the end of Table 2) or both."
 However. one notes that the error in (he WD mass of O.LAL. (~0.2 in log g) produces a computed μι between 0.55 (lor a 0.9... WD mass) and ~1.5 (for à 0.7. WD mass).," However, one notes that the error in the WD mass of $0.1M_{\odot}$ $\sim 0.2$ in $\log{g}$ ) produces a computed $L_{BL}/L_{disk}$ between 0.55 (for a $0.9M_{\odot}$ WD mass) and $\sim$ 1.5 (for a $0.7M_{\odot}$ WD mass)."
 Since the BL model used here is rather simplistic. a perfect agreement. between the computed bolometric Iuminosity of the BL and that computed from eq.6 is not expected.," Since the BL model used here is rather simplistic, a perfect agreement between the computed bolometric luminosity of the BL and that computed from eq.6 is not expected."
" HLowever. within (he limits of the errors. the results of the DL model are consistent with a broad BL (of size ~0.2/8,) with a rather low temperature (~LOO. 000Ix or slishtlv less) aud a mass accretion rate of the order of zz2xLOM. /vr (or slightly larger)."," However, within the limits of the errors, the results of the BL model are consistent with a broad BL (of size $\sim 0.2 R_*$ ) with a rather low temperature $\sim 100,000$ K or slightly less) and a mass accretion rate of the order of $ \approx 2 \times 10^{-9} M_{\odot}$ /yr (or slightly larger)."
 These models are located the lower part of Table 2 and the fit improves (lower 42 and better distance) as the temperature of the WD increases. reaching a best fit lor Z7= 10.000Ix. Though the temperature of the WD is certainly nol that high. (his certainly points to the fact that the temperature of the WD is elevated during the high state reaching ~50. 000IX. or a little higher.," These models are located the lower part of Table 2 and the fit improves (lower $\chi^2_{\nu}$ and better distance) as the temperature of the WD increases, reaching a best fit for $T=70,000$ K. Though the temperature of the WD is certainly not that high, this certainly points to the fact that the temperature of the WD is elevated during the high state reaching $\sim 50,000$ K or a little higher."
 This work was supported by the National Aeronauties and Space Administration (NASA) under erant number NNX08ÀJ39G. issued through the Office of Astrophysics Data Analysis Program (ADP) to Villanova University., This work was supported by the National Aeronautics and Space Administration (NASA) under grant number NNX08AJ39G issued through the Office of Astrophysics Data Analysis Program (ADP) to Villanova University.
 We have used some of the online data [rom the AAVSO. and are thankful to the AAVSO and its members worldwide for making this data public aud their constant monitoring of cataclysmic variables.," We have used some of the online data from the AAVSO, and are thankful to the AAVSO and its members worldwide for making this data public and their constant monitoring of cataclysmic variables."
Conversion of de-reddened magnitudes into flux densities was done with respect to Vega.,Conversion of de-reddened magnitudes into flux densities was done with respect to Vega.
" The European Photon Imaging Camera (EPIC) onboard Newton includes three detectors: MOS1, MOS22001)., and pn2001)."," The European Photon Imaging Camera (EPIC) onboard XMM-Newton includes three detectors: MOS1, MOS2, and pn."
. All instruments were used with thin filter., All instruments were used with a thin filter.
" The two MOS cameras observed in small-windowa imaging mode, while pn was used in timing mode."," The two MOS cameras observed in small-window imaging mode, while pn was used in timing mode."
" We followed the standard prescription to reduce the data, including filtering of high background periods with a threshold of 0.35 counts s! for MOS, but with a stricter threshold of 0.1 counts s! for pn."," We followed the standard prescription to reduce the data, including filtering of high background periods with a threshold of 0.35 counts $\rm s^{-1}$ for MOS, but with a stricter threshold of 0.1 counts $\rm s^{-1}$ for pn."
" For both MOSI and MOS2, we created a filtered sky image, and extracted the source counts from a 50 arcsec radius circular region, while background was evaluated in a circle on an external CCD."," For both MOS1 and MOS2, we created a filtered sky image, and extracted the source counts from a 50 arcsec radius circular region, while background was evaluated in a circle on an external CCD."
" As for pn, we extracted the source counts from a strip between RAWX=35 and 39, and the background from two strips at columns 24—28 and 48—52."," As for pn, we extracted the source counts from a strip between RAWX=35 and 39, and the background from two strips at columns 24–28 and 48–52."
" To get the most reliable and best calibrated events, we used the FLAG==0 selection expression and kept only single and double events (PATTERN<=4)."," To get the most reliable and best calibrated events, we used the FLAG==0 selection expression and kept only single and double events $<$ =4)."
 We verified that pile-up effects were not affecting the MOS data with the task., We verified that pile-up effects were not affecting the MOS data with the task.
 Through the task of the FTOOL package we binned the source spectra to have a minimum of 25 counts in each bin and then analysed them together by means of the task of the XANADU package., Through the task of the FTOOL package we binned the source spectra to have a minimum of 25 counts in each bin and then analysed them together by means of the task of the XANADU package.
" Only spectral bins corresponding to energies between 0.3 and 10 keV for MOSI and MOS2 and in the range 0.5—10 keV for pn were considered, because they have both a better calibration and a higher signal-to-noise ratio."," Only spectral bins corresponding to energies between 0.3 and 10 keV for MOS1 and MOS2 and in the range 0.5–10 keV for pn were considered, because they have both a better calibration and a higher signal-to-noise ratio."
" The three EPIC spectra were analysed together by first fitting a single power law with free absorption, and then fixing the Galactic absorption to Ny=3.4x10?!cm."," The three EPIC spectra were analysed together by first fitting a single power law with free absorption, and then fixing the Galactic absorption to $N_{\rm H} = 3.4 \times 10^{21} \, \rm cm^{-2}$."
 We also tried a double power law with the same Galactic absorption., We also tried a double power law with the same Galactic absorption.
 The results are shown in Table 3 (see also refxmm))., The results are shown in Table \ref{fit} (see also \\ref{xmm}) ).
" In agreement with(2009), the y7/v suggests that a single power law with Galactic absorption of Ny=34xI0?!cm? does not represent a good fit to the data."," In agreement with, the $\chi^2/\nu$ suggests that a single power law with Galactic absorption of $N_{\rm H} = 3.4 \times 10^{21} \, \rm cm^{-2}$ does not represent a good fit to the data."
" As for the other two fits, the double power law seems to better fit the data, which is also confirmed by a very low F- probability of ~6.8x10716."," As for the other two fits, the double power law seems to better fit the data, which is also confirmed by a very low F-test probability of $\sim 6.8 \times 10^{-16}$."
 This implies a strong spectral curvature., This implies a strong spectral curvature.
" To check for possible flux variations, we extracted X-ray light curves from the same source and background regions defined for the spectra, with the same selection expressions."," To check for possible flux variations, we extracted X-ray light curves from the same source and background regions defined for the spectra, with the same selection expressions."
" We considered only the events in the time intervals free from high background and belonging to the 0.3-10 keV energy range for MOS1 and MOS2, and 0.5-10 keV for pn."," We considered only the events in the time intervals free from high background and belonging to the 0.3–10 keV energy range for MOS1 and MOS2, and 0.5–10 keV for pn."
 The source counts were corrected for the background and then binned in one hour intervals., The source counts were corrected for the background and then binned in one hour intervals.
" The results are shown in refom+epic,, which also displays the behaviour of the background to check the reliability of the flux variations."," The results are shown in \\ref{om+epic}, which also displays the behaviour of the background to check the reliability of the flux variations."
 The background increased significantly only in the last 6 hours., The background increased significantly only in the last 6 hours.
 Just, Just
making detailed comparisons between theory and observations. these questions must be answered before any quantitative progress. can be achieved.,"making detailed comparisons between theory and observations, these questions must be answered before any quantitative progress can be achieved."
"[ausE,|ESEus with E, and fs the total internal energies of the two merging progenitors. and fy, their orbital energv.","$E_{\rm after}=E_1+E_2+E_{\rm orb}$, with $E_1$ and $E_2$ the total internal energies of the two merging progenitors, and $E_{\rm orb}$ their orbital energy."
" Each galaxy is characterized bv its mass ancl radius. estimated assuming a A?!"" profile. with n—4 usually assumed for earlv-tvpe galaxies."," Each galaxy is characterized by its mass and radius, estimated assuming a $R^{1/n}$ profile, with $n=4$ usually assumed for early-type galaxies."
 The energy of cach galaxy is simply written as £)=KC AR. with Ad; the mass within its radius. & a constant depending on the profile. ancl {7 the half-mass radius.," The energy of each galaxy is simply written as $E_i=kGM_i^2/R_i$ , with $M_i$ the mass within its radius, $k$ a constant depending on the profile, and $R_i$ the half-mass radius."
 From the virial condition. the radius of the remnant obevs the condition with 0-—fn-2 1parameterizing5 the (uncertain) orbital energy of the progenitors (c.g..?)..," From the virial condition, the radius of the remnant obeys the condition with $0 \lesssim f_{\rm orb}\lesssim 2$ parameterizing the (uncertain) orbital energy of the progenitors \citep[e.g.,][]{Cole00}."
 One of the main drivers for the strong evolution of hulge-dominated galaxies in size and stellar mass in hierarchical models is mergers (see also discussions in. e.g. ?77)).," One of the main drivers for the strong evolution of bulge-dominated galaxies in size and stellar mass in hierarchical models is mergers (see also discussions in, e.g., \citealt{DeLucia06,DeLucia07,Parry08}) )."
 Figure 1. shows the mean number Ανεμος of wet and drv mergers per Civr a galaxy had since its formation epoch as a function of lookback time £., Figure \ref{fig|NumberMergersFromModels} shows the mean number $N_{\rm MERGERS}$ of wet and dry mergers per Gyr a galaxy had since its formation epoch as a function of lookback time $t$ .
 Each row shows the mean merger history. averaged over 100 realizations of the merger trees in the ? catalog. of galaxies with stellar mass at z—0 residing in the mass bin indicated at the top of each. panel. as labeled.," Each row shows the mean merger history, averaged over 100 realizations of the merger trees in the \citet{Bower06} catalog, of galaxies with stellar mass at $z=0$ residing in the mass bin indicated at the top of each panel, as labeled."
 In the left column we plot the mean number of minor mergers. with mass ratio <1:3. while the right column shows the mean number of major mergers with mass ratio >l1:3.," In the left column we plot the mean number of minor mergers, with mass ratio $<1:3$, while the right column shows the mean number of major mergers with mass ratio $>1:3$."
 The dotted and solid lines refer to the mean number of wet and dry mergers defined to have a cold gas-to- mass fraction in the progenitors higher and lower than 0.15. respectively.," The dotted and solid lines refer to the mean number of wet and dry mergers defined to have a cold gas-to-total mass fraction in the progenitors higher and lower than 0.15, respectively."
 On average. the number of dry. mergers erows with final stellar mass. and galaxies that end up with ALLG;101 end to undergo significantly more numerous merging events than galaxies with lower final stellar mass.," On average, the number of dry mergers grows with final stellar mass, and galaxies that end up with $> 10^{11}\, $ tend to undergo significantly more numerous merging events than galaxies with lower final stellar mass."
 We can sketch a general. trend for the evolution of massive earlv-tvpe galaxies in hierarchical mocels., We can sketch a general trend for the evolution of massive early-type galaxies in hierarchical models.
 A larec portion of earlv-tvpe. galaxies is usually formed. at. high redshifts through a wet merger of gas-rich disk. progenitors and then continued accreting stellar mass mainly through minor. drv mergers.," A large portion of early-type galaxies is usually formed at high redshifts through a wet merger of gas-rich disk progenitors and then continued accreting stellar mass mainly through minor, dry mergers."
 Therefore. the epoch of formation is eencrally identified to be at high-z. when the first starburst event took place and the central potential well was settled.," Therefore, the epoch of formation is generally identified to be at $z$, when the first starburst event took place and the central potential well was settled."
 We also find that a significant fraction of massive bulges is also formed through instability of eas-rich disk. galaxies., We also find that a significant fraction of massive bulges is also formed through instability of gas-rich disk galaxies.
 Even in this case the initial size of the newly formed bulge is set by virial equilibrium and energy. conservation. adopting a condition very similar to Eq.," Even in this case the initial size of the newly formed bulge is set by virial equilibrium and energy conservation, adopting a condition very similar to Eq."
 1. (see ?7 for details).," \ref{eq|virialcondition}
 (see \citealt{Cole00} for details)."
 lrrespective of their exact formation process. most. of the massive spheroids in the model kept on accreting mass and increasing their sizes through dry merecers. largely extending the epoch of stellar mass assembly.," Irrespective of their exact formation process, most of the massive spheroids in the model kept on accreting mass and increasing their sizes through dry mergers, largely extending the epoch of stellar mass assembly."
 The 2? model predicts that all massive earlv-tvpe galaxies. on average. undergo ~3T minor mergers and 1 major cry mergers since their formation epoch (i.c.. identified as the epoch of the major wet merece among the eas-rich disk. progenitors).," The \citet{Bower06} model predicts that all massive early-type galaxies, on average, undergo $\sim 3-7$ minor mergers and $\lesssim 1$ major dry mergers since their formation epoch (i.e., identified as the epoch of the major wet merger among the gas-rich disk progenitors)."
 These late evolutionary features are a general trend for most hierarchical models., These late evolutionary features are a general trend for most hierarchical models.
 For example. we have checked that the 7. model (see also ?2)) predicts a similar pattern for the erowth of earlv-tvpe galaxies. first. characterized by a wet. formation phase pealked at high-redshifts. and a subsequent evolution domünated by a series of minor. dry mergers.," For example, we have checked that the \citet{DeLucia06} model (see also \citealt{GuoWhite08}) ) predicts a similar pattern for the growth of early-type galaxies, first characterized by a wet, formation phase peaked at high-redshifts, and a subsequent evolution dominated by a series of minor, dry mergers."
 The latter model similarly also predicts a rate of mergers increasing with increasing final stellar mass., The latter model similarly also predicts a rate of mergers increasing with increasing final stellar mass.
 The grev lines in the upper and lower panels of Figure 2 garow how the sizes and. masses. respectively. change for a hundred merger histories drawn from the ? catalog. so that the final stellar mass at >=0 will fall within the mass bin labeled at the top of cach panel.," The grey lines in the upper and lower panels of Figure \ref{fig|RezModels} show how the sizes and masses, respectively, change for a hundred merger histories drawn from the \citet{Bower06} catalog, so that the final stellar mass at $z=0$ will fall within the mass bin labeled at the top of each panel."
 In each case the trees are followed back in time. choosing the most massive early-tvpe progenitor. until this is no longer possible.," In each case the trees are followed back in time, choosing the most massive early-type progenitor, until this is no longer possible."
 We have checked that our randomly selected bulge-dominated galaxies in the model have mainlv grown in mass through mergers. with disk instabilities increasing the spheroid masses by only 10A. decreasing to =2% for the most massive galaxies.," We have checked that our randomly selected bulge-dominated galaxies in the model have mainly grown in mass through mergers, with disk instabilities increasing the spheroid masses by only $\lesssim 10\%$, decreasing to $\lesssim 2\%$ for the most massive galaxies."
 This is clearly visible from the lower panels of Figure 2.. where most of the stellar mass accretion histories remain almost [at most of the time and have sudden: jumps in correspondence of merging events.," This is clearly visible from the lower panels of Figure \ref{fig|RezModels}, where most of the stellar mass accretion histories remain almost flat most of the time and have sudden jumps in correspondence of merging events."
 Figure 2. shows that only a small fraction of low mass objects (with. i104 M.) were earlv-tvpes LO Civrs ago. but their mass has changed little since. they first xcame carly types (550%5 ).," Figure \ref{fig|RezModels} shows that only a small fraction of low mass objects (with $\, < 10^{11}\,$ ) were early-types 10 Gyrs ago, but their mass has changed little since they first became early types $\lesssim 50$ )."
 The sizes of this population of galaxies. however. have grown by at least a factor of hree over this time. as expected if their evolution is driven »v minor mergers.," The sizes of this population of galaxies, however, have grown by at least a factor of three over this time, as expected if their evolution is driven by minor mergers."
 In contrast. a larger fraction of massive ealaxies had formed LO Civrs ago: however. whereas the mass of the population has grown by about a factor of three since hen (with most of the growth occurring at lookback times ereater than about 6 Gives). the sizes have grown by a smaller actor (~ 2).," In contrast, a larger fraction of massive galaxies had formed 10 Gyrs ago; however, whereas the mass of the population has grown by about a factor of three since then (with most of the growth occurring at lookback times greater than about 6 Gyrs), the sizes have grown by a smaller factor $\sim 2$ )."
 Indeed. the models predict that a substantia raction of massive galaxies (with z0 AL.) have not changed in size for a long time.," Indeed, the models predict that a substantial fraction of massive galaxies (with $\, \gtrsim 10^{11}\,$ ) have not changed in size for a long time."
 More specifically. in he highest mass bin considered. we find that about of he galaxies have elliciently increased their sizes by a factor ereater than 3. a significant fraction of remains instead. extremely compact (although stil &rowing in mass). and the rest undergoes a milder evolution with a size increase contained within a factor <3.," More specifically, in the highest mass bin considered, we find that about of the galaxies have efficiently increased their sizes by a factor greater than 3, a significant fraction of remains instead extremely compact (although still growing in mass), and the rest undergoes a milder evolution with a size increase contained within a factor $< 3$."
 We have verified that while most (ον 60%) of the mass growth is adde via major mergers. most (~ 90%) of the size growth. where this actually happens. is via mergers.," We have verified that while most $\sim 60\%$ ) of the mass growth is added via major mergers, most $\sim 90\%$ ) of the size growth, where this actually happens, is via mergers."
 As extensively discussed in 3.3... the survival of a non-negligible fraction of compact and. massive galaxies until the present epoch is at variance with the SDSS distribution of early-type galaxies (with. BYP z 0.5). and we will discuss possible causes and improvements to this problem in 3.4.3.," As extensively discussed in \ref{subsec|comparingwiththeERFandSMF}, the survival of a non-negligible fraction of compact and massive galaxies until the present epoch is at variance with the SDSS distribution of early-type galaxies (with B/T $\gtrsim 0.5$ ), and we will discuss possible causes and improvements to this problem in \ref{subsec|progenitors}."
 However. we will also show that when restricting the analysis to spheroid-dominated systems (with D/ZTz 0.7). the predicted number density of cllipticals with size 1 kpe is with the data.," However, we will also show that when restricting the analysis to spheroid-dominated systems (with $>0.7$ ), the predicted number density of ellipticals with size $\sim 1$ kpc is with the data."
 In this section wecompare the data on the size and mass distributions of SDSS carly-type galaxies. with the predictions of SAAIs., In this section wecompare the data on the size and mass distributions of SDSS early-type galaxies with the predictions of SAMs.
 As partly explained above. it is bevond the scope of the current paper to buildan ab initio complete hierarchical model able to predict the sizes. stellar masses," As partly explained above, it is beyond the scope of the current paper to buildan ab initio complete hierarchical model able to predict the sizes, stellar masses"
The number density and the correlation strength of pixels abovebelow a temperature threshold v can be generically expressed by where Nyistet ds the total number of pixels. and. P and D» are defined in equations (17)) and (18)).,"The number density and the correlation strength of pixels above/below a temperature threshold $\nu$ can be generically expressed by where $N_{\rm pix, tot}$ is the total number of pixels, and $P_1$ and $P_2$ are defined in equations \ref{P1}) ) and \ref{P2}) )."
 By inserting the corresponding one- and. two-dimensional PDEs in those equations. and by using their output in (B1)) and (B2)). one can readily characterize the pixel number density and the clustering statistics above/below threshold in the Cully Gaussian case or the weak non-Gaussian limit (equations 12- 249).," By inserting the corresponding one- and two-dimensional PDFs in those equations, and by using their output in \ref{nd_gen}) ) and \ref{corr_gen}) ), one can readily characterize the pixel number density and the clustering statistics above/below threshold in the fully Gaussian case or the weak non-Gaussian limit (equations \ref{nd_gauss_eq}- \ref{corr_smart_gauss}) )."
 The analytic expressions derived in the main text apply to full-sky intrinsic CAIB signal: the cllect of noise is not included., The analytic expressions derived in the main text apply to full-sky intrinsic CMB signal; the effect of noise is not included.
 Llowever. with the formalism introduced by Rossi et al. (," However, with the formalism introduced by Rossi et al. ("
2009) we can also describe analytically the excursion set clustering in the weak non-Gaussian limit. in. presence of inhomogeneous noise.,"2009) we can also describe analytically the excursion set clustering in the weak non-Gaussian limit, in presence of inhomogeneous noise."
 Maintaining the same notation. we indicate the observed. value in a pixel bv D=T n. which is the sum of the true signal s plus noise n. both of which have mean zero.," Maintaining the same notation, we indicate the observed value in a pixel by $D = T - \langle T \rangle
\equiv \delta T = s + n$ , which is the sum of the true signal $s$ plus noise $n$, both of which have mean zero."
 We consider a mocel in which the signal is homogeneous ancl may have spatial correlations whereas the noise. independent. of the signal. may be inhomogeneous anc have spatial correlations.," We consider a model in which the signal is homogeneous and may have spatial correlations whereas the noise, independent of the signal, may be inhomogeneous and have spatial correlations."
" We denote p(D) the observed one-point distribution of D. p(s) the distribution of s with rms ex. play) the distribution of the rms value of the noise in a pixel. and. p(n|e,) the distribution of the noise when the rms value of the noise is αν "," We denote $p(D)$ the observed one-point distribution of $D$, $p(s)$ the distribution of $s$ with rms $\sigma_{\rm S}$, $p(\sigma_{\rm n})$ the distribution of the rms value of the noise in a pixel, and $p(n|\sigma_{\rm n})$ the distribution of the noise when the rms value of the noise is $\sigma_{\rm n}$."
Lhe one-point observed. distribution is where dp is the Dirac delta., The one-point observed distribution is where $\delta_{\rm D}$ is the Dirac delta.
 Phe fraction of pixels above some temperature threshold D is Similarly. for two pixels separated. by the angular distance 8. or having correlation w—w(8) the two-point observed. distributionis specified by: where Since poo=οἱσ—ασ where gr ds the variable used. in the main text to indicate the threshold level. then.p(s)dsprodi and p(s;.5Luycdsypelss= ," The fraction of pixels above some temperature threshold $D_{\rm t}$ is Similarly, for two pixels separated by the angular distance $\theta$, or having correlation $w \equiv w(\theta)$, the two-point observed distribution is specified by: where Since $\mu=\delta T/ \sigma \equiv s/\sigma_{\rm S}$, where $\mu$ is the variable used in the main text to indicate the threshold level, then$p(s) {\rm d}s \equiv p(\mu) {\rm d} \mu$ and $p(s_1,
s_2, w) {\rm d}s_1 {\rm d} s_2 \equiv p(\mu_1, \mu_2, w) {\rm d} \mu_1 {\rm d} \mu_2$ ."
Therefore we can use m PDFs (15)) andnon-Gaussian (21)) to characterize (B3)). (D4)) and (D5)) ) in the weak limit. when inhomogeneous noise is present.," Therefore we can use the PDFs \ref{one_d_pdf_fnl}) ) and \ref{2d_edge_eq}) ) to characterize \ref{pD}) ), \ref{fDt}) ) and \ref{pD1D2}) ) in the weak non-Gaussian limit, when inhomogeneous noise is present."
 Once (D3)). (B4)) and. (DB5)) are known. then the pixel number density and the clustering abovefbelow threshold can be inferred from (DI1)) and CD2)). where now andThe corresponding. Gaussian TM case has been presented in detail in ltossi ct al. ," Once \ref{pD}) ), \ref{fDt}) ) and \ref{pD1D2}) ) are known, then the pixel number density and the clustering above/below threshold can be inferred from \ref{nd_gen}) ) and \ref{corr_gen}) ), where now andThe corresponding Gaussian limiting case has been presented in detail in Rossi et al. ("
m.,2009).
 In. particular. if pass.) isD bivariatequ Gaussian|. . 581)2=(ss)ai. 5185)(0) as delined in equation (26)). and the noise pinoy) is Gaussian with variable rms e. then = (03|o1)Tp.Qo=(03 |o3)op.andCu(8) | where Cis the covariance matrix of the temperature field. a the variance of D. CP the power spectrum of the noise map. and Mpm the additional smoothing due to finite pixel size. optional Gaussianbeam smoothing and mask inlluence.," In particular, if $p(s_1,s_2,w)$ is bivariate Gaussian with $\langle s_1^2\rangle = \langle s_2^2\rangle = \sigma_{\rm S}^2$, $\langle s_1s_2\rangle = C_{\rm S}(\theta)$ as defined in equation \ref{cs}) ), and the noise $p(n|\sigma_{\rm n})$ is Gaussian with variable rms $\sigma_{\rm n}$, then with $\alpha_1 = (\sigma_{\rm S}^2 + \sigma_1^2)/\sigma_{\rm D}^2$, $\alpha_2 = (\sigma_{\rm S}^2 + \sigma_2^2)/\sigma_{\rm D}^2$, and where $C$ is the covariance matrix of the temperature field, $\sigma_{\rm D}^2$ the variance of D, $C_{\rm \ell}^{\rm N}$ the power spectrum of the noise map, and $W^{\rm smooth}_{\rm \ell}$ the additional smoothing due to finite pixel size, optional Gaussianbeam smoothing and mask influence."
 Note in fact that in presence of incomplete sky coverage one needs to add an extra window function in (26)) and in 3113). according to the geometry of the survey. to account for extra-correlations introduced by the mask.," Note in fact that in presence of incomplete sky coverage one needs to add an extra window function in \ref{cs}) ) and in \ref{ctheta_noise}) ), according to the geometry of the survey, to account for extra-correlations introduced by the mask."
 Lf the noise is spatially uncorrelated. then clearly Cx(4)=0 and therefore woCB) op.," If the noise is spatially uncorrelated, then clearly $C_{\rm
 N}(\theta) = 0$ and therefore $w \equiv C_{\rm S}(\theta)/\sigma_{\rm D}^2$ ."
" In the approximation where m,= c». rms noise varies spatially on scales much larger than those of interest. then ay= o»."," In the approximation where $\sigma_1=\sigma_2$ , rms noise varies spatially on scales much larger than those of interest, then $\alpha_1=\alpha_2$ ."
" The ""standard"" approximation. rms noise independent of position. has à,=à» 1."," The “standard” approximation, rms noise independent of position, has $\alpha_1=\alpha_2=1$ ."
We produced an optical surface brightness profile based on elliptical isophote fitting using the projection on the sky as determined by our rotation curve fit (Sect. 4.2)).,We produced an optical surface brightness profile based on elliptical isophote fitting using the projection on the sky as determined by our rotation curve fit (Sect. \ref{Rotation curve analysis}) ).
 Obvious foreground stars were removed and replaced by 2—D interpolation using pixel values of an annulus surrounding the affected area., Obvious foreground stars were removed and replaced by 2--D interpolation using pixel values of an annulus surrounding the affected area.
 A 2-D second order spline was fit to remove the background., A 2–D second order spline was fit to remove the background.
" Although the background fit produced a remarkably good result, we could see some slight systematic offset due to the bright foreground star towards the south-east corner of the field, potentially affecting the area due South of the galaxy."," Although the background fit produced a remarkably good result, we could see some slight systematic offset due to the bright foreground star towards the south–east corner of the field, potentially affecting the area due South of the galaxy."
" We therefore restricted the radial profile, using only the northern half of 7765, employing rradial bins."," We therefore restricted the radial profile, using only the northern half of 765, employing radial bins."
 The resulting profile is shown in Fig. 4.., The resulting profile is shown in Fig. \ref{profile}.
 The INT data were not calibrated so we bootstrapped our radial profile to the one published by ?.., The INT data were not calibrated so we bootstrapped our radial profile to the one published by \citet{dej94}.
" Where our profiles overlap, agreement is excellent."," Where our profiles overlap, agreement is excellent."
" Our data go deeper by almost 2 magnitudes in R, down to aarcsec""?, allowing us to follow the faint stellar disk out to about kkpc in radius."," Our data go deeper by almost 2 magnitudes in $R$, down to $^{-2}$, allowing us to follow the faint stellar disk out to about kpc in radius."
" We derive a scale length for the stellar disc between 5 and 25kkpc of 7.8kkpc in good agreement with ? who found values of 8.4kkpc and kkpc in B and Ks, respectively."," We derive a scale length for the stellar disc between 5 and kpc of kpc in good agreement with \citet{dej94} who found values of kpc and kpc in $B$ and $K_\mathrm{S}$ , respectively."
" The extrapolated central surface brightness at R-band is aarcsec? which, assuming a B—R=1.40 (taken then agrees with their B-band value of ug(0)= 22.27."," The extrapolated central surface brightness at $R$ –band is $^{-2}$ which, assuming a $B-R = 1.40 $ \citep[taken from][]{dej94} then agrees with their $B$ –band value of $\mu_{\mathrm B}(0) = 22.27$ ."
" Between 30kkpc and 38kkpc the profile shows a secondary maximum, beyond which, it declines again at the same rate."," Between kpc and kpc the profile shows a secondary maximum, beyond which, it declines again at the same rate."
" This feature can be traced to a faint, broad stellar arm, i.e., this is not an artefact or due to a problem with background subtraction."," This feature can be traced to a faint, broad stellar arm, i.e., this is not an artefact or due to a problem with background subtraction."
" ? present 0.5 arcsec resolution X-ray observations of a small sample of Malinll-type galaxies, including 7765."," \citet{das09} present 0.5 arcsec resolution X–ray observations of a small sample of 1–type galaxies, including 765."
" As they only refer to emission coming from its centre, we decided to retrieve the observations from the archive (project ID 7764) and independently reduce and analyse them."," As they only refer to emission coming from its centre, we decided to retrieve the observations from the archive (project ID 7764) and independently reduce and analyse them."
" The data were obtained with the ACIS-S instrument (AXAF CCD Imaging Spectrometer) on 2007 July 11, for a totalexposure time of 3.79 ks."," The data were obtained with the ACIS–S instrument (AXAF CCD Imaging Spectrometer) on 2007 July 11, for a totalexposure time of 3.79 ks."
 Data reduction of the observations was performed using, Data reduction of the observations was performed using
 (277?7).. (22777?).. (2777)..," \citep{1996ApJ...462..563N,1998ApJ...499L...5M,2004MNRAS.353..624D,2006AJ....132.2685M,2006AJ....132.2701G}, \citep{2004ApJ...604..116B,2005A&A...435....1P,2005A&A...441..893A,2006ApJ...640..691V,2006A&A...446..429P}, \citep{2004ApJ...604...88S,2005ApJ...619L.143B,2006ApJ...642...39C,2008arXiv0802.4292L}."
 σᾷ 62 (€2).. (2??)..," $\sigma^2_t$ $\sigma^2_r$ \citep{1987gady.book.....B}. \citep{1997ApJ...485L..13C,1996MNRAS.281..716C,2006NewA...11..333H}."
 ο) test of whether dark matter is in fact collisionless. as assuned in the standard model of structure formation.," $\beta$ test of whether dark matter is in fact collisionless, as assumed in the standard model of structure formation."
 On this note. it has heen shown that the Galactic velocity anisotropy can affect the detection rates of direct dark matter searches (2).. and it is in principle iieasurable im a cdirectiou-seusitive detector (?)..," On this note, it has been shown that the Galactic velocity anisotropy can affect the detection rates of direct dark matter searches \citep{2008PhRvD..77b3509V}, and it is in principle measurable in a direction-sensitive detector \citep{2007JCAP...06..016H}."
 The most massive bound structures m the Universe are clusters of galaxies. which consist of an extended dark matter halo. an X-rav ciuitting plasma mating up the intracluster iiedium (ICAL). aud the iudividual ealaxies.," The most massive bound structures in the Universe are clusters of galaxies, which consist of an extended dark matter halo, an X-ray emitting plasma making up the intracluster medium (ICM), and the individual galaxies."
 While the contribution of galaxies to the total mass is small. approximately 10 4 of the cluster mass resides iu the ICAL," While the contribution of galaxies to the total mass is small, approximately 10 $\%$ of the cluster mass resides in the ICM."
" The preseut generation of X-rav satellites, audChandra. allows very accurate measurements of agiuuthall-averaged radial profiles of density aud temperature of the ICAL"," The present generation of X-ray satellites, and, allows very accurate measurements of azimuthally-averaged radial profiles of density and temperature of the ICM."
 These are used. uuder the assuuptiou of hwdrostatie equilibrium and spherical svuuuetry of both eas and total mass distributions. to estimate total. eas. aud dark matter mass profiles (?)..," These are used, under the assumption of hydrostatic equilibrium and spherical symmetry of both gas and total mass distributions, to estimate total, gas, and dark matter mass profiles \citep{1980ApJ...241..552F}."
 Below we infer the radial velocity anisotropy profile of dark matter in 16 ealaxy clusters using a ecnerally applicable framework without any parametrized uodeling of the clusters., Below we infer the radial velocity anisotropy profile of dark matter in 16 galaxy clusters using a generally applicable framework without any parametrized modeling of the clusters.
 Iu short. we assume a universal relation between the effective temperature of dark matter and the ICAL temperature. which allows us to solve he ciwnamics of the dark matter halo using the radial eas temperature aud density profiles deteriuüued frou N-rav data.," In short, we assume a universal relation between the effective temperature of dark matter and the ICM temperature, which allows us to solve the dynamics of the dark matter halo using the radial gas temperature and density profiles determined from X-ray data."
 We investigate the shape aud validity of this eniperature relation in two cosmological simulations of ealaxy clusters. based on independent nuunucrical codes.," We investigate the shape and validity of this temperature relation in two cosmological simulations of galaxy clusters, based on independent numerical codes."
 We apply our method to 16 ealaxy clusters frou wo different samples aud find a velocity anisotropy sienificautly different from zero in the outer parts. in qualitative agreement with simulations.," We apply our method to 16 galaxy clusters from two different samples and find a velocity anisotropy significantly different from zero in the outer parts, in qualitative agreement with simulations."
 Our approach here is a generalization of the non- analysis iu?) where σας interred ucelectingthe radial dependence., Our approach here is a generalization of the non-parametric analysis in \citet{2007A&A...476L..37H} where $\beta$was inferred neglectingthe radial dependence.
 We also note the parametrized, We also note the parametrized
the sample.,the sample.
 For the clusters NGC 2244. NGC 2264. and NGC 6611 such a study has alreacky been carried out. by Oeura & Ishida (1981). Sagar & Joshi (1983) ancl Sagar & Joshi (1979) respectively.," For the clusters NGC 2244, NGC 2264, and NGC 6611 such a study has already been carried out by Ogura $\&$ Ishida (1981), Sagar $\&$ Joshi (1983) and Sagar $\&$ Joshi (1979) respectively."
 Phe spatial variation of οV) could. not be studied in Coll 228 as the cluster members occupy a small area on the sky while in NGC 1502. Ir 15 and “Pr 37. statistically insignificant number (see Table 1) of cluster members denied such a study.," The spatial variation of $E(B-V)$ could not be studied in Coll 228 as the cluster members occupy a small area on the sky while in NGC 1502, Tr 15 and Tr 37, statistically insignificant number (see Table 1) of cluster members denied such a study."
 Except for Tr 14. there is no systematic correlation of colour excess with position implying that gas and dust responsible for variable extinction may be distributed randomly within the cluster.," Except for Tr 14, there is no systematic correlation of colour excess with position implying that gas and dust responsible for variable extinction may be distributed randomly within the cluster."
 Similar behaviour has also been found. by Sagar (1987) in voung clusters NGC 654. NGC 2264. NGC 6823. NGC 6913. IC 1805. NGC 6530 and NGC 6611.," Similar behaviour has also been found by Sagar (1987) in young clusters NGC 654, NGC 2264, NGC 6823, NGC 6913, IC 1805, NGC 6530 and NGC 6611."
 In Ir 14. kipY) appears to vary svstematicallv with position (see Table 3).," In Tr 14, $E(B-V)$ appears to vary systematically with position (see Table 3)."
 The reddening increases [from east to west in the southern part of the cluster., The reddening increases from east to west in the southern part of the cluster.
 The clusters NGC 663. NGC 869. NGC SSA. NGC 1893. Tr 15 ane Be 86 do not show any positional variation of E(D-V).," The clusters NGC 663, NGC 869, NGC 884, NGC 1893, Tr 15 and Be 86 do not show any positional variation of E(B-V)."
 In order to stucly the variation of colour excess with uminosity. we have plotted colour excess (13)V) against absolute magnitude Ady for the clusters under study in Fig.," In order to study the variation of colour excess with luminosity, we have plotted colour excess $E(B-V)$ against absolute magnitude $M_{V}$ for the clusters under study in Fig."
 4. except for NGC 2244. NGC 2264 and NGC 6611 since for hem such plots are provided by Sagar (1987).," 4, except for NGC 2244, NGC 2264 and NGC 6611 since for them such plots are provided by Sagar (1987)."
" In order to convert apparent V values into My: we use the relation 4A, = 3.25E(DVJ) and distances given in Fable 1.", In order to convert apparent V values into $M_{V}$ we use the relation $A_{v}$ = $E(B-V)$ and distances given in Table 1.
 We also plot in he figure the variation of mean (5V) and its standard deviation with Aly., We also plot in the figure the variation of mean $E(B-V)$ and its standard deviation with $M_{V}$.
 For estimating these values we grouped cluster members in such a way that five or more stars are resent in a group., For estimating these values we grouped cluster members in such a way that five or more stars are present in a group.
 An inspection of Fig., An inspection of Fig.
 4 indicates that:, 4 indicates that:
the rms of the differences were calculated for each coordinate.,the rms of the differences were calculated for each coordinate.
 Under the assumption that both frames contribute with equa weight to the differences. we have calculated from the rms the mean uncertainty of one position on one frame.," Under the assumption that both frames contribute with equal weight to the differences, we have calculated from the rms the mean uncertainty of one position on one frame."
 These are given in Table 4. for several CCD pairs with nearly identical limiting magnitudes., These are given in Table \ref{t_ccdacc} for several CCD pairs with nearly identical limiting magnitudes.
 In this comparison we included all stars which were detected on the CCD frames., In this comparison we included all stars which were detected on the CCD frames.
 In a second test we consider only the stars which contribute to the final catalogue of our investigation., In a second test we consider only the stars which contribute to the final catalogue of our investigation.
 These are stars at the brighter end of the magnitude distribution., These are stars at the brighter end of the magnitude distribution.
 Reducing the plates with one catalogue (ACT or Hipparcos) leads to positions of the stars of each plate/CCD frame in a common system., Reducing the plates with one catalogue (ACT or Hipparcos) leads to positions of the stars of each plate/CCD frame in a common system.
 The position and proper motion of each star in our final solution described in Sect., The position and proper motion of each star in our final solution described in Sect.
 2 are determined by a fit to the positions and epochs of the different plates/CCD frames for each star., 2 are determined by a fit to the positions and epochs of the different plates/CCD frames for each star.
 The mean position and proper motion of each star is then used to update the positions of each star for the epoch of the individual plates/CCD frames., The mean position and proper motion of each star is then used to update the positions of each star for the epoch of the individual plates/CCD frames.
 For each plate the mean and rms of the positional differences from the initial positions are determined., For each plate the mean and rms of the positional differences from the initial positions are determined.
 The rms will give an indication of the accuracy of each individual plate/CCD frame., The rms will give an indication of the accuracy of each individual plate/CCD frame.
 Table 5 summarizes for the Hoher List frames the mean and standard deviations for each frame., Table \ref{t_posdiff} summarizes for the Hoher List frames the mean and standard deviations for each frame.
 Table 5 shows a slight difference in the B and V frames of the order of a few mas., Table \ref{t_posdiff} shows a slight difference in the $B$ and $V$ frames of the order of a few mas.
 Nevertheless the systematic deviations between the B and V frames are small., Nevertheless the systematic deviations between the $B$ and $V$ frames are small.
 The positional accuracy of each star is of the order of one tenth of a pixel., The positional accuracy of each star is of the order of one tenth of a pixel.
 This value is a little bit larger with respect to other studies (e.g. Geffert 1998)., This value is a little bit larger with respect to other studies (e.g. Geffert 1998).
 The reason may be the crowding in the region of M10., The reason may be the crowding in the region of M10.
 In general. the accuracy of one single frame is of the order of the accuracy of one refractor plate. which justfies the use of CCD frames for the second epoch observation.," In general, the accuracy of one single frame is of the order of the accuracy of one refractor plate, which justfies the use of CCD frames for the second epoch observation."
 Figure | gives the vector-point-plot diagram of all our proper motions indicating the concentration of the cluster stars., Figure \ref{f_vppdia} gives the vector-point-plot diagram of all our proper motions indicating the concentration of the cluster stars.
 For the separation of cluster and field stars we have concentrated our investigation on stars up to the limiting radius of 14 (Webbink 1988) around the cluster centre., For the separation of cluster and field stars we have concentrated our investigation on stars up to the limiting radius of $\arcmin$ (Webbink 1988) around the cluster centre.
 284 stars remained in the data sample., 284 stars remained in the data sample.
 For these stars a bivariate Gaussian fitting to the proper motions was performed using the method of Sanders (1971)., For these stars a bivariate Gaussian fitting to the proper motions was performed using the method of Sanders (1971).
 Table 6 gives the result of the analysis., Table \ref{t_fitpar} gives the result of the analysis.
 The cluster standard deviations are larger than the internal errors of the proper motion., The cluster standard deviations are larger than the internal errors of the proper motion.
 This difference is clearly not an indication of a possible detection of internal motions of stars in the cluster., This difference is clearly not an indication of a possible detection of internal motions of stars in the cluster.
crucial difference to the scenario ofheterogeneous uncleationt!.. where inhomoge ο temperature distribi tion.Bubble nuc cation effectively takes,"cold spot propagates in all directions, which provides the length scale If the typical distance from the boundary of a cold spot to the boundary of a neighboring cold spot is less than $l_{\rm heat}$, then no hadronic bubbles can nucleate in the intervening space."
" placewhie the temperature drops w thetiny anuout Anne.To determine the mechuusm ofnucleation. weος mupare Anne witjithe ruisteniperature fluctuatio LAR:Tllin,"," In this case the nucleation process is totally dominated by the cold spots, and the average distance between their centers gives the spatial scale for the resulting inhomogeneities."
 l. Tf APY< Aine.theprobabili vto uncleate abubble ata giventime is ho," In the following analysis for a more realistic scenario we concentrate in this case, $l_{\rm heat} > l_{\rm smooth}$."
mogeneous ispace. Thisisthecase of homogencot snucleatiol. 2.Tf A>Anne. the probabili vto uncleate a," The real Universe consists of smooth patches of typical linear size $l_{\rm smooth}$, their temperatures given by the distribution \ref{pd}) )."
 bubble atagiven timeis iidiomogcneonsii space. We call thisinhomogeneous mic," As discussed above, the merging of tiny bubbles within a cold spot can here be treated as an instantaneous process."
leation. The quenched lattice QCD dat: vand a CODE normalized fi atspectrum leacto the values Aqu 10 9a idAP Tillis10 5. We con," The fraction of space that is not reheated by the released latent heat (and not transformed to hadron phase), is given at time $t$ by where we neglect overlap and merging of heat fronts."
clude that the CORSI nologicalOCD transition may]sroceed Via inhomoecucous The temperature chanee ata eiven point is governed by the," At time $t$ heat, coming from a cold spot which wastransformed into hadron phase at time $t'$, occupies the volume $V(t,t') = (4\pi/3) [l_{\rm smooth}/2 + v_{\rm heat}(t-t')]^3$."
 Ihn bble expansion alc the c»fiuctuatioC»is.For the," The other factor in Eq. \ref{fihn}) ), $\Gamma_{\rm ihn}$,"
 fastestOo changing⋅ fluctuations. with by ⋜⋯∶↴∙⊾∏↕⋜∐⋅↕⋟↥⋅↸∖≺∣⋯∖∐↸⊳⋅↖↽↙⋅⋅∖⋅∣∖⋯⋅⋯⊤↨↓∙↖↖↽↸∖↴∎∐≼↧temperature aT(t.," is the volume fraction converted into the new phase, per physical time and volume as a function of the mean temperature $T=\bar{T}(t)$."
" x) T fu) lt  c""E ο Arot 09 (The Hull e expansionis the dominant coitribution. exceptToby "," $\Gamma_{\rm ihn}$ is proportional to the fraction of space for which temperature is in the interval $[T_{\rm f}, T_f(1 + d\Delta)]$ ."
exin insieltiuthe plavsics divingof , This fraction of space is given by Eq. \ref{pd}) )
iwhomogencouserowth. some, with $\Delta = T_{\rm f}/T - 1$.
 We have distributed uucleatio1. s, Rewriting ${\rm d}\Delta$ by means of Eq. \ref{Tteq}) )
"pheresletusfirstof luspectametera La,sim dlifiedWithcase. equal aud witormsomeraudoun.teiiperavyture. coldbythe amount ΔΑ. rh again uniforii1 "," leads to the expression where the relevant physical volume is ${\cal V}_{\rm smooth} = 
(4\pi/3) (l_{\rm smooth}/2)^3.$ The end of the nucleation period, $t_{\rm ihn}$, is defined through the condition $f(t_{\rm ihn}) = 0$."
teiiperati in thewhichrestisof Universe. When sunalley thanthe the re Tr. homogeucoustje place uperaturein them.coldDueto spotsthehasIIub de roppede," We introduce the variables $N \equiv (1 - T_{\rm f}/T)/\Delta_T^{\rm rms}$ and ${\cal N} \equiv N(t_{\rm ihn})$ .Since $c_s$ may be assumed to be constant during the tiny temperature interval where nucleations actually take place, we find from Eq. \ref{Tteq}) ):"
xpansionto tle restof c," $1 - t/t_{\rm ihn} \approx 2/(3c_s^2) 
\Delta_T^{\rm rms} (N - {\cal N})$ ."
onditionshould (detofparameters.ονThusThis the coldspots, Putting everything together we determine ${\cal N}$ fromThe expression /2}$ is valid for the COBE normalized spectrum.
 havefully been transformediutothe hadron phasewhilethe vestoftheUniverse," For $l_{\rm heat}/l_{\rm smooth} = 1, 2, 5, 10$ wefind ${\cal N} \approx 0.8, 1.4, 2.1, 2.6$ , respectively."
Plummer-like model. with v3=Ry. and with a physical basis for the normalization of ihe density profile.,"Plummer-like model, with $\sqrt{8} H = R_0$, and with a physical basis for the normalization of the density profile."
 A evlindrical model can therefore reproduce the observational properties of pre-stellar cores Chat provided the motivation for the Plummer-like models., A cylindrical model can therefore reproduce the observational properties of pre-stellar cores that provided the motivation for the Plummer-like models.
 In addition. because the isothermal cvlinder aud (he D-E sphere both represent equilibria between and gas pressure. the spherically averaged density. profile of an isothermal cvlinder can also mimic closely that of a B-E sphere. in particular a [lal inner region wilh a steeply falline envelope (Boss Hartmann 2001).," In addition, because the isothermal cylinder and the B-E sphere both represent equilibria between self-gravity and gas pressure, the spherically averaged density profile of an isothermal cylinder can also mimic closely that of a B-E sphere, in particular a flat inner region with a steeply falling envelope (Boss Hartmann 2001)."
 The evindrical model also provides a basis for interpreting the departures from spherical sviumetry in the LGQ42 core (larvey et 2003b)., The cylindrical model also provides a basis for interpreting the departures from spherical symmetry in the L694–2 core (Harvey et 2003b).
" A slightly tilted. embedded evlinder with seale height //=13.5""41.5"" reproduces (he extinction prolile for the inner 83” (0.1 pe) of the core."," A slightly tilted, embedded cylinder with scale height $H=13.5''\pm 1.5''$ reproduces the extinction profile for the inner $83''$ (0.1 pc) of the core."
 In the present study we consider isothermal evlinders viewed along the axis. since the subtle effect of a small till angle can not be constrained with the visibility dataset.," In the present study we consider isothermal cylinders viewed along the axis, since the subtle effect of a small tilt angle can not be constrained with the visibility dataset."
 Both PIhummer-like and Isothermal Cylinder models ean successfully describe the extinction observations. if the cores are embedded: in an extended. distribution of gas.," Both Plummer-like and Isothermal Cylinder models can successfully describe the near-IR extinction observations, if the cores are embedded in an extended distribution of gas."
 This additional component to the density structure is suggested by (the shape of the radial extinction profile. and must be accounted Lor in (he fitting of these types of model.," This additional component to the density structure is suggested by the shape of the radial extinction profile, and must be accounted for in the fitting of these types of model."
 We include the extended cloud structure in the visibility analvsis as follows., We include the extended cloud structure in the visibility analysis as follows.
 The extended structure is asstuned (o be smooth and is therefore resolved out by the interferometers., The extended structure is assumed to be smooth and is therefore resolved out by the interferometers.
 The only effect of the additional structure is (o reduce the total flux that is attributable to the core in (his context., The only effect of the additional structure is to reduce the total flux that is attributable to the core in this context.
" The extinction prolile of the L6942 core asvmptotes to a color-excess that is approximately 0.2 magnitudes higher than the background. and about a tenth (1/10) of the color excess at 30"" radius (the edge of the flux normalization aperture)."," The extinction profile of the L694–2 core asymptotes to a color-excess that is approximately 0.2 magnitudes higher than the background, and about a tenth $1/10$ ) of the color excess at $30''$ radius (the edge of the flux normalization aperture)."
" We approximate the intensity profile to be flat within 30"" of the core. and assume that the temperature of the extended eas is equal to that in the core. so that the extended structure accounts for of the flux normalization for each of these tvpes of mocel."," We approximate the intensity profile to be flat within $30''$ of the core, and assume that the temperature of the extended gas is equal to that in the core, so that the extended structure accounts for of the flux normalization for each of these types of model."
 A detailed study. of the expected dust temperature distribution in starless cores has been performed by Evans et ((2001)., A detailed study of the expected dust temperature distribution in starless cores has been performed by Evans et (2001).
 Thev caleulate the temperature distribution. T;(7). sell-consistentlv. using a 1D radiative transport code. ancl assuming Ossenkopf Ilenning (1994) opacities lor grains that have grown by coagulation aud accretion of thin ice mantles.," They calculate the temperature distribution, $T_d(r)$, self-consistently using a 1D radiative transport code, and assuming Ossenkopf Henning (1994) opacities for grains that have grown by coagulation and accretion of thin ice mantles."
donor has a chance to reestablish thermal equilibrium.,donor has a chance to reestablish thermal equilibrium.
 The donor star max continue to lose mass. but as il comes into equilibrium with a smaller mass than its initial mass. and with a core (hat is still modest (less (han roughly 0.25M. ). it begins to shrink into its Roche lobe.," The donor star may continue to lose mass, but as it comes into equilibrium with a smaller mass than its initial mass, and with a core that is still modest (less than roughly $0.25\, M_\odot$ ), it begins to shrink into its Roche lobe."
 This leads to a quiescent interval., This leads to a quiescent interval.
" AM, is the mass of the donor during this Gime of quiescence.", $M_\ast$ is the mass of the donor during this time of quiescence.
" The mass of the accretor is approximately equal to M, as well. allhough the accretor may be slightly more massive than the donor at this point."," The mass of the accretor is approximately equal to $M_\ast$ as well, although the accretor may be slightly more massive than the donor at this point."
" Thus. during phase 1. the donor has lost an amount of mass M4(0)—M,. and the accretor has gained. M,—35(2). Generally. AL,—Afe(2)<M4(0)M,. since the (thermal (me scales of the two stars ave different."," Thus, during phase 1, the donor has lost an amount of mass $M_1(0)-M_{\ast},$ and the accretor has gained $M_{\ast}-M_2(2).$ Generally, $M_{\ast}-M_2(2) < M_1(0)-M_{\ast},$ since the thermal time scales of the two stars are different."
 The continued growth of the core of the first star. ancl the accompanying stellar expansion. perhaps combined with magnetic braking. eventually cause the donor to fill its Roche lobe again.," The continued growth of the core of the first star, and the accompanying stellar expansion, perhaps combined with magnetic braking, eventually cause the donor to fill its Roche lobe again."
 Mass transler during the second phase of mass transfer is stable and ends when the donors envelope is depleted., Mass transfer during the second phase of mass transfer is stable and ends when the donor's envelope is depleted.
 Depending on the time elapsed since the start of phase 1. the donors core will generally have grown by an amount 9. The first question to answer for KOI-81 and INOI-74 is whether each could be an end state of stable mass transfer.," Depending on the time elapsed since the start of phase 1, the donor's core will generally have grown by an amount $\delta.$ The first question to answer for KOI-81 and KOI-74 is whether each could be an end state of stable mass transfer."
 If the answer is “ves”. the donor star would have been filling ils Roche lobe until the time mass transfer ceased. ancl (he orbital period is: Given a measured value of the orbital period. Equation (1) aud Equation (3) combine to produce a set of possible values for AL. and A... The value of AL. should correspond to the present-cday mass of the core observed today. and it can be measured (through radial velocity or other methods (R2010. van Nerkwijk et 2010 |vIN2010]).," If the answer is “yes”, the donor star would have been filling its Roche lobe until the time mass transfer ceased, and the orbital period is: Given a measured value of the orbital period, Equation (1) and Equation (3) combine to produce a set of possible values for $M_\ast.$ and $M_c.$ The value of $M_c$ should correspond to the present-day mass of the core observed today, and it can be measured through radial velocity or other methods (R2010, van Kerkwijk et 2010 [vK2010])."
" The value of M, represents {he mass of the primary. generally as it was during the quiescent interval between phase 1 and phase 2."," The value of $M_\ast$ represents the mass of the primary, generally as it was during the quiescent interval between phase 1 and phase 2."
 The black points in the top (wo panels of Figure 1 show the results for KOLS81 and KOL74., The black points in the top two panels of Figure 1 show the results for KOI-81 and KOI-74.
 The mass of IXOI-31b is constrained to lie in a very narrow range: 0.215—0.219M... (Note however that (he svstematic uncertainty associated with using the Iunctional forms in Equation (1) is larger than this formal range indicates.)," The mass of KOI-81b is constrained to lie in a very narrow range: $0.215-0.219\, M_\odot.$ (Note however that the systematic uncertainty associated with using the functional forms in Equation (1) is larger than this formal range indicates.)"
" The mass M, ranges from roughly 1.6M. and 2.4M... R2019 interpreted light curve features in terms of tidal effects aud found ihe mass of IKOlI-31b to be 0.21240.031AZ... This is consistent with our mass (transler model."," The mass $M_\ast$ ranges from roughly $1.6\, M_\odot$ and $2.4\, M_\odot.$ R2019 interpreted light curve features in terms of tidal effects and found the mass of KOI-81b to be $0.212\pm0.031\, M_\odot.$ This is consistent with our mass transfer model."
 The R2010 value is shown as a evan triangle centered on a evan line which delineates the uncertainty limits., The R2010 value is shown as a cyan triangle centered on a cyan line which delineates the uncertainty limits.
 vAZOLO used Doppler boosting. ancl measured the mass to be 0.3AL.. ," vK2010 used Doppler boosting, and measured the mass to be $0.3\, M_\odot.$ "
Examination of the eleven final images revealed that only (wo sources were detected and neither was a target galaxy.,	Examination of the eleven final images revealed that only two sources were detected – and neither was a target galaxy.
 Both were identified as lower-redshift galaxies in the fields of view of the higher-redshift galaxies., Both were identified as lower-redshift galaxies in the fields of view of the higher-redshift galaxies.
 The first of these detections was in the ACCUAL mode exposure targeted al SSA22-16. ancl appears to be SSA 22-10 at z = 0.132. located 4.5 areseconds east (left in our image) of SSA 22-16.," The first of these detections was in the ACCUM mode exposure targeted at SSA22-16, and appears to be SSA 22-10 at z = 0.132, located 4.5 arcseconds east (left in our image) of SSA 22-16."
 Figure 1 compares a WFPC2 visible image of SSA 22-16 and SSA 22-10 (right) with our STIS ultraviolet exposure of the same field (left)., Figure 1 compares a WFPC2 visible image of SSA 22-16 and SSA 22-10 (right) with our STIS ultraviolet exposure of the same field (left).
 The images have a common plate scale (the arrows are 4.5 arcseconds long) ancl are both oriented with north at top., The images have a common plate scale (the arrows are 4.5 arcseconds long) and are both oriented with north at top.
 The lower redshilt galaxy SSA 22-10 is visible in the UV but our targeted galaxy SSA 22-16 isn, The lower redshift galaxy SSA 22-10 is visible in the UV but our targeted galaxy SSA 22-16 is.
"ol, After subtraction of à sky value of 0.1241 counts !. the image of SSA 22-10 contained 720 counts within an aperture of radius of 65 pixels."," After subtraction of a sky value of 0.1241 counts $^{-1}$, the image of SSA 22-10 contained 720 counts within an aperture of radius of 65 pixels."
 This corresponds to a flux level of 5 x ' eres 7 sec! Abat ~ 1650.4., This corresponds to a flux level of 5 x $^{-18}$ ergs $^{-2}$ $^{-1}$ $\AA$$^{-1}$ at $\sim$ $\AA$.
 This is about ten times brighter than its [απ measured fIux of 5.4 x P. making SSA 22-10 a bluish galaxy with Fy ~ Ate," This is about ten times brighter than its I-band measured flux of 5.4 x $^{-19}$ , making SSA 22-10 a bluish galaxy with $_{\lambda}$ $\sim$ $\lambda$$^{-1.4}$."
 A second source was detected in the image targeted at ILDE-IW4-1002.1353., 	A second source was detected in the image targeted at HDF-IW4-1002.1353.
 The source appeared in the lower left corner of the frame. and is believed to be the optically faint. \-raa- source J123627.2 4-621308. and is located 0.3. arcseconds east ancl 12.8 arcseconds north of the target.," The source appeared in the lower left corner of the frame, and is believed to be the optically faint, X-ray source J123627.2 +621308, and is located 0.3 arcseconds east and 12.8 arcseconds north of the target."
 The net counts from this object were determined to be 293 at a radius of 50 pixels and a sky value of 0.15., The net counts from this object were determined to be 293 at a radius of 50 pixels and a sky value of 0.15.
 This corresponds to 3 x P eres 7 t Af. or about 30 times its -Lhand flux of 9.," This corresponds to 3 x $^{-18}$ ergs $^{-2}$ $^{-1}$ $\AA$$^{-1}$, or about 30 times its I-band flux of $^{-19}$."
" This suggests an inverse wavelength squared dependence in Fy. or a flat spectrum in E,. probably from a quasar."," This suggests an inverse wavelength squared dependence in $_{\lambda}$, or a flat spectrum in $_{\nu}$, probably from a quasar."
 We compared (he radial growth of the number of counts in (the two detected sources with each other and with WEPC? images we had on hand of our targeted intermeciate-recdshilt ealaxies., We compared the radial growth of the number of counts in the two detected sources with each other and with WFPC2 images we had on hand of our targeted intermediate-redshift galaxies.
 We used (hese observed profiles to estimate how the FUY light from our target ealaxies should have been distributed spatially to better estimate our upper limits., We used these observed profiles to estimate how the FUV light from our target galaxies should have been distributed spatially to better estimate our upper limits.
 The two sources had quite similar curves of growth. with half of the counts contained wilhin a radius ol ~ 20 pixels.," The two sources had quite similar curves of growth, with half of the counts contained within a radius of $\sim$ 20 pixels."
 Not unexpectedly. the light is less concentrated in (he centers of our detected sources (han it is in the WEDPC? images of our targeted intermecdiate-redshilt galaxies.," Not unexpectedly, the light is less concentrated in the centers of our detected sources than it is in the WFPC2 images of our targeted intermediate-redshift galaxies."
 No Lyman continuum light was detected [rom any of our eleven targeted sources. setting new [lux upper limits on thepotential contributions to the UV. background. from normal," No Lyman continuum light was detected from any of our eleven targeted sources, setting new flux upper limits on thepotential contributions to the UV background from normal"
New observations often. provide a [resh perspective on (he Universe. (hus providing a new window through which to view ancient problems.,"New observations often provide a fresh perspective on the Universe, thus providing a new window through which to view ancient problems."
 Such is (he case lor a new survey by Disney οἱ al! in which they provide a catalog of galaxies that were detected during a large blind survey of the skv in the 21-em line of neutral hydrogen., Such is the case for a new survey by Disney et $^{1}$ in which they provide a catalog of galaxies that were detected during a large blind survey of the sky in the 21-cm line of neutral hydrogen.
 For each of the ~200 objects in their catalog the authors measured the total hycrogen mass. the width of the line. the redshift and inclination to the line of sight. two radii and the optical Iuminosity in four different color bands.," For each of the $\sim$ 200 objects in their catalog the authors measured the total hydrogen mass, the width of the 21-cm line, the redshift and inclination to the line of sight, two radii and the optical luminosity in four different color bands."
 The III-selected galaxies appear to have colors made up of two components: a rogue color. which probably correlates wilh recent star forming history. and a svstemaltic component related to the mean age of the stellar population in that e&alaxy. (," The HI-selected galaxies appear to have colors made up of two components; a `rogue' color, which probably correlates with recent star forming history, and a systematic component related to the mean age of the stellar population in that galaxy. ["
Both rogue color and. the Hubble morphological types of galaxies are strongly correlated with environment].,Both rogue color and the Hubble morphological types of galaxies are strongly correlated with environment].
 Since the nature of a galaxy's color is complex Disney et al., Since the nature of a galaxy's color is complex Disney et al.
 initially neglect it and concentrate on (he other [actors that describe the galaxies in their sample., initially neglect it and concentrate on the other factors that describe the galaxies in their sample.
 From a principal component analvsis of their data they. [find that the six components that they use to describe the galaxies in (heir sample (including the systematic color) are all correlated. with each other and with a single principal component (mass)., From a principal component analysis of their data they find that the six components that they use to describe the galaxies in their sample (including the systematic color) are all correlated with each other and with a single principal component (mass).
" In other words ealaxies appear (o constitute a single ""Fundamental Line’ in parameter space.", In other words galaxies appear to constitute a single `Fundamental Line' in parameter space.
 Disney et al., Disney et al.
 argue that such simplicity is difficult to understand within the framework of (he hierarchical ealaxy merging paradigm., argue that such simplicity is difficult to understand within the framework of the hierarchical galaxy merging paradigm.
 This is so because it is expected that the evolution of individual ealaxies will depend on (1) their initial spins (2) on a the details of their chaotic merger history and (3) on the density. temperature and turbulence of the environment in which a galaxy is assembled.," This is so because it is expected that the evolution of individual galaxies will depend on (1) their initial spins (2) on a the details of their chaotic merger history and (3) on the density, temperature and turbulence of the environment in which a galaxy is assembled."
nearby erand-desien spiral galaxy. with a Sevlert 2 nucleus.,nearby grand-design spiral galaxy with a Seyfert 2 nucleus.
 The proximity of (his galaxy. as well as its nearly [ace-on orientation has made it the target of numerous large scale multi- studies (Scoville&Young1983:Seovilleetal.2001:Schuster2007).," The proximity of this galaxy as well as its nearly face-on orientation has made it the target of numerous large scale multi-wavelength studies \citep{Scoville83,Scoville01,Schuster07}."
. Its interaction with the companion galaxy 55195 seems (o have been the origin of a past period of intense star formation (Thronsonetal.1991:Greenawalt1998)..," Its interaction with the companion galaxy 5195 seems to have been the origin of a past period of intense star formation \citep{Thronson91,Greenawalt98}.,"
.7409. the only example of Sevífert 1 nucleus in our sample. also shows a circummnuclear star-orming ring of3” in diameter (Wilsonetal.1991).," the only example of Seyfert 1 nucleus in our sample, also shows a circumnuclear star-forming ring of $3''$ in diameter \citep{Wilson91}."
".220 is one of the best studied nearby ULIBGs (Dopitaetal.2005) Nn more than a 95% of its luminosity radiated at IR/submiim wavelengths (Sandersοἱue-."")3).", is one of the best studied nearby ULIRGs \citep{Dopita05} with more than a $\%$ of its luminosity radiated at IR/submm wavelengths \citep{Sanders03}.
". AU a distance of D~77 MMpe (z= 0.018) ancl star formation rates of M. vvyr olten referred as a nearby template of the Iuminous star-lorming galaxies al high-z. 2220 is the result of an advanced merger svstem with two nuclei separated by ~1"" »“ as seen [rom near-IR ancl radio images (Baan&IIaschick1995:Scovilleοἱal.)0) with an enormous concentration of molecular gas within its central region (a[few10?1999"," At a distance of $\sim77$ Mpc $z=0.018$ ) and star formation rates of $\,M_\odot$ $^{-1}$, 220 is often referred as a nearby template of the luminous star-forming galaxies at high-z. 220 is the result of an advanced merger system with two nuclei separated by $\sim1''$ $\sim300$ pc) as seen from near-IR and radio images \citep{Baan95,Scov00}
 with an enormous concentration of molecular gas within its central region \citep[a few $10^{9}."
"), We reler to shows2421s as a “normal galaxy as being the closest spiral galaxies resembling our own Galaxy.", We refer to is as a “normal” galaxy as being the closest spiral galaxies resembling our own Galaxy.
 It a ninispiral structure meeting at (he inner e ns surrounding the central stellar cluster (Ishizukietal.1990:Boker1997:Helfer2003).," It shows a minispiral structure meeting at the inner molecular ring surrounding the central stellar cluster \citep{Ishizuki90,Boker97,Helfer03}."
". Chemical differences have been observed between (he gas in the nuclear region. MN by the intense star formation throughthe radiation from the central cluster. aud "" molecular PM in (he spiral structure. mainiv affected by shocks (Meier&Turner2005:Useroetal.2006)."," Chemical differences have been observed between the gas in the nuclear region, affected by the intense star formation throughthe radiation from the central cluster, and the molecular material in the spiral structure, mainly affected by shocks \citep{Meier05,Usero06}."
". In (his work we have observed (wo positions. one at (he central region M the other al i. ollset position (4-5"". +15""). herealter located just in one of the arms of the minispiral."," In this work we have observed two positions, one at the central region and the other at the offset position $(+5'',+15'')$ , hereafter, located just in one of the arms of the minispiral."
 We have derived the abundancesof CS. CS. and HNCO relative to II».," We have derived the abundancesof CS, $^{34}$ S, and HNCO relative to $_2$ ."
 In order, In order
sources in the First Look Survey studied by Appletoneal.(200 1).,sources in the First Look Survey studied by \citet{Appleton04}.
". However. when we examine the qo», for SBS0335-052E. adopting a MIPS 2112 flux of 66uunJy. we fud a qo ratio of 32.201."," However, when we examine the $_{24}$ for SBS0335-052E, adopting a MIPS $\mu$ m flux of mJy, we find a $_{24}$ ratio of $\pm$ 0.1."
" We sce a 26 excess in the q parameter compared with the mean qo, of 1.340. iu the chwart siuuple.", We see a $\sigma$ excess in the q parameter compared with the mean $_{24}$ of $\pm$ 0.4 in the dwarf sample.
 If this excess is real. it would be cousisteutl with the unique shape of the SED of the ealaxy. which suggests that the dust eraiu distribution is dominated by sal erains with temperatures of —150I& and a total dust muss of ~107? AL. (loudetal.20015).," If this excess is real, it would be consistent with the unique shape of the SED of the galaxy, which suggests that the dust grain distribution is dominated by small grains with temperatures of $\sim$ 150K and a total dust mass of $\sim10^3$ $_{\odot}$ \citep{Houck04b}."
 Whether the laree erains were never created or they were destrovec by shocks is unknown., Whether the large grains were never created or they were destroyed by shocks is unknown.
" The elevated qo, ratio could also be due to the lack of svuchrotron cussion.", The elevated $_{24}$ ratio could also be due to the lack of synchrotron emission.
 Rousseetal.(2003.2006) have shown their «παν of three starburst salaxies. all of which lave qgig more than 30 lieher the mean gry and categorized them to be nascent starbursts.," \citet{Roussel03,Roussel06} have shown their study of three starburst galaxies, all of which have $_{\rm FIR}$ more than $\sigma$ higher the mean $_{\rm FIR}$ and categorized them to be nascent starbursts."
 SBS0335-052E though. could also be a candidate of this group.," SBS0335-052E though, could also be a candidate of this group."
" It is based partly on the high (qo, value. as well as its low ITo Iumninositv as compared to the imfrared or radio luminosities (see Table 3))."," It is based partly on the high $_{24}$ value, as well as its low $\alpha$ luminosity as compared to the infrared or radio luminosities (see Table \ref{tab3}) )."
 Finally. IIuutetal.(2001). have shown the existence of free- absorption in the radio spectrum of SBS0335-052E. which is usually caused by vounus. dense and heavily embeddedclusters.," Finally, \citet{Hunt04} have shown the existence of free-free absorption in the radio spectrum of SBS0335-052E, which is usually caused by young, dense and heavily embedded."
 [Zwls.ρα despite its similar metallicity to SDS0335-052E (12|los(O/II)27.17 and 7.32 respectively). shows a rather differeut q ratio.," IZw18, despite its similar metallicity to SBS0335-052E (12+log(O/H)=7.17 and 7.32 respectively), shows a rather different q ratio."
 It also has an IB. TJuuinosity of Lin~ lL... just of the Lig in SBS0335-052E. In low huninosity galaxies. radio enission is kuown to decrease faster than dust cuussion (Devereux&Eales1989). and hieh IR/radio ratios have been observed in low huninosity dwart galaxies (IXleiuctal.L98L).," It also has an IR luminosity of $_{\rm
 IR}$$\sim$ $^7$ $_\odot$, just of the $_{\rm IR}$ in SBS0335-052E. In low luminosity galaxies, radio emission is known to decrease faster than dust emission \citep{Devereux89}, and high IR/radio ratios have been observed in low luminosity dwarf galaxies \citep{Klein84}."
. In IZxvl8 though. we fud a rather low iufrared to radio ratio.," In IZw18 though, we find a rather low infrared to radio ratio."
 The qo; is found to be 0.50.1. nearly 26 lower than the average value of our sample.," The $_{24}$ is found to be $\pm$ 0.1, nearly $\sigma$ lower than the average value of our sample."
 At longer waveleusthlis. IZwils is faint and noJRAS FIR data are available.," At longer wavelengths, IZw18 is faint and no FIR data are available."
 ILlowever. as noted by Wuetal.(2007a) κος their Fig.," However, as noted by \citet{Wu07a} (see their Fig."
 5). it has a very similar 38yan continu slope o the typical starburst galaxy NGCT?TLI (Brandlctal.2001).," 5), it has a very similar $\mu$ m continuum slope to the typical starburst galaxy NGC7714 \citep{Brandl04}."
". If we were to asstune that this sinularitv extends ο the FIR and scale down theJRAS 60 aud 424 flux densities of NCCTTLL by a factor of 375 so that its corresponding 22,448 flux density matches the one of Zwls. we fine itsJRAS 60 aud jm Hux density to be 29.8 aud nuuJy respectively,"," If we were to assume that this similarity extends to the FIR and scale down the 60 and $\mu$ m flux densities of NGC7714 by a factor of 375 so that its corresponding $\mu$ m flux density matches the one of IZw18, we find its 60 and $\mu$ m flux density to be 29.8 and mJy respectively."
 This would result iu qgi of 1.3 for the galaxy. which deviates roni the average «μια ratio of 2.540.2 calibrated by Condon(1992) by nearly 5o.," This would result in $_{\rm FIR}$ of 1.3 for the galaxy, which deviates from the average $_{\rm FIR}$ ratio of $\pm$ 0.2 calibrated by \citet{Condon92} by nearly $\sigma$."
 If we were to use the MIPS TOyan detection of παν for Zwls (Eugelbrachtal.2007) aud calculate its q ratio. we would fud qzo— 1.1. again So away from the average qry suggested by Appletonetal.(2001).," If we were to use the MIPS $\mu$ m detection of mJy for IZw18 \citep{Engelbracht07} and calculate its q ratio, we would find $_{70}$ =1.4, again $\sigma$ away from the average $_{70}$ suggested by \citet{Appleton04}."
 A qnmunber of plausible scenarios were cousidercd to explain this result. though noue appears convincing.," A number of plausible scenarios were considered to explain this result, though none appears convincing."
 As discussed in Wuetal.(2007a).. because the optical deptl of IZwls is iuall. it could be that a significant fraction of the UV light has leaked out without being absorbed by the dust. thus resulting in a damped 2142 cussion.," As discussed in \citet{Wu07a}, because the optical depth of IZw18 is small, it could be that a significant fraction of the UV light has leaked out without being absorbed by the dust, thus resulting in a damped $\mu$ m emission."
" Alternatively. [IZwls may simply have an uuusually hieh radio luminosity at αν,"," Alternatively, IZw18 may simply have an unusually high radio luminosity at GHz."
 Could it be that [Zwls is observed at a special niomieut right after the explosion of a supernovae event?, Could it be that IZw18 is observed at a special moment right after the explosion of a supernovae event?
 Radio supernovae fade by more than a factor of LO within ~3yvr (Chevalier1982)., Radio supernovae fade by more than a factor of 10 within $\sim$ yr \citep{Chevalier82}.
. The radio continu observations of [Zwls span over a period of more than Swvrs (untetal.2005):Ciunonu but show no variation. thus this is not likely.," The radio continuum observations of IZw18 span over a period of more than yrs \citep{Hunt05b,Cannon05} but show no variation, thus this is not likely."
 The recent results by Murpliyetal.(2006b) provide another possible scenario., The recent results by \citet{Murphy06b} provide another possible scenario.
 These authors analyzed a siuuple of nearby spiral galaxies aud found that svstenis with hieher disk-averaged SFRs (Xugg) have usually experienced a recent episode of cuhanced star formation.," These authors analyzed a sample of nearby spiral galaxies and found that systems with higher disk-averaged SFRs $\Sigma\,_{\rm
 SFR}$ ) have usually experienced a recent episode of enhanced star formation."
 Asaresult they contain a higher faction of vouneg cosmic rav electrons that have traveled only a few Lhuudred parsecs frou. their acceleration sites i supernova relmnauts., As a result they contain a higher fraction of young cosmic ray electrons that have traveled only a few hundred parsecs from their acceleration sites in supernova remnants.
 This is perhaps the case for Zwls., This is perhaps the case for IZw18.
 However. other sources in our sample also have elevated “srr and show no radio excess.," However, other sources in our sample also have elevated $\Sigma\,_{\rm SFR}$ and show no radio excess."
 It could also be that the extremely low metal abunudauce of IEZwls. daex lower than that of SDS0335-052E. is below a critical threshold.," It could also be that the extremely low metal abundance of IZw18, dex lower than that of SBS0335-052E, is below a critical threshold."
 The newly formed stars in the uupolluted interstellar media may produce. aud subsequently heat. less dust than electrons which are accelerated aud coutribute 1 the radio enussion.," The newly formed stars in the unpolluted interstellar medium may produce, and subsequently heat, less dust than electrons which are accelerated and contribute in the radio emission."
 We also note that the rate of SNR i1 IZwls is a factor of ~30 lower than that in SBS0335-052E (see Table 3)) but its morphology is niuchli mere disturbed with filamentary structure and outflows (seeIzotov&Thuan 2001)., We also note that the rate of SNR in IZw18 is a factor of $\sim$ 30 lower than that in SBS0335-052E (see Table \ref{tab3}) ) but its morphology is much more disturbed with filamentary structure and outflows \citep[see][]{Izotov04}.
 If we were to asstuue that both sources lave similar mass-to-lieht ratios aud estimate their mass rou their IK-baud Iuniuosities. we fud that the mass of IZwls is almost a factor of SO less than that of SBS0335-," If we were to assume that both sources have similar mass-to-light ratios and estimate their mass from their K-band luminosities, we find that the mass of IZw18 is almost a factor of 80 less than that of SBS0335-052E."
 Thus the rate of SNR normalized with mass in IZwls would be ~2.5 times that of SBS0335-052E. Could it be that the disturbed morphology of IZwls iu addition ο its low metal content that it created the couditious iu he interstellar muiediuu for this abuormally high radio Hux’?, Thus the rate of SNR normalized with mass in IZw18 would be $\sim$ 2.5 times that of SBS0335-052E. Could it be that the disturbed morphology of IZw18 in addition to its low metal content that it created the conditions in the interstellar medium for this abnormally high radio flux?
 The question remains open., The question remains open.
spin. accretion rate. radiative efficiency. and viewing angle.,"spin, accretion rate, radiative efficiency, and viewing angle."
 There is still much work aliead belore we completely understand. how basic plwsical parameters regulate (he activity. of supermassive black hole svstems., There is still much work ahead before we completely understand how basic physical parameters regulate the activity of supermassive black hole systems.
 Models that tie jet production to accretion onto a spinning black hole are particularly promising (e.g..Meier1999:Hawley&τομ2006).," Models that tie jet production to accretion onto a spinning black hole are particularly promising \citep[e.g.,][]{m99,hk06}."
. Aluch progress has been made in understxding (he aspect-dependent appearance of AGN disks and jets. as a consequence of relativistic beaming and obscuration 1995)... OurS," Much progress has been made in understanding the aspect-dependent appearance of AGN disks and jets, as a consequence of relativistic beaming and obscuration \citep{up95}."
pizer observations confir (hat many FR. IE radio galaxies would appear as powerful quasars if viewed [rom an unobscured direction (e.g. along the radio axis)., Our observations confirm that many FR II radio galaxies would appear as powerful quasars if viewed from an unobscured direction (e.g. along the radio axis).
 However. just as many FR ID radio galaxies would not.," However, just as many FR II radio galaxies would not."
 OurSpitzer observations also demonstrate that powerful radio jets may be produced even by mid-IR weak AGN., Our observations also demonstrate that powerful radio jets may be produced even by mid-IR weak AGN.
 A powerful. luminous accretion disk is not always necessary {ο produce a highly collimated. relativistic jet. (," A powerful, luminous accretion disk is not always necessary to produce a highly collimated, relativistic jet. ("
1.),1.)
" We report on a largeSpizer spectroscopic survey of 38CRR EH. II radio sources wilh Sir,>16.4 Jv at 2<I.", We report on a large spectroscopic survey of 3CRR FR II radio sources with $S_{178}>16.4$ Jy at $z<1$.
 We find strong mid-IR emission from 45412% (14/31) of NLRGs. which have huminosiües comparable to matched. DLIGs ancl quasars.," We find strong mid-IR emission from $45 \pm 12\%$ (14/31) of NLRGs, which have luminosities comparable to matched BLRGs and quasars."
 Other indicators including high-ionization mic-IR lines and highlv polarized broad emission lines confirm that some of these sources contain hidden quasar or BLRG nmiclei;, Other indicators including high-ionization mid-IR lines and highly polarized broad emission lines confirm that some of these sources contain hidden quasar or BLRG nuclei.
 This demonstrates the power ofSpitzer IRS lor unveiling hidden quasars ancl estimating their Iuminosities. (, This demonstrates the power of IRS for unveiling hidden quasars and estimating their luminosities. (
2.),2.)
 We presentSpitzer spectra of the 1H mid-IR. luminous radio galaxies., We present spectra of the 14 mid-IR luminous radio galaxies.
 In most cases. the mic-IR conünuum bump from 3-30 jm can be produced by a distribution of hot dust with temperatures in the range 210-660 Ix. These hieh temperatures are most likely maintained by hidden AGNs.," In most cases, the mid-IR continuum bump from 3-30 $\mu$ m can be produced by a distribution of hot dust with temperatures in the range $660$ K. These high temperatures are most likely maintained by hidden AGNs."
 The silicate absorption trough at 9.7 jm has an apparent optical depth of T—()—0.2 in most cases. consistent wilh dust temperatures decreasing outward from the center of a dusty torus.," The silicate absorption trough at 9.7 $\mu$ m has an apparent optical depth of $\tau=0-0.2$ in most cases, consistent with dust temperatures decreasing outward from the center of a dusty torus."
 Two sources. 3C 55 and 432. have deeper silicate (roughs which may be produced by additional cool dust in the host galaxy. (," Two sources, 3C 55 and 433, have deeper silicate troughs which may be produced by additional cool dust in the host galaxy. ("
3.),3.)
 However. not all FI II radio galaxies emit strongly in the mic-IR.," However, not all FR II radio galaxies emit strongly in the mid-IR."
" Contrary to unification schemes. the majority of narrow-line radio galaxies in our sample (17/31 or 55zc 134) have weak or undetected mid-IR emission compared to matehed quasars and DLRGs. with pL,(15 jm)<8xLO"" erg +."," Contrary to single-population unification schemes, the majority of narrow-line radio galaxies in our sample (17/31 or $55 \pm 13\%$ ) have weak or undetected mid-IR emission compared to matched quasars and BLRGs, with $\nu L_\nu(15$ $\mu\mathrm{m}) < 8 \times 10^{43}$ erg $^{-1}$."
 For a few sources. this may possibly be the result of anisotropic torus emission viewed through a large column density of dust.," For a few sources, this may possibly be the result of anisotropic torus emission viewed through a large column density of dust."
 Llowever. it ds likely that most of the weakest sources do not contain a powerful accretion disk.," However, it is likely that most of the weakest sources do not contain a powerful accretion disk."
 These mav be trulv nonthermal. jet-dominated. AGNs. where the jet is powered by a radiatively," These may be truly nonthermal, jet-dominated AGNs, where the jet is powered by a radiatively"
Clearly. the high energy οταν cluission Is au mrportant piece in the blazar puzzle because the 5-ray observations of blazars provide a new probe of deuse radiation field released through accretion outo a supermassive black hole in the central engine (Breeman 1990).,"Clearly, the high energy $\gam$ -ray emission is an important piece in the blazar puzzle because the $\gam$ -ray observations of blazars provide a new probe of dense radiation field released through accretion onto a supermassive black hole in the central engine (Bregman 1990)."
 The Enecrectic CGanuna Rav Experiment Telescope (EGRET) which works in the 0.1.1066V. energv domain has now detected and identified 66 extragalactic sources iu 3th catalog (Mukhlerjee et al 1999)., The Energetic Gamma Ray Experiment Telescope ) which works in the 0.1–10GeV energy domain has now detected and identified 66 extragalactic sources in 3th catalog (Mukherjee et al 1999).
 All these objects are blazay-type AGNs whose relativistic jets are assumed to be close to the line of sight to the observer., All these objects are blazar-type AGNs whose relativistic jets are assumed to be close to the line of sight to the observer.
 It. secs unaunhbiguous that the intense gamma-ray clussion is related with highly relativistic jet., It seems unambiguous that the intense gamma-ray emission is related with highly relativistic jet.
 It has been generally accepted that the Iuniuous ealuua-ray cussion is radiated frou inverse Compton. but the problemi of seed photons remains open for debate.," It has been generally accepted that the luminous gamma-ray emission is radiated from inverse Compton, but the problem of seed photons remains open for debate."
 The following arguments have been proposed: (1) svuchrotrou photons in jet Guhomogencous model of svuchrotron self Compton) (Maraschi. (ακομα Celotti 1992): (2) optical aud ultraviolet photons directly from the accretion disk (Dermer Schlikeiser 1993): (3) diffusive photons in broad liue region (BER) (Sikora. Degeliuan Rees 1991. Blaudford Leviusoufan 1995): CD) the reflected svuchrotron plotons bv electron nürror iu broad dine region. namely. the reflected svuchrotrou inverse Compton (RSC) (Cliselliii Macau 1996).," The following arguments have been proposed: (1) synchrotron photons in jet (inhomogeneous model of synchrotron self Compton) (Maraschi, Ghisellini Celotti 1992); (2) optical and ultraviolet photons directly from the accretion disk (Dermer Schlikeiser 1993); (3) diffusive photons in broad line region (BLR) (Sikora, Begelman Rees 1994, Blandford Levinson 1995); (4) the reflected synchrotron photons by electron mirror in broad line region, namely, the reflected synchrotron inverse Compton (RSC) (Ghisellini Madau 1996)."
 These mechamisis may operate in differcut kinds of objects. however there is not vet a consensus on how these mechanisms work.," These mechanisms may operate in different kinds of objects, however there is not yet a consensus on how these mechanisms work."
 Also it is uot clear where the οταν emission is taking place larecly because of uncertainties of soft radiation field im the ceutral engenie., Also it is not clear where the $\gam$ -ray emission is taking place largely because of uncertainties of soft radiation field in the central engine.
 Ou the other haud. VIIE observations (I&erick et al 1995. Chadwick et al 1999. Roberts et al 1999. Aliaroniau ct al 1999) are making attempts to explore the radiation miechanisuni because they may provide some restrictive constraints (Beechnan. Rees Sikora 1991. \lastichiaclis Wark 1997. Tavecchio. Maraschi ΠΕ Coppi Aharonian 1999. Ihuwit. Protheroe and Biermann 1999).," On the other hand, VHE observations (Kerrick et al 1995, Chadwick et al 1999, Roberts et al 1999, Aharonian et al 1999) are making attempts to explore the radiation mechanism because they may provide some restrictive constraints (Begelman, Rees Sikora 1994, Mastichiadis Kirk 1997, Tavecchio, Maraschi Ghisellini 1998, Coppi Aharonian 1999, Harwit, Protheroe and Biermann 1999)."
 Based ou the simple version of SSC model. Stecker. de Jager Salamon (1996) predicted a huge umber of ow redshift N-rav selected BL Lacs as TeV eaudidates. aking iuto account that the presence of intergalactic infrared radiation field including cosiuic background leads o strong absorption of TeV photons from cosmological enütters (Stecker de Jager 19098).," Based on the simple version of SSC model, Stecker, de Jager Salamon (1996) predicted a large number of low redshift X-ray selected BL Lacs as TeV candidates, taking into account that the presence of intergalactic infrared radiation field including cosmic background leads to strong absorption of TeV photons from cosmological emitters (Stecker de Jager 1998)."
 It is sueeested to orn an exteuded pair halo iu cosmological distance due o theexterna? absorption (Aharonian. Coppi. Voclk 1991).," It is suggested to form an extended pair halo in cosmological distance due to the absorption (Aharonian, Coppi, Voelk 1994)."
 ILowever. so far oulv three N-rav selected BL Lacs wave been found to be TeV cinitters by Whipple telescope GE2 300CeV). in addition. photons higher than 0.3TeV iu he N-rav-selected PISS 2155-301 with redshift :=0.116 ws been detected photous O.38TeV by Durham Mrk 6 clescope (Chadwick et al 1999).," However, so far only three X-ray selected BL Lacs have been found to be TeV emitters by Whipple telescope $E>300$ GeV), in addition, photons higher than 0.3TeV in the X-ray-selected PKS 2155-304 with redshift $z=0.116$ has been detected photons 0.3TeV by Durham Mrk 6 telescope (Chadwick et al 1999)."
 The recent measurements of intergalactic infrared field is quite different from the xevious observations (Aladau ct al 1998. Steidel 1998).," The recent measurements of intergalactic infrared field is quite different from the previous observations (Madau et al 1998, Steidel 1998)."
 Althoueh thisοἱ absorption is definitely important. he critical redshitt +. bevoud which cosmological back eround radiation and intergalactic infrared ficlds will absorb VIE photons remains uncertain.," Although this absorption is definitely important, the critical redshift $z_{c}$ beyond which cosmological back ground radiation and intergalactic infrared fields will absorb VHE photons remains uncertain."
 Especially the recent VITE observations slow that Mrk 501 enmits 25 TeV Xiotous (Aharonian et al 1999)., Especially the recent VHE observations show that Mrk 501 emits 25 TeV photons (Aharonian et al 1999).
 Evidently this sugeests hat theπα absorption cau not efiicicuth attenuate he VIIE photons from reaching us across distances of LOO Προ., Evidently this suggests that the absorption can not efficiently attenuate the VHE photons from reaching us across distances of 100 Mpc.
 It is highly desired to accurately probe the star orlation rate in order to determune the critical redshift , It is highly desired to accurately probe the star formation rate in order to determine the critical redshift $z_{c}$.
Thus it secs significant to study theinfrinsic uechanisia for the ceficicney of TeV photous from 2-av oud ACNs disregardiug the absorption bv interealactic infrared radiation field., Thus it seems significant to study the mechanism for the deficiency of TeV photons from $\gamma$ -ray loud AGNs disregarding the absorption by intergalactic infrared radiation field.
 A Larger Lorentz factor of the, A larger Lorentz factor of the
06 Tutermediate polars are scuui-detached interacting binaries in which a magnetic white dwarf accretes material from a Roche-lobe filling. usually late-type. main sequence colupamion star.,"		08.13.1;\tikzmark{mainBodyEnd2} % Stars: magnetic fields
\tikzmark{mainBodyStart3}		02.01.2;\tikzmark{mainBodyEnd3} % Accretion, accretion disks
\tikzmark{mainBodyStart4}		08.09.02\tikzmark{mainBodyEnd4} \tikzmark{mainBodyStart5}YY\tikzmark{mainBodyEnd5} \tikzmark{mainBodyStart6}Dra;\tikzmark{mainBodyEnd6} % Stars: individual: YY Dra
\tikzmark{mainBodyStart7}		08.09.02\tikzmark{mainBodyEnd7} \tikzmark{mainBodyStart8}V709\tikzmark{mainBodyEnd8} \tikzmark{mainBodyStart9}Cas\tikzmark{mainBodyEnd9} % Stars: individual: V709 Cas
\tikzmark{mainBodyStart10}		)} Intermediate polars are semi-detached interacting binaries in which a magnetic white dwarf accretes material from a Roche-lobe filling, usually late-type, main sequence companion star."
 T1ο accretion fiow from tιο secondary xoceeds towards the white dwuf ether through an accretion disce. au aceretion strea1. Or ποιο colbination of both (sown as disc overflow accretion). wutil it reaches he mmaenetospheric radius.," The accretion flow from the secondary proceeds towards the white dwarf either through an accretion disc, an accretion stream, or some combination of both (known as disc overflow accretion), until it reaches the magnetospheric radius."
 Hore the material attaches to he magnetic field lues aud follows them towards the naenetic xoles of the white dut., Here the material attaches to the magnetic field lines and follows them towards the magnetic poles of the white dwarf.
 The iufalliug material hat originates from an accretion disc takes the formu of arc-shaped accretion curtains. standing above the white dwarf surface.," The infalling material that originates from an accretion disc takes the form of arc-shaped accretion curtains, standing above the white dwarf surface."
 At some distance from this surface. the accretion flow uudergoes a strong shock. below which material settles onto the white chwart. releasing N-ravs as it cools by thermal bremsstrahlung processes.," At some distance from this surface, the accretion flow undergoes a strong shock, below which material settles onto the white dwarf, releasing X-rays as it cools by thermal bremsstrahlung processes."
 Simce the magnetic axis is offset from the spin axis of the white dwarf. this gives rise to the defining characteristic of the class. namely N-ray endssion mused at the white dwarf spin period.," Since the magnetic axis is offset from the spin axis of the white dwarf, this gives rise to the defining characteristic of the class, namely X-ray emission pulsed at the white dwarf spin period."
 If auv of the material accretes directly from an accretion stream. the xoportion falling onto cach pole of the white dw wil vary according to the rotation phase of the white dwarf in the reference frame of the binary.," If any of the material accretes directly from an accretion stream, the proportion falling onto each pole of the white dwarf will vary according to the rotation phase of the white dwarf in the reference frame of the binary."
 Cousequenthy. stream-tfed (or dise overflow) accretion will eive rise to N-rav cuuission that varies with the beat period. whereμετLfPoinL/Porviir.," Consequently, stream-fed (or disc overflow) accretion will give rise to X-ray emission that varies with the beat period, where $1/P_{\rm beat} = 1/P_{\rm spin} - 1/P_{\rm orbit}$."
 About twenty coufirmed intermediate polars are now recognized with a similar nuuniber of candidate svstems having becu proposed., About twenty confirmed intermediate polars are now recognized with a similar number of candidate systems having been proposed.
 Comprehensive reviews of various aspects of their behaviour are given by Patterson (1991)). Warner (1995)). Teller (1995:; 1996)) and. Norton (1995)).," Comprehensive reviews of various aspects of their behaviour are given by Patterson \cite{Patt}) ), Warner \cite{War95}) ), Hellier \cite{Hell95}; \cite{Hell96}) ) and Norton \cite{Nor2}) )."
 The 16th magnitude star YY Dra was discovered iu 1931 and originally mis-classified as an Algol-like svsteu., The 16th magnitude star YY Dra was discovered in 1934 and originally mis-classified as an Algol-like system.
 Detected as an N-rav source byV (3À& 11181719) and (2E 1110.7|7158). it was subsequentlv reclassified as a cataclysmic variable (see the discussions in Patterson et al.," Detected as an X-ray source by (3A 1148+719) and (2E 1140.7+7158), it was subsequently reclassified as a cataclysmic variable (see the discussions in Patterson et al."
 1992— and Patterson Szkocly 1993 for the history of this source)., \cite{P92} and Patterson Szkody \cite{PS} for the history of this source).
 Optical radial velocity. observations by Fricud et al. (1988)), Optical radial velocity observations by Friend et al. \cite{Friend}) )
 revealed its orbital period as 3.97 hy. whilst time resolved," revealed its orbital period as 3.97 hr, whilst time resolved"
"noticeable before reionization and in its early stages (?,, ΜΕΟΤ).","noticeable before reionization and in its early stages \citealt{McQuinn06}, MF07)."
" As we are interested in accurately simulating the 21-cm signal from all cosmological epochs, including pre-reionization, here we will compare the velocity gradient term from 21cmFAST and hydrodynamic simulations."," As we are interested in accurately simulating the 21-cm signal from all cosmological epochs, including pre-reionization, here we will compare the velocity gradient term from 21cmFAST and hydrodynamic simulations."
" Using the Zel'Dovich approximation on our 3D realizations, we can again efficiently move beyond the linear regime into the quasi-linear regime, and take into account correlations in the velocity gradient field."," Using the Zel'Dovich approximation on our 3D realizations, we can again efficiently move beyond the linear regime into the quasi-linear regime, and take into account correlations in the velocity gradient field."
" In this first-order perturbation theory, the velocity field can be written as: and so the derivative of the line-of-sight velocity, v,, where r for simplicity is oriented along a basis vector, can be written in k-space as: where differentiation is performed in k-space."," In this first-order perturbation theory, the velocity field can be written as: and so the derivative of the line-of-sight velocity, $v_r$ where ${\bf r}$ for simplicity is oriented along a basis vector, can be written in k-space as: where differentiation is performed in k-space."
" The last approximation is used for 21cmFAST, while the first, exact expression is used for the numerical "," The last approximation is used for 21cmFAST, while the first, exact expression is used for the numerical ."
si, In Fig.
"mulation?.. In Fig. 4 we show the PDFs of the comoving LOS derivative of v. [in units of H(z)], smoothed on scale Raiter = 0.5 Mpc (left) and 5.0 Mpc (right)."," \ref{fig:filter_dvdr_pdfs} we show the PDFs of the comoving LOS derivative of $v_r$ [in units of $H(z)$ ], smoothed on scale $R_{\rm filter}$ = 0.5 Mpc ) and 5.0 Mpc )."
" Solid red curves are generated from the hydrodynamic simulation, while the dashed blue curves are generated by 21cmFAST."," Solid red curves are generated from the hydrodynamic simulation, while the dashed blue curves are generated by 21cmFAST."
" Redshifts corresponding to z= 20, 15, 10, 7 are shown top to bottom."," Redshifts corresponding to $z=$ 20, 15, 10, 7 are shown top to bottom."
 We see that our perturbation theory approach again does remarkably well in reproducing results from the hydrodynamic simulation., We see that our perturbation theory approach again does remarkably well in reproducing results from the hydrodynamic simulation.
" The velocity gradients agree even better than the density fields, since the velocity field is coherent over larger scales."," The velocity gradients agree even better than the density fields, since the velocity field is coherent over larger scales."
 The shape of the distributions are noticeably non-linear on small scales and late times., The shape of the distributions are noticeably non-linear on small scales and late times.
" The curves resemble PDFs of the sign-flipped non-linear density field, δι, which is understandable from eq. (4))."," The curves resemble PDFs of the sign-flipped non-linear density field, $\delta_{\rm nl}$, which is understandable from eq. \ref{eq:mydvdr}) )."
" The dotted magenta curves in the bottom right panels were generated on comparable scales by 21cmFAST with different initial conditions; however, they assume linear evolution of the density field, instead of the perturbation theory approach."," The dotted magenta curves in the bottom right panels were generated on comparable scales by 21cmFAST with different initial conditions; however, they assume linear evolution of the density field, instead of the perturbation theory approach."
" As expected, linear evolution results in a symmetric Gaussian PDF."," As expected, linear evolution results in a symmetric Gaussian PDF."
" Do we reproduce the geometric, scale-free enhancement of the power spectrum on linear scales?"," Do we reproduce the geometric, scale-free enhancement of the power spectrum on linear scales?"
" In the top panel of Fig. 5,"," In the top panel of Fig. \ref{fig:just_ratios_large_box},"
" we plot 21-cm power spectra, Abi(k,z)=K*/(2*V)(lómi(k,z)?)& where δοι(κ,2)= 1."," we plot 21-cm power spectra, $\Delta^2_{21}(k, z) = k^3/(2\pi^2 V) ~ \langle|\delta_{\rm 21}({\bf k}, z)|^2\rangle_k$ where $\delta_{21}({\bf x}, z) \equiv \delT({\bf x}, z)/ \bar{\delT}(z) - 1$ ."
" The spectra are generated by 21cmFAST in the limit of Ts>>T, and assuming zu;=1.", The spectra are generated by 21cmFAST in the limit of $\Ts \gg \Tcmb$ and assuming $\avenf=1$.
" The solid red curves correspond to a 5 Gpc box with Ax = 10 Mpc cells, while the blue and dashed green curves correspond to a 1 Gpc box with different resolutions."," The solid red curves correspond to a 5 Gpc box with $\Delta x$ = 10 Mpc cells, while the dot-dashed blue and dashed green curves correspond to a 1 Gpc box with different resolutions."
" The upper set of curves were computed including peculiar velocities, while the lower set were computed not including peculiar velocities."," The upper set of curves were computed including peculiar velocities, while the lower set were computed not including peculiar velocities."
 The bottom three panels show the ratios of the power spectra that include redshift space distortions to those that do not., The bottom three panels show the ratios of the power spectra that include redshift space distortions to those that do not.
" Indeed the red curves in Fig. 5,,"," Indeed the red curves in Fig. \ref{fig:just_ratios_large_box},"
" which were evolved linearly, accurately capture the enhancement factor of 1.87, shown with a dottedhorizontal line."," which were evolved linearly, accurately capture the enhancement factor of 1.87, shown with a dottedhorizontal line."
" The other two curves, which include first order non-linear effects, show an enhancement of powerf"," The other two curves, which include first order non-linear effects, show an enhancement of power."
"actor. From eq. (4)),"," From eq. \ref{eq:mydvdr}) ),"
" one sees that a high-value tail in the density distribution resulting from non-linear evolution would drive a corresponding negative tail in the dv./dr distributions, which in turn enhances the 21- signal through the (l/(dv./dr/H)+1) termin eq. 1. "," one sees that a high-value tail in the density distribution resulting from non-linear evolution would drive a corresponding negative tail in the $dv_r/dr$ distributions, which in turn enhances the 21-cm signal through the $(1 / (dv_r/dr/H) + 1)$ termin eq. \ref{eq:delT}. ."
"Although the ἄν,/dr distributions are zero-mean, the distributions"," Although the $dv_r/dr$ distributions are zero-mean, the distributions"
1960).,.
. This is shown by working out the Fokker-Planck equation for the evolution of actions of the particles in this random field., This is shown by working out the Fokker-Planck equation for the evolution of actions of the particles in this random field.
 Phe potential of a mass me with action-angle variables Jo. we ona particle 1 with action-angle variables Ji. Wi is: The lluctuating part of the potential created by the discreteness of the dressed. particles is the sum over all particles 2 and all non-vanishing Κι. k» of potentials like (39)).," The potential of a mass $m_2$ with action-angle variables ${\mathbf{J}}_2$, ${\mathbf{w}}_2$ on a particle $1$ with action-angle variables ${\mathbf{J}}_1$, ${\mathbf{w}}_1$ is: The fluctuating part of the potential created by the discreteness of the dressed particles is the sum over all particles $2$ and all non-vanishing ${ {\mathbf{k}}_1 }$, ${ {\mathbf{k}}_2 }$ of potentials like \ref{potuneparthabillee}) )."
" Phe rate of change of the action J, of a particle 1 in this fluctuating field is: The braking ancl diffusion coellicients of the corresponding Fokker-Planck equation are obtained from. respectively. the first and second moments of the random change AJ) sullered by the particle 1 in a time A’."," The rate of change of the action ${\mathbf{J}}_1$ of a particle $1$ in this fluctuating field is: The braking and diffusion coefficients of the corresponding Fokker-Planck equation are obtained from, respectively, the first and second moments of the random change $\Delta {\mathbf{J}}_1$ suffered by the particle $1$ in a time $\Delta t$."
 The averaging is performed on the values of the angle variables of particles 2 and on their action distribution functions., The averaging is performed on the values of the angle variables of particles $2$ and on their action distribution functions.
 Equation (38)) is recovered. that wav., Equation \ref{LAequation}) ) is recovered that way.
 In the calculation of the braking coelficient. small departures from uniform angular motion should be accounted for. as shown by Ecker(1972). in à similar context.," In the calculation of the braking coefficient, small departures from uniform angular motion should be accounted for, as shown by \citet{Ecker} in a similar context."
 Phe Fokker-Planek form of equation (38)). although equivalent to it. looks more complex than equation (38)) itself because the braking coellicient involves the derivative of a Dirac distribution.," The Fokker-Planck form of equation \ref{LAequation}) ), although equivalent to it, looks more complex than equation \ref{LAequation}) ) itself because the braking coefficient involves the derivative of a Dirac distribution."
 Equation (38)) and its quasi-homogeneous limit. equation (47)). both result from a weak collision theory.," Equation \ref{LAequation}) ) and its quasi-homogeneous limit, equation \ref{LAequationhomograv}) ), both result from a weak collision theory."
 Strong collisions involving substancial deviation of at least one of the colliding particles are not adequately. described., Strong collisions involving substancial deviation of at least one of the colliding particles are not adequately described.
 This inappropriate deseription of the rare strong collisions can be fixed hy limiting the range of impact. parameters to values larger than some critical limit 577 which depends on the masses of the colliding species., This inappropriate description of the rare strong collisions can be fixed by limiting the range of impact parameters to values larger than some critical limit $b_{cr}^{ab}$ which depends on the masses of the colliding species.
 This critical impact parameter for particles of species e and b is such that the tvpical kinetic energy in their relative motion be equal to their interaction energy. that is: Llere AZ is the total svstem's mass and. 2 a typical global size of it.," This critical impact parameter for particles of species $a$ and $b$ is such that the typical kinetic energy in their relative motion be equal to their interaction energy, that is: Here $M$ is the total system's mass and $R$ a typical global size of it."
 Were this cut to be omitted. the expressions of the coefficients in equations (38)) ancl (47)) would diverge logarithmically at large wavenumbers. where the response function 5 approaches unity.," Were this cut to be omitted, the expressions of the coefficients in equations \ref{LAequation}) ) and \ref{LAequationhomograv}) ) would diverge logarithmically at large wavenumbers, where the response function $\varepsilon$ approaches unity."
 This divergence results from the neglect of large deviations in strong collisions., This divergence results from the neglect of large deviations in strong collisions.
" A physically sound result is obtained by limiting the K integration in equation (47)) to the domain |IzONUStad. where: Similarly the summations on the angle Fourier variables k; (7= 1 or 2) in equation (38)) should be limited. in the term associated to species e and b. to values such that the physical wavenumbers along the quasi-intersecting orbits be smaller than ΑΟ, "," A physically sound result is obtained by limiting the ${\mathbf{K}}$ integration in equation \ref{LAequationhomograv}) ) to the domain $\mid \! {\mathbf{K}}\! \mid < K_{cr}^{ab}$ where: Similarly the summations on the angle Fourier variables ${\mathbf{k}}_i$ $i=$ 1 or 2) in equation \ref{LAequation}) ) should be limited, in the term associated to species $a$ and $b$, to values such that the physical wavenumbers along the quasi-intersecting orbits be smaller than $K_{cr}^{ab}$ ."
phis modulus of the physical wavenumber can be erudely related to the dimensionless angle wavenumber by A=hfde. where 2 is a typical global size of the svstem ancl & the modulus of the angle Fourier variable.," This modulus of the physical wavenumber can be crudely related to the dimensionless angle wavenumber by $K = k/R$, where $R$ is a typical global size of the system and $k$ the modulus of the angle Fourier variable."
 Thus. the summation on Κι and ke in equation (38)) should be limited to wave vectors. the modulus of which is bounded by: When solving equation (38)). the secular evolution of the response matrix z. the svstem's collective potential C(r./) ancl the Fourier transform coetllicients oy(J) should be followed in time together with the I-body distributions.," Thus, the summation on ${\mathbf{k}}_1$ and ${\mathbf{k}}_2$ in equation \ref{LAequation}) ) should be limited to wave vectors, the modulus of which is bounded by: When solving equation \ref{LAequation}) ), the secular evolution of the response matrix $\varepsilon$, the system's collective potential $U({\mathbf{r}},t)$ and the Fourier transform coefficients $\psi^{\alpha}_{\mathbf{k}}({\mathbf{J}})$ should be followed in time together with the 1-body distributions."
" We return to this. in the case of spherical potentials. in section δι,"," We return to this, in the case of spherical potentials, in section \ref{secsystemcouple}."
 Prior to that. let us discuss various limits and approximate forms of equation (38)) and show that. as it should. it satisfies an H-theorem.," Prior to that, let us discuss various limits and approximate forms of equation \ref{LAequation}) ) and show that, as it should, it satisfies an H-theorem."
 The irreversibility stemuns from the fact that information is lost when the real issues of collisions are replaced in the equation by average ones. in particular by. averaging over the angles of the colliding particles.," The irreversibility stemms from the fact that information is lost when the real issues of collisions are replaced in the equation by average ones, in particular by averaging over the angles of the colliding particles."
 Although the limit of an homogeneous medium cannot be rigourously taken for a self gravitating svstem. it isnevertheless possible to assume local homogeneity at the price of artificially limiting the interaction distance between particles by cutting," Although the limit of an homogeneous medium cannot be rigourously taken for a self gravitating system, it isnevertheless possible to assume local homogeneity at the price of artificially limiting the interaction distance between particles by cutting"
a key role in this investigation.,a key role in this investigation.
 Phen a few methodological remarks will be made in Sec., Then a few methodological remarks will be made in Sec.
 ??. before we come to the velocity dispersion profiles in Sec., \ref{Sec:Method} before we come to the velocity dispersion profiles in Sec.
 ?? and then to the surface density. profiles in Sec. ??.., \ref{Sec:VDP} and then to the surface density profiles in Sec. \ref{Sec:SDP}.
 In the last section we will give a summary with a brief discussion., In the last section we will give a summary with a brief discussion.
 A major problem in producing velocity dispersion and surface density. profiles from. observations is how to cliscntanele cluster members from. background/foreground stars., A major problem in producing velocity dispersion and surface density profiles from observations is how to disentangle cluster members from background/foreground stars.
 By only looking at stars which are inside a projected. estimated. Jacobi radius with similar radial velocities ancl colours it is at least possible to distinguish. between the cluster. population and field. stars.," By only looking at stars which are inside a projected, estimated Jacobi radius with similar radial velocities and colours it is at least possible to distinguish between the cluster population and field stars."
 Even here. however. the question arises whether the choice of the cut in radial velocity. significantly inlluences the results. especially. of the velocity dispersion. profile. (see. Kupper& Ixroupa 2010)).," Even here, however, the question arises whether the choice of the cut in radial velocity significantly influences the results, especially of the velocity dispersion profile (see \citealt{Kuepper10b}) )."
 Moreover. one has to be careful with how the Jacobi radius was estimated. e. was it evaluated using a mass estimate and was the mass estimated. through the velocity dispersion?," Moreover, one has to be careful with how the Jacobi radius was estimated, i.e. was it evaluated using a mass estimate and was the mass estimated through the velocity dispersion?"
 Or was the Jacobi radius estimated by a cut-olf radius in the profile and. is the assumption that this cut-off. radius is equal to the Jacobi radius reasonable?, Or was the Jacobi radius estimated by a cut-off radius in the profile and is the assumption that this cut-off radius is equal to the Jacobi radius reasonable?
 What if the cluster is on an eccentric. orbit about the galaxy: how does this inlluence the eut-olf Desides. the observer does not. know if the stars in the sample which was extracted in this way are actually members of the cluster or if they are already evaporated from the cluster anc are now part of its tidal debris. and just lic in projection within the 3ut even if the observer could distinguish between stars inside the Jacobi radius and those that are. bevond. this radius. it would still be unclear if the stars in the sample are bound to the cluster or have already. gained enough energy to leave the cluster but. just. haven't done so vet.," What if the cluster is on an eccentric orbit about the galaxy; how does this influence the cut-off Besides, the observer does not know if the stars in the sample which was extracted in this way are actually members of the cluster or if they are already evaporated from the cluster and are now part of its tidal debris, and just lie in projection within the But even if the observer could distinguish between stars inside the Jacobi radius and those that are beyond this radius, it would still be unclear if the stars in the sample are bound to the cluster or have already gained enough energy to leave the cluster but just haven't done so yet."
 These. so-called. potential escapers will have a significant inlluence on both the surface density and the velocity dispersion profile. if there is a non-negligible fraction of them in the cluster. as these stars will make the profiles deviate from any theory which does not take them into account - which most theoretical approaches do 1n numerical modelling of star clusters we have detailed phase space information on every single star in the computation.," These, so-called, potential escapers will have a significant influence on both the surface density and the velocity dispersion profile, if there is a non-negligible fraction of them in the cluster, as these stars will make the profiles deviate from any theory which does not take them into account - which most theoretical approaches do In numerical modelling of star clusters we have detailed phase space information on every single star in the computation."
 Mainly by numerical investigations it has been found that the escape process through which stars escape [rom a cluster in a constant tidal field. e.g. on a circular orbit about a galaxy. is divided into two steps.," Mainly by numerical investigations it has been found that the escape process through which stars escape from a cluster in a constant tidal field, e.g. on a circular orbit about a galaxy, is divided into two steps."
" First the stars get unbound via two-bocly relaxation. thus on a relaxation time scale (ignoring constants) where Nis the number of stars in the cluster and ἐς, is the crossing time of the cluster (note that we neglected the slowly. varving Coulomb logarithm in eq. 1.."," First the stars get unbound via two-body relaxation, thus on a relaxation time scale (ignoring constants), where $N$ is the number of stars in the cluster and $t_{cr}$ is the crossing time of the cluster (note that we neglected the slowly varying Coulomb logarithm in eq. \ref{eq:trel},"
 for further details see e.g. Hegeie&Lut 2003))., for further details see e.g. \citealt{Heggie03}) ).
 In the second. step. these energetically unbound stars. or. potential escapers. with specific energv Lo higher than some critical escape energy Leoni. escape from the cluster on an escape time scale which is given by (Fukushige&Llegeic2000... equation 9 therein) where {ο is the critical energy at the Lagrange points. i.c. at the Jacobi radius.," In the second step, these energetically unbound stars, or potential escapers, with specific energy $E$ higher than some critical escape energy $E_{crit}$, escape from the cluster on an escape time scale which is given by \citealt{Fukushige00}, equation 9 therein) where $E_{crit}$ is the critical energy at the Lagrange points, i.e. at the Jacobi radius."
" From this it follows that the excess energv can be written as On the other hand. the relation holds. whence we find that l]lence. a fraction of stars with exeess energy. (LeLou)fog escapes on a time scale /,,, and the time scale of mass loss. e.g. the time on which a cluster dissolves. (ij... is given by which was also found by Daumgardt(2001)."," From this it follows that the excess energy can be written as On the other hand, the relation holds, whence we find that Hence, a fraction of stars with excess energy $(E-E_{crit})/E_{crit}$ escapes on a time scale $t_{esc}$ and the time scale of mass loss, e.g. the time on which a cluster dissolves, $t_{diss}$, is given by which was also found by \citet{Baumgardt01}."
". Phis result is in contrast to the ""classic pieture where the dissolution times of clusters scale. with the relaxation time (see e.g. Annev&Trenaine 2008)). Le. and demonstrates the importance of potential escapers on the dissolution process of star clusters."," This result is in contrast to the `classic' picture where the dissolution times of clusters scale with the relaxation time (see e.g. \citealt{Binney87}) ), i.e. and demonstrates the importance of potential escapers on the dissolution process of star clusters."
 Ehe remaining question is whether the population of potential escapers is large enough that it also has an inlluence on the velocity dispersion and surface density. profiles., The remaining question is whether the population of potential escapers is large enough that it also has an influence on the velocity dispersion and surface density profiles.
 For clusters of a few 10 stars in a constant tidal field Baumearclt(2001). finds about of all stars within the Jacobi radius to be potential escapers. Justetal.(2009). even find the fraction of potential escapers for similar clusters to be 1/3 of the cluster. population.," For clusters of a few $10^4$ stars in a constant tidal field \citet{Baumgardt01} finds about of all stars within the Jacobi radius to be potential escapers, \citet{Just09} even find the fraction of potential escapers for similar clusters to be 1/3 of the cluster population."
 Moreover. Daumgzardt.(2001) found that for clusters in a constant tidal field the fraction of potential escapers varies with the number of stars within a ister approximately as IN.E71.," Moreover, \citet{Baumgardt01} found that for clusters in a constant tidal field the fraction of potential escapers varies with the number of stars within a cluster approximately as $N^{-1/4}$."
 Thus. this fraction should μα—I be significant lor high-N. globular Star clusters. in. time-dependent tidal fields have not been investigated in this respect vet. but as tidal perturbations tend to increase the energy of the stars in a cluster (e.g. Cnedin.Lee&Ostriker 19993). the population of potential escapers should be even larger in such clusters.," Thus, this fraction should still be significant for $N$ globular Star clusters in time-dependent tidal fields have not been investigated in this respect yet, but as tidal perturbations tend to increase the energy of the stars in a cluster (e.g. \citealt{Gnedin99}) ), the population of potential escapers should be even larger in such clusters."
 ‘Thus. potential escapers should have a significant elfect on both the velocity dispersion and the surface density profiles of all kines of star clusters.," Thus, potential escapers should have a significant effect on both the velocity dispersion and the surface density profiles of all kinds of star clusters."
calculations. including a new approach which reduces significantly the amount of data to be precaleulated and allows for a flexibility in terms of the emissivity of the accretion dise and the limb-darkening law (Sect. 2.49.,"calculations, including a new approach which reduces significantly the amount of data to be precalculated and allows for a flexibility in terms of the emissivity of the accretion disc and the limb-darkening law (Sect. \ref{sec:calculations}) )."
 The implementation of this scheme in a new code for calculating relativistic lines.LLinc.. and the comparison of this scheme with other models is described in Sect. ??..," The implementation of this scheme in a new code for calculating relativistic lines, and the comparison of this scheme with other models is described in Sect. \ref{sec:relline}. ."
 Section presents results for line profiles and summarizes our results., Section \ref{sec:discussion} presents results for line profiles and summarizes our results.
 In order to account for the strongly curved space and allow a spinning black hole. a fully relativistic approach in the metric was chosen.," In order to account for the strongly curved space and allow a spinning black hole, a fully relativistic approach in the metric was chosen."
 This metric is characterized by the mass. AZ. and the angular momentum. ./. of the black hole. which is commonly parametrized as a=J/A.," This metric is characterized by the mass, $M$ , and the angular momentum, $J$, of the black hole, which is commonly parametrized as $a=J/M$."
 We will call the black hole in a system where it spins in the opposite direction of the accretion dise a black hole (i.e. e« 0)., We will call the black hole in a system where it spins in the opposite direction of the accretion disc a black hole (i.e. $a < 0$ ).
 Throughout this paper. units ofC—c= Lare chosen.," Throughout this paper, units of $ \mathrm{G} \equiv \mathrm{c} \equiv
1$ are chosen."
 The line element in coordinates is where τιΑΗ|e? and X—97|a?cos?6. the angle Ó is measured in the plane of the disc. and the black hole's angular momentum points towards 6=0.," The line element in coordinates is where $\Delta = r^2 - 2Mr +a^2$ and $\Sigma = r^2 +
a^2\cos^2{\theta}$, the angle $\phi$ is measured in the plane of the disc, and the black hole's angular momentum points towards $\theta=0$."
 Taking into account the black hole's interaction with thermal photons from the accretion dise. its spin is restricted fo @(hax las capturing photons with negative angular momentum (with respect to the movement of the disc) becomes more likely for increasing e and thus prevents a spin up to the extreme value of @=1ο).," Taking into account the black hole's interaction with thermal photons from the accretion disc, its spin is restricted to $a \le
 a_\mathrm{max} < 1$ as capturing photons with negative angular momentum (with respect to the movement of the disc) becomes more likely for increasing $a$ and thus prevents a spin up to the extreme value of $a=1$."
 Assuming that a negatively spinning system is created by flipping the spin of a system with a>0 sets the lower limit of the spin at eMas. as infalling matter from the couterrotating disc clearly decreases the absolute value of the spin with time.," Assuming that a negatively spinning system is created by flipping the spin of a system with $a>0$ sets the lower limit of the spin at $a \ge -a_\mathrm{max}$, as infalling matter from the couterrotating disc clearly decreases the absolute value of the spin with time."
 We choose μμ=0.998. which is commonly used and has been calculated by?.," We choose $a_\mathrm{max}
 = 0.998$, which is commonly used and has been calculated by."
. As we are interested in particle orbits around the black hole. we need to derive the equations of motion for a test particle in the Kerr metric.," As we are interested in particle orbits around the black hole, we need to derive the equations of motion for a test particle in the Kerr metric."
 This can. e.g.. be done by solving the Geodesic equation directly. which formally is a general equation of motion for allpossible metrics in General Relativity.," This can, e.g., be done by solving the Geodesic equation directly, which formally is a general equation of motion for allpossible metrics in General Relativity."
 Using the conserved quantities of motion(?).. i.e. the energy 7. the angular momentum L.the rest mass jr of the particle. and the general equations of motion are(?)}:: where and The signs in Eq.," Using the conserved quantities of motion, i.e., the energy $E$, the angular momentum $L$ , the rest mass $\mu$ of the particle, and the general equations of motion are: where and The signs in Eq."
 + and Eq., \ref{eq:m2} and Eq.
 5. can be chosen independently and account for the direction of the photon., \ref{eq:m3} can be chosen independently and account for the direction of the photon.
 The upper sign means a movement with growing 7/8 and the lower sign stands for the opposite behaviour. respectivly.," The upper sign means a movement with growing $r$ $\theta$ and the lower sign stands for the opposite behaviour, respectivly."
 Thus they can be chosen arbitrarily. but change. e.g.. when a turning point occurs.," Thus they can be chosen arbitrarily, but change, e.g., when a turning point occurs."
 For simplicity we assume a geometrically thin accretion dise which lies in the equatorial plane of the system. Le. €=7/2 and 6—0.," For simplicity we assume a geometrically thin accretion disc which lies in the equatorial plane of the system, i.e., $\theta = \pi/2$ and $\dot{\theta} = 0$."
 Additionally we require the dise to be stationary and to consist of particles orbiting the compact object on circular orbits., Additionally we require the disc to be stationary and to consist of particles orbiting the compact object on circular orbits.
 This approach fully determines the system(2)., This approach fully determines the system.
. Taking into account that the particles can be on pro- and retrograde orbits with respect to the spinning direction of the black hole. the particles have an angular velocity The four-velocity of the accretion dise is given by where Further calculation reveals that there exists a radius of (often referred to as innermost stable circular orbit. ISCO) at where and Thus the inner edge of the accretion dise has to be at a radius rinMus. as no stable circular orbits can exist inside of it.," Taking into account that the particles can be on pro- and retrograde orbits with respect to the spinning direction of the black hole, the particles have an angular velocity The four-velocity of the accretion disc is given by where Further calculation reveals that there exists a radius of (often referred to as innermost stable circular orbit, ISCO) at where and Thus the inner edge of the accretion disc has to be at a radius $r_\mathrm{in}>r_\mathrm{ms}$, as no stable circular orbits can exist inside of it."
" The minimum inner radius of an accretion dise is μία=[0.008)= L23r.. where r,=CAL/e7 is called gravitational radius."," The minimum inner radius of an accretion disc is $r_{\mathrm{ms}}(a=+0.998)=1.23\,r_\mathrm{g}$ , where $r_\mathrm{g}
= GM/c^2$ is called gravitational radius."
 This orbit is only possible for particles circulating around a maximally rotating black hole with positive angular momentum. as the orbits are supported by frame-dragging effects.," This orbit is only possible for particles circulating around a maximally rotating black hole with positive angular momentum, as the orbits are supported by frame-dragging effects."
 In the case of a negative spin. the same effects push the inner edge out to FuseΞ0.998)—9ru.," In the case of a negative spin, the same effects push the inner edge out to $r_{\mathrm{ms}}(a=-0.998) \sim 9
\,r_\mathrm{g}$."
 Having described the accretion disc. ie. the frame where the photonsare emitted. we can now trace them back to a distant observer.," Having described the accretion disc, i.e. the frame where the photonsare emitted, we can now trace them back to a distant observer."
 Following. e.g.. 2.. we use the effective Lagrangian for massless particles (Gf= 0) in orderto calculate the photon’smomentum," Following, e.g., , we use the effective Lagrangian for massless particles $\mu = 0$ ) in orderto calculate the photon'smomentum"
which gives. Therefore. we set the masses of planetary embryos and Xdanetesimals. following the relationship MiyssnryoXTN oportional to the total mass in the embryvo's. feeding zone (Raymondetal.2004).,"which gives, Therefore, we set the masses of planetary embryos and planetesimals following the relationship $M_{embryo}\propto a^{3/4}$, proportional to the total mass in the embryo's feeding zone \citep{raym04}."
. On the other hand. all the Xdanetesipials in our simulations were set with an equal massof 0.017 Mj.," On the other hand, all the planetesimals in our simulations were set with an equal massof 0.017 $M_{\oplus}$."
 The initial orbital elements. of cach embryo. and janetesimal were randomly generated: argument οἱ »ericentre. longitude. of the ascending node. and mean anomaly of cach small object were randomly. set. between Y to 3607: the eccentricities range from 0 to 0.02. while he inclination vary from 0 to 1.," The initial orbital elements of each embryo and planetesimal were randomly generated: argument of pericentre, longitude of the ascending node, and mean anomaly of each small object were randomly set between $0^{\circ}$ to $360^{\circ}$; the eccentricities range from 0 to 0.02, while the inclination vary from $0^{\circ}$ to $1^{\circ}$."
 For giant. planets. to investigate terrestrial planetary. formation in an inclined configuration. the inclination of the outer. giant planet changes for each group but that of the inner gas-giant remains. in the meantime all other orbital cata keep unchanged in the each initial run.," For giant planets, to investigate terrestrial planetary formation in an inclined configuration, the inclination of the outer giant planet changes for each group but that of the inner gas-giant remains, in the meantime all other orbital data keep unchanged in the each initial run."
 As mentioned. one of the main goals of this work is to explore terrestrial planet. formation in the late stage uncler the circumstance of highlv-inclined planetary system. where the mutual inclination of the outer. giant planet is taken into account.," As mentioned, one of the main goals of this work is to explore terrestrial planet formation in the late stage under the circumstance of highly-inclined planetary system, where the mutual inclination of the outer giant planet is taken into account."
 Consequently. we carried. out. live groups of simulations. containing 46 runs in total.," Consequently, we carried out five groups of simulations, containing 46 runs in total."
 The major dillerence between each group. is the. distribution range of the initial bodies., The major difference between each group is the distribution range of the initial bodies.
" In all groups. two giant planets were set to emulate the OCGLIE-06-1081, svstemin each run. with initial orbital parametors(Alp. a. ὃν) = 1Mj,. AAU. 0.001) and. Mj, 4.6.NAU."," In all groups, two giant planets were set to emulate the OGLE-06-109L systemin each run, with initial orbital parameters$M_{P}$, $a$ , $e_{p}$ ) $=$ $M_{jup}$ , AU, 0.001) and $M_{jup}$ , AU,"
iurpacts on dwarf orbits over time 2010).. bu his potential makes modelling the history of observe cwarfs backavards inch harder.,"impacts on dwarf orbits over time , but this potential makes modelling the history of observed dwarfs backwards much harder."
 Ou the other haud it wav allow more ofthe cawarts observed today the possibility of cing associated with the \lagclanic system at an earlier 1ne., On the other hand it may allow more of the dwarfs observed today the possibility of being associated with the Magellanic system at an earlier time.
 Models iu which the Magellanic svstem is on its firs orbit of the Galaxy show a auch reduced loss., Models in which the Magellanic system is on its first orbit of the Galaxy show a much reduced loss.
 This is xwtiallv due to the perturbation of the LAIC aud SAICSs orbits by chwarfs over long times., This is partially due to the perturbation of the LMC and SMC's orbits by dwarfs over long times.
 The possiblity of dwarf colpanious therefore needs to be taken into accoun when determing the orbit of the LAIC and SAIC., The possiblity of dwarf companions therefore needs to be taken into account when determing the orbit of the LMC and SMC.
 The LAIC. and to a lesser extent the SAIC. were assiucec o be tidally stripped before cutering the Calactic halo.," The LMC, and to a lesser extent the SMC, were assumed to be tidally stripped before entering the Galactic halo."
 Tidal stripping that happens as the LMC euters the halo will increase dvuaiical friction aud subsequently result in a lower velocity today than those present iu model F. As most dwarfs ave lost when the SAIC binds to the LAIC or at porigalaction (approximately today). dwarts in this scenario nav be better represented by model C. The restriction that dwarts initially speud their eutire orbit within the tidal radius of the LAC (with respect to the Galaxy) clearly leaves out bouud orbits (those witli neeative cacrev with respect to the LMC).," Tidal stripping that happens as the LMC enters the halo will increase dynamical friction and subsequently result in a lower velocity today than those present in model F. As most dwarfs are lost when the SMC binds to the LMC or at perigalaction (approximately today), dwarfs in this scenario may be better represented by model C. The restriction that dwarfs initially spend their entire orbit within the tidal radius of the LMC (with respect to the Galaxy) clearly leaves out bound orbits (those with negative energy with respect to the LMC)."
 Dwarfs ou these extra-tidal orbits are extremely Likely to be tidallv stripped aud aud could also be the source of some chvart ealaxies that reside iu the disk-of-satellites., Dwarfs on these extra-tidal orbits are extremely likely to be tidally stripped and and could also be the source of some dwarf galaxies that reside in the disk-of-satellites.
 We have modelled the orbits of a group of dwurf ealaxies bound to the LMC at a previous apogalacticon using a Moute Carlo approach. varving the orbits within observational errors.," We have modelled the orbits of a group of dwarf galaxies bound to the LMC at a previous apogalacticon using a Monte Carlo approach, varying the orbits within observational errors."
 Dwarf galaxies bound to the LMC are unlikely to iuteract with each other. aud a significant action become uubouud from the Magellanic svstei after only half an orbit.," Dwarf galaxies bound to the LMC are unlikely to interact with each other, and a significant fraction become unbound from the Magellanic system after only half an orbit."
 These dwarts would be located around the Alagellanic svstem today and likely be roticeably associated with it., These dwarfs would be located around the Magellanic system today and likely be noticeably associated with it.
 Dwarfs that were bond oue and a half orbits agothat is at the LMCs secoucd-ast apogalacticonare over six times more likely to )ecome umbonund than remain bound. with mauy οσαΕς πο located either iu au extended structure of orbits. or iu a tight disk around the Galaxy.," Dwarfs that were bound one and a half orbits ago—that is at the LMC's second-last apogalacticon—are over six times more likely to become unbound than remain bound, with many dwarfs being located either in an extended structure of orbits, or in a tight disk around the Galaxy."
 This disk encompasses he locations of a nuuber of dwarfs observed today around the A\Glky Way. so a nunber of these cawarfs nay originally have fallen in with the Magelliuic svstem and been captured by the Galaxy.," This disk encompasses the locations of a number of dwarfs observed today around the Milky Way, so a number of these dwarfs may originally have fallen in with the Magellanic system and been captured by the Galaxy."
 The common rotation direction of the dwarfs in this ring provides a test o rule out any counter-crotating dwarts as originally associated with the Alaecllanic svstem., The common rotation direction of the dwarfs in this ring provides a test to rule out any counter-rotating dwarfs as originally associated with the Magellanic system.
 The extended disk-ofsatellites cannot be explained by the cavarts being vound to the LMC within the last two apogalacticons. and may have another origin.," The extended disk-of-satellites cannot be explained by the dwarfs being bound to the LMC within the last two apogalacticons, and may have another origin."
 In addition. the anomalous velocity and position of Leo I is not explained by this nechanisin. with no dwarfs in auv of the sinulations approaching the position. let alone the velocity. of Leo I. J.D.-IT. is supported by a Federation Fellowship from he Australian Research. Council.," In addition, the anomalous velocity and position of Leo I is not explained by this mechanism, with no dwarfs in any of the simulations approaching the position, let alone the velocity, of Leo I. J.B.-H. is supported by a Federation Fellowship from the Australian Research Council."
eigenfrequency.,eigenfrequency.
 In Section ?? we present our numerical computations for the stability of the exact solutions of the zero-th order problem by AmatoandBlasi(2005)., In Section \ref{sec:results} we present our numerical computations for the stability of the exact solutions of the zero-th order problem by \cite{amatoblasi2005}.
. In Section ??.. we will compare our results with other works in the literature. ancl briefly summarize our work.," In Section \ref{sec:discussion}, we will compare our results with other works in the literature, and briefly summarize our work."
 We give here. for future relerence. our basic equations.," We give here, for future reference, our basic equations."
 They are the conventional hyvdrodynanmice equations: which contain a term for (he momentum exchange between the fluid and the non-thermal particles represented by the gradient of the particle pressure 77. plus the usual Bolizimann equation in Skilling(1975): We assume D=Dip.p) to be a given function of p and p.," They are the conventional hydrodynamic equations: which contain a term for the momentum exchange between the fluid and the non-thermal particles represented by the gradient of the particle pressure $P_c$, plus the usual Boltzmann equation in \citet{skilling1975}: We assume $D = D(p,\rho)$ to be a given function of $\rho$ and $p$."
 We consider small-amplitucde perturbations around a homogeneous solution where the particles are supposed to exert a non-neegligible pressure., We consider small-amplitude perturbations around a homogeneous solution where the particles are supposed to exert a non-negligible pressure.
 First. we consider entropy perturbations.," First, we consider entropy perturbations."
 Perturbations ean be taken in the form so lo obtain. from the equation of entropy conservation. eq. 3..," Perturbations can be taken in the form so to obtain, from the equation of entropy conservation, eq. \ref{entropycons},"
 where α is the unperturbed fluid velocity in the x-direction., where $u$ is the unperturbed fluid velocity in the x-direction.
 Perturbation of the mass conservalion equation vields, Perturbation of the mass conservation equation yields
least correlation is observed for the frequency pair with the widest separation.,least correlation is observed for the frequency pair with the widest separation.
 In order to study the behaviour of profile components. we again define pulse wiudows as shown for PSR D1153]16 iu Fig. s.," In order to study the behaviour of profile components, we again define pulse windows as shown for PSR B1133+16 in Fig. \ref{prof1133}."
 These two coniponenuts are also only an approximation. since Kramer (1991) showed that the central bridge cussion should be modelled as a separate component. perhaps represcutine the eraze of an inner cone iu a nested cone structure.," These two components are also only an approximation, since Kramer (1994) showed that the central bridge emission should be modelled as a separate component, perhaps representing the graze of an inner cone in a nested cone structure."
 Generally. the correlation cocficicuts for the two profile conrponeuts (again in brackets) are larger than that for the full profile.," Generally, the correlation coefficients for the two profile components (again in brackets) are larger than that for the full profile."
 The only exception is for the correlation between 1112. ΣΠ. aud 1850. MIIz. where at both frequencies the leading component is heavily dominating.," The only exception is for the correlation between 1412 MHz and 4850 MHz, where at both frequencies the leading component is heavily dominating."
 Again. our results are consistent with those by Nardashey ct al. (," Again, our results are consistent with those by Kardashev et al. ("
1986) who also find the first component to be better correlated than the secoud.,1986) who also find the first component to be better correlated than the second.
 Manchester et al., Manchester et al.
" looked at this pulsar at three different frequency pairs. ie. 10928 MIIz. [D)5860. MIIZ and 9285600 ΠΕ. respectively,"," \nocite{mps89} looked at this pulsar at three different frequency pairs, i.e. 410–928 MHz, 410–5860 MHz and 928–5600 MHz, respectively."
 As Kardashey et al. (, As Kardashev et al. (
986). they performed a phase-resolved correlation analysis. fudiug again a better correlation for the first component.,"1986), they performed a phase-resolved correlation analysis, finding again a better correlation for the first component."
 While a proper coluparison is difficult due to tie difference in freqencies aud the lack of estimaed uncertainties. their Cl appears to show the least correlation beween 928 aud 5600 ΠΠ». while C2 exhibits he kmwvest correlaion coefficient for 110 and 58560 MIIz.," While a proper comparison is difficult due to the difference in freqencies and the lack of estimated uncertainties, their C1 appears to show the least correlation between 928 and 5600 MHz, while C2 exhibits the lowest correlation coefficient for 410 and 5860 MHz."
 SoLe O ‘this difference is most likely due to a frequeney-selective nulliug bemaviour of this pulsar., Some of this difference is most likely due to a frequency-selective nulling behaviour of this pulsar.
 We note that during «πι observations nulliug did not always occur simultaneously at all foir frequencies., We note that during our observations nulling did not always occur simultaneously at all four frequencies.
 As we will detail iu Bhat et al.. (," As we will detail in Bhat et al., ("
in prep.).,"in prep.),"
 while the majority of nulls are broadband. a sjeuificaut fraction of them occur oulv over a narrow frecuenev rouge.," while the majority of nulls are broadband, a significant fraction of them occur only over a narrow frequency range."
 It is clear from Fig., It is clear from Fig.
 29. that the radio spectra of PSR D0329|51 exhibits à 1naxinuni at around 300 MITz. close to or even above our lowest observing frequencies.," \ref{spectra} that the radio spectrum of PSR B0329+54 exhibits a maximum at around 300 MHz, close to or even above our lowest observing frequencies."
 In order to compare the single pulse spectra to the average radio spectrin. we therefore will not include this frequency in the process of fitting a power law spectrum Sv)xwa to the sinele pulse fux densities of this pulsar.," In order to compare the single pulse spectra to the average radio spectrum, we therefore will not include this frequency in the process of fitting a power law spectrum $S(\nu)\propto \nu^\alpha$ to the single pulse flux densities of this pulsar."
 The, The
otoplanets were introduced into the simulations.,protoplanets were introduced into the simulations.
 In. the case of Bal. the running average was started somewhat later.," In the case of Ba1, the running average was started somewhat later."
 The averages were calculated over. time periods of vpically 50 orbits at the centre of the box., The averages were calculated over time periods of typically $50$ orbits at the centre of the box.
 In cach case he average torques from the regions exterior to and interior o the protoplanet drag and accelerate. the protoplanet as expected., In each case the average torques from the regions exterior to and interior to the protoplanet drag and accelerate the protoplanet as expected.
 Although. as in the global simulations. luctuations in the one sided torques can be very large amounting to an order of magnitude or more greater than 1 typical average value. the averages tend. to approach reasonably steady values.," Although, as in the global simulations, fluctuations in the one sided torques can be very large amounting to an order of magnitude or more greater than the typical average value, the averages tend to approach reasonably steady values."
 Note that in a shearing box. symmetry considerations require that the mean torques from. re two sides of the cise should. ultimately be equal and opposite.," Note that in a shearing box, symmetry considerations require that the mean torques from the two sides of the disc should ultimately be equal and opposite."
 LLowever. some noise remains even after fifty orbits.," However, some noise remains even after fifty orbits."
 ‘The noise is stronger in the embedded cases and remains at 10 five to ten percent level after fifty orbits., The noise is stronger in the embedded cases and remains at the five to ten percent level after fifty orbits.
 Lhe resulting mean net torque which would be zero in a laminar sipulation sullers corresponding Uuetuations., The resulting mean net torque which would be zero in a laminar simulation suffers corresponding fluctuations.
 However. the effects. of," However, the effects of"
EGRET cataky. aud for many of these. we have used the likelihood test statistic (TS) maps available from the on-line catalog to generate the positional contours on our images.,"EGRET catalog, and for many of these, we have used the likelihood test statistic (TS) maps available from the on-line catalog to generate the positional contours on our images."
 Most of the maps used are based ou LGeV and above photous., Most of the maps used are based on 1GeV and above photons.
 Iu [our cases (CieV JQOOS-+7:301. GeV 10951L+6102. GeV J1837-0610. aud GeV JL856+0115) we used e 2 300MeV positional contotrs which were lly consistent. with the GeV contours. but P)eller constraiued.," In four cases (GeV J0008+7304, GeV J0241+6102, GeV J1837-0610, and GeV J1856+0115) we used the $>300$ MeV positional contours which were fully consistent with the GeV contours, but better constrained."
 Several soices are Lot the BEC catalog. mis-ilentilied. have ouly »)w-energv luaDs. Or are near sources Lot the BEG caalog (such as i the Cyenus 'egion).," Several sources are not in the 3EG catalog, mis-identified, have only low-energy maps, or are near sources not in the 3EG catalog (such as in the Cygnus region)."
 Fo “these we generatect lew TS maps. sine the orogram of Jolu Matον ancl Joe Esposio Gaeliked.LO. Matto Xela.," For these we generated new TS maps, using the program of John Mattox and Joe Esposito (jaelike5.49, Mattox et al."
 1996). OM 1aps of ICeV and above photons.," 1996), on maps of 1GeV and above photons."
 We included iu tle fits all neaby ποσος in the 3e ist. (courtesy h. Hartinan) which was used to c‘eate the 3rd. EGRET souve Catalog., We included in the fits all nearby sources in the $\sigma$ list (courtesy R. Hartman) which was used to create the 3rd EGRET source catalog.
 The fluxes derived. fixuu these fits are systeuatically lower tlat di1 LM. since a »ortion of tle GeV yhotous may be assigned o t]e softer sowces whicl were not iuclu«ed iu tle LM fits.," The fluxes derived from these fits are systematically lower than in LM, since a portion of the GeV photons may be assigned to the softer sources which were not included in the LM fits."
 Whe'e we jave refit the da we Ise lie ΠιNOS derived. from those [i," Where we have refit the data, we use the fluxes derived from those fits."
 Otherwise. we se1ie LA \alues.," Otherwise, we use the LM values."
 These are istecl in Table ble, These are listed in Table \ref{MULtab}.
 As aco15isteucy check. we lave also exani1ος] he TS uaps of MacomaudLamb( 2000). wl16i only iuclucdea sources which |acl a >30 Significauce 1n the GeV maps lor ie positioial fits.," As a consistency check, we have also examined the TS maps of \citet{ml00}, which only included sources which had a $>3\sigma$ significance in the GeV maps for the positional fits."
 In. general. the fits were similar exce(X for noticable Changes iu Colour slape of some of the sources witli so{ sources 1earby. as expected.," In general, the fits were similar except for noticable changes in contour shape of some of the sources with soft sources nearby, as expected."
 The 3EC catale lists photOL spectral iudices. aud for those sources witl finu BEC ids (see Table 1)). we rave inchiu those values iu Table 2..," The 3EG catalog lists photon spectral indices, and for those sources with firm 3EG ids (see Table \ref{OBStab}) ), we have included those values in Table \ref{MULtab}."
 All of the BEC sources were searcled for variability by Tompkins (1999). using the 7 statistic. which is the standard deviaion of the flux. divided by the average flux. and ence a measure of how valiable a sotyce is (as opposed to the more usua u lest. which measures how Icosistent a sources Ix ds with being constarο).," All of the 3EG sources were searched for variability by Tompkins (1999), using the $\tau$ statistic, which is the standard deviation of the flux divided by the average flux, and hence a measure of how variable a source is (as opposed to the more usual $\chi^2$ test, which measures how inconsistent a source's flux is with being constant)."
 The iuciviual IX 1ueasureiments used to determile 7 wele derived. from 3 parameter fits to he entire ibinued. likelihood «listriution o‘the ]ux above LOO MeV. A flux weis derived for each viewing period ( two weeks) where tle source was withiu 25° of the pointing center., The individual flux measurements used to determine $\tau$ were derived from 3 parameter fits to the entire unbinned likelihood distribution of the flux above 100 MeV. A flux was derived for each viewing period $\sim$ two weeks) where the source was within $25^{\circ}$ of the pointing center.
 Therefore. the timescale of the variability srobed is 1 month — ~2 wears.," Therefore, the timescale of the variability probed is $\sim 1$ month – $\sim 2$ years."
 The joulsars all tend to have 7~0.1. consistent within systeuatlic uncertainty with Q. w“hile dlazars tend o TrZLl.," The pulsars all tend to have $\tau\sim 0.1$, consistent within systematic uncertainty with 0, while blazars tend to $\tau \ga 1$."
 Extreme caution should je used when iuterpretiug the variability of sources iu crowded regious. since the ikelihoocl analysis may occasionally imisassigu R9LOLOLS. Lestting in time bins witli auomolo [unich or low luxes.," Extreme caution should be used when interpreting the variability of sources in crowded regions, since the likelihood analysis may occasionally misassign photons, resulting in time bins with anomolously high or low fluxes."
 Iu addition. variability in a nearby souce may result in an appareut variability of the source of interest.," In addition, variability in a nearby source may result in an apparent variability of the source of interest."
 With these warulngs. the 7 values. where available. are also listed in Table 2..," With these warnings, the $\tau$ values, where available, are also listed in Table \ref{MULtab}."
 Table 1. gives the observing parameters of all the fields in our survey., Table \ref{OBStab} gives the observing parameters of all the fields in our survey.
 The observations were taken over several vears. with differiug exposure tiuies.," The observations were taken over several years, with differing exposure times."
 Some of the archival observations had the GIS tu modes with limited spectral or spatial resolution and the inagine aud spectral analysis was adapted accoringly., Some of the archival observations had the GIS in modes with limited spectral or spatial resolution and the imaging and spectral analysis was adapted accordingly.
 Iu a lew cases. the SIS data were also ised.," In a few cases, the SIS data were also used."
 Teu of the images were obtained specifically for his campaign., Ten of the images were obtained specifically for this campaign.
 Iun these cases. the poiutings were based solely on the GeV positious.," In these cases, the pointings were based solely on the GeV positions."
 Positional and spect‘al iuformation ou X-ay sources found in these fields are given iu Table 3.., Positional and spectral information on X-ray sources found in these fields are given in Table \ref{NEWfit}.
 Some of the yolutines were based ou LMO97 values. and su»equent positional fits lave resulted in a significantly shifted error contour.," Some of the pointings were based on LM97 values, and subsequent positional fits have resulted in a significantly shifted error contour."
 Stellar sources witli soft spectra are Commo, Stellar sources with soft spectra are common
Molecule production rates were caleulated from a Laser(1957) model.,Molecule production rates were calculated from a \citet{H57} model.
 For a detailed explanation of how this model was applied to NAST data. please see Turner&Smith(1996).," For a detailed explanation of how this model was applied to KAST data, please see \citet{TS96}."
. Fluorescence efficiencies ave from Ixim.ΑHearn.&Cochran(1989) lor NUL. [or Cy and Cy. and Tatum(1984). lor CN.," Fluorescence efficiencies are from \citet{K+89} for NH, \citet{NS89} for $_2$ and $_3$, and \citet{T84} for CN."
 For NIIS. we used the blue band fluorescence efficiencies of Tegler&Wrvekoll(1939)... sealed to the newer red band efficiencies of INawakita&Watanabe(2002).," For $_2$ we used the blue band fluorescence efficiencies of \citet{TW89}, scaled to the newer red band efficiencies of \citet{KW02}."
". Following AIlearnetal.(1995).. the gas outflow velocity scales with heliocentric distance as 1.0xΑΙ)"" kins |,"," Following \citet{A+95}, the gas outflow velocity scales with heliocentric distance as $1.0 \times r_h({\rm AU})^{-0.5}$ km $^{-1}$."
 Sets of scale lengths were determined for (he NIL. NIIS. and Cs bands in each spectrum by experimenting wilh arange of possible values.," Sets of scale lengths were determined for the NH, $_2$, and $_2$ bands in each spectrum by experimenting with arange of possible values."
 Where (he best-fit scale lengths for NIIs bands blueweard of (0.12.0) noisily exceeded LOOX LO? km. the mean of the other cleaner scale lengths was used instead.," Where the best-fit scale lengths for $_2$ bands blueward of (0,12,0) noisily exceeded $\times$ $^3$ km, the mean of the other cleaner scale lengths was used instead."
 Scale lengths for the CN and CS bands followed from Turner&Smith(1996)., Scale lengths for the CN and $_3$ bands followed from \citet{TS96}.
". The scale lengths (applicable at the comets heliocentric distance rj,=0.754 AU). and the resulting gas production rates (Q) with 1-o error bars. are given in Table 2.. "," The scale lengths (applicable at the comet's heliocentric distance $r_h = 0.754$ AU), and the resulting gas production rates $Q$ ) with $\sigma$ error bars, are given in Table \ref{ProdRates}. “"
ΝΑ in Table 2. refers to an undefined production rate where the net fIux in a non-detected emission band was less than the adjacent continuum.,NA” in Table \ref{ProdRates} refers to an undefined production rate where the net flux in a non-detected emission band was less than the adjacent continuum.
 SOT report log Q(OII) = 27.33. while we did not detect OIL.," S07 report log $Q$ (OH) = 27.33, while we did not detect OH."
 Our production rate for NID is a factor of 3 higher than SOT. consistent with our smaller rj than S07. but our production rate for C» is of S0vs.," Our production rate for NH is a factor of 3 higher than S07, consistent with our smaller $r_h$ than S07, but our production rate for $_2$ is of S07's."
 Our upper limits for CN and Cy are consistent will S07., Our upper limits for CN and $_3$ are consistent with S07.
" 96P may be sputtering somewhat unevenly as its global eas production turis olf,", 96P may be sputtering somewhat unevenly as its global gas production turns off.
 The only other comet in the literature noted to be this deficient in CN and Co is Yanaka (1983r or C/1908 Y1: IXosai et al., The only other comet in the literature noted to be this deficient in CN and $_2$ is Yanaka (1988r or C/1998 Y1; Kosai et al.
 1988)., 1988).
 Yanaka was observed posi-perihelion in 1989 with the [/1.2 spectrograph at the University of Arizona 1.54-m Mount. Bigelow telescope 1992).," Yanaka was observed post-perihelion in 1989 with the f/1.2 spectrograph at the University of Arizona 1.54-m Mount Bigelow telescope \citep{F91,F92}."
. The observational parameters are listed in Table 3: where not given in (1992).. thev were looked up at the Minor Planet Comet Ephemeris provided by the LAU.," The observational parameters are listed in Table \ref{C1998Y1}; where not given in \citet{F92}, they were looked up at the Minor Planet Comet Ephemeris provided by the IAU."
" Comet Yanaka displavs a series of NII, emission bands from5300-3500A.", Comet Yanaka displays a series of $_2$ emission bands from.
. Fink's spectrum ol it and our spectrum of 96P/Machholz overlap from 5300-5800A.. in the region of the NIIS (0.10.0) and (0.11.0) bands.," Fink's spectrum of it and our spectrum of 96P/Machholz overlap from , in the region of the $_2$ (0,10,0) and (0,11,0) bands."
 Noticeably absent in the Yanaka spectrum are the CN 1-0. 2-0. 2-1.and 3-1 bands. and the prominent C5 Av=—1 band.," Noticeably absent in the Yanaka spectrum are the CN 1-0, 2-0, 2-1,and 3-1 bands, and the prominent $_2$ $\Delta {\rm v} = -1$ band."
collation of ? (fromthestudiesof:???)..,"collation of \citet{Fan08} \citep[from the studies of:][]{Huchra91,Barmby00,Perrett02}."
 These data cover ~50% of the confirmed old clusters., These data cover $\sim50\%$ of the confirmed old clusters.
 The currently available spectroscopy for M31’s clusters is biased towards the more massive (brighter) clusters., The currently available spectroscopy for M31's clusters is biased towards the more massive (brighter) clusters.
" However, LMXBs are known to reside primarily in more massive clusters (as discussed below), so this work provides metallicities for 72% of the LMXB hosting clusters."," However, LMXBs are known to reside primarily in more massive clusters (as discussed below), so this work provides metallicities for $\%$ of the LMXB hosting clusters."
 We also consider the (i--K) colour of these clusters from ?.., We also consider the -K) colour of these clusters from \citet{Peacock10}.
 These colours are dereddened using the values of ? and provide an alternative estimation of the metallicity of the clusters., These colours are dereddened using the values of \citet{Fan08} and provide an alternative estimation of the metallicity of the clusters.
" It can be seen from figure 4 that LMXBs favour redder, metal rich, clusters."," It can be seen from figure \ref{fig:lmxb_Z} that LMXBs favour redder, metal rich, clusters."
 A K-S test between the colour of all clusters and the LMXB hosting clusters suggests that there is a 98% likelihood that these clusters are drawn from different populations., A K-S test between the colour of all clusters and the LMXB hosting clusters suggests that there is a $\%$ likelihood that these clusters are drawn from different populations.
 For the spectroscopic metallicities this probability is 91%., For the spectroscopic metallicities this probability is $\%$.
" The statistical significance of this relationship is relatively weak, but is similar to that found in the previous studies of ? and ?.."," The statistical significance of this relationship is relatively weak, but is similar to that found in the previous studies of \citet{Bellazzini95} and \citet{Trudolyubov04}."
 A more significant metallicity effect has been previously observed in many other galaxies (e.g.??)..," A more significant metallicity effect has been previously observed in many other galaxies \citep[e.g.][]{Kundu02,Kim06}."
 There are several reasons why this relationship may be less obvious in M31., There are several reasons why this relationship may be less obvious in M31.
" Firstly, there are relatively few metal rich clusters in M31 compared with many early type galaxies."," Firstly, there are relatively few metal rich clusters in M31 compared with many early type galaxies."
 It should also be noted that the spectroscopic metallicities of M31’s clusters have relatively large errors (with a mean error of ~0.25)., It should also be noted that the spectroscopic metallicities of M31's clusters have relatively large errors (with a mean error of $\sim$ 0.25).
 The effect of this would be to weaken any genuine relationships between the clusters., The effect of this would be to weaken any genuine relationships between the clusters.
 In principle the colours of the clusters may give a more accurate measure of metallicity., In principle the colours of the clusters may give a more accurate measure of metallicity.
" However, the colours of M31’s clusters are complicated due to variable extinction across the galaxy."," However, the colours of M31's clusters are complicated due to variable extinction across the galaxy."
 It has also been proposed that decreasing metallicity may lead to hardening of the soft X-ray emission from GC LMXBs (??7)..," It has also been proposed that decreasing metallicity may lead to hardening of the soft X-ray emission from GC LMXBs \citep{Irwin99,Maccarone03,Maccarone04}."
" To investigate this, we perform a Spearman Rank test between the four X-ray hardness ratios (listed in table 2)) and the metallicity of a cluster."," To investigate this, we perform a Spearman Rank test between the four X-ray hardness ratios (listed in table \ref{tab:m31gc_2xmmi}) ) and the metallicity of a cluster."
 No strong correlations are observed., No strong correlations are observed.
" The only marginally significant correlation is between HR» and the metallicity, which has a probability of correlation of 92%."," The only marginally significant correlation is between $_{2}$ and the metallicity, which has a probability of correlation of $\%$."
" To investigate any potential relationships further, we split these data into metal rich ([Fe/H]> —0.7) and metal poor clusters."," To investigate any potential relationships further, we split these data into metal rich $[Fe/H]>-0.7$ ) and metal poor clusters."
 The choice of this split is based on the bimodal peaks in the metallicity identified by ?.., The choice of this split is based on the bimodal peaks in the metallicity identified by \citet{Perrett02}.
" The fluxes of the X-ray sources, as functions of hardness ratio for the rich and poor clusters, are shown in figure 5.."," The fluxes of the X-ray sources, as functions of hardness ratio for the rich and poor clusters, are shown in figure \ref{fig:lmxb_HR_Fx}."
 The most significant trend is identified between the metal rich and poor clusters was in the HR2 (0.5-1keV and 1-2keV)., The most significant trend is identified between the metal rich and poor clusters was in the $_{2}$ (0.5-1keV and 1-2keV).
" This relationship has a confidence of 99%, but is based primarily on only five metal rich clusters."," This relationship has a confidence of $\%$, but is based primarily on only five metal rich clusters."
" While significant, the observed relationship is weaker than the relatively strong relationship observed in"," While significant, the observed relationship is weaker than the relatively strong relationship observed in"
It is widelv believed that the 11-vear sunspot activity is produced and organized by large-scale magnetic fields generated somewhere in the deep convection zone.,It is widely believed that the 11-year sunspot activity is produced and organized by large-scale magnetic fields generated somewhere in the deep convection zone.
 Most of the solar dvnamo models suggest that the toroidal magnetic field that emerges on the surface and forms sunspots is generated near the bottom of the convection zone. in the tachocline or just beneath it in a convection overshoot laver. (see. e.g.. Choucdhuri 2007)).," Most of the solar dynamo models suggest that the toroidal magnetic field that emerges on the surface and forms sunspots is generated near the bottom of the convection zone, in the tachocline or just beneath it in a convection overshoot layer, (see, e.g., \citealp{choud-shu-dik,bra-rue:05,dikchar,bonnano,tob-wei:07}) )."
 The belief in a deep-seated solar dvnamo comes from the fact that (his region is sullicientlv stable. aud. can store magnetic flux despite the magnetic flux-tube buovancy effect (Parker.1975:Spiegel&Weiss.1980:vanBallegooijen.1982:SpruitRoberts.1983:vanDallegooijen&Choudhuri.1988: 1990).," The belief in a deep-seated solar dynamo comes from the fact that this region is sufficiently stable, and can store magnetic flux despite the magnetic flux-tube buoyancy effect \citep{par:75,spie-weiss:80,vball:82,spruit-rob:83,vball-choud:88,choud:90}."
. The tachocline represents a strong radial shear of the angular velocity., The tachocline represents a strong radial shear of the angular velocity.
 Yet. (ποπ diamagnetism (see. e.g.. Zeldovich. or kitchatinov&Rüdiger. 1992)) pumps the magnetic fields [rom (he intensively mixed interior of convection zone to its boundaries.," Yet, turbulent diamagnetism (see, e.g., \citealp{zeld:57} or \citealp{kit:91}) ) pumps the magnetic fields from the intensively mixed interior of convection zone to its boundaries."
 This effect. can substantially amplify the, This effect can substantially amplify the
"temperatures. Zip. nieasured with the two telescopes are related by the expression where OL is the FWIIM of the source. aud. Oxy, aud Og, are the instrumental IIPBWs.","temperatures, $T_{\rm MB}$, measured with the two telescopes are related by the expression where $\Theta_{\rm s}$ is the FWHM of the source, and $\Theta_{\rm 30m}$ and $\Theta_{\rm fcrao}$ are the instrumental HPBWs."
" From this equation one obtains the expression for O.: The values of ©, are isted in Table 7 aud the corresponding linear diameters. D. are given iu Table 9.."," From this equation one obtains the expression for $\Theta_{\rm s}$: The values of $\Theta_{\rm s}$ are listed in Table 7 and the corresponding linear diameters, $D$, are given in Table \ref{mvir-mcd}. ."
 The errors have been computed from Eq. (3)), The errors have been computed from Eq. \ref{eth}) )
 with the usual propagation of the statistical crrors and heuce depend upon the errors on Zip. which will be discussed iu Sect. 3.2..," with the usual propagation of the statistical errors and hence depend upon the errors on $T_{\rm MB}$, which will be discussed in Sect. \ref{stempden}."
" The mean values are Ο.~30"" aud Dz0.9 pe.", The mean values are $\Theta_{\rm s}\simeq30\arcsec$ and $D\simeq0.9$ pc.
" We stress that in all cases OQ, is consistent with the upper Πές obtained from the FCRAO maps.", We stress that in all cases $\Theta_{\rm s}$ is consistent with the upper limits obtained from the FCRAO maps.
 Also. for C31.LL the value derived iu this wav cau be compared with the direct estimate obtained from the cinission map iade Evith the IRAM. 30-11 telescope.," Also, for G31.41 the value derived in this way can be compared with the direct estimate obtained from the emission map made with the IRAM 30-m telescope."
 Figures 2 aud 30 show the maps of CO.1L obtained by integrating respectively the (65) and (87) enuission uuder the A —0 aud 1 ues.," Figures \ref{fmap65} and \ref{fmap87}
 show the maps of G31.41 obtained by integrating respectively the (6–5) and (8–7) emission under the $K$ =0 and 1 lines."
 For a Gaussian source. one can compute the decouvolved iup diameter fom the observed EWIIN," For a Gaussian source, one can compute the deconvolved clump diameter from the observed FWHM."
"E We find Ο.=29"" from the CIT;CoII((G5) map and OL=26"" from (57).", We find $\Theta_{\rm s}=29\arcsec$ from the (6–5) map and $\Theta_{\rm s}=26\arcsec$ from (8–7).
 These estimates are consistent within the uncertainties with that obtained from Eq. (3)).," These estimates are consistent within the uncertainties with that obtained from Eq. \ref{eth}) ),"
" ο.=32""+ S"", thus confirnning the reliabilitv of the method."," $\Theta_{\rm s}=32\arcsec\pm 8\arcsec$ , thus confirming the reliability of the method."
 No size estimate can be derived. from the CIT4IT(C1312) map because emission was detected ouly towards the central position: however. the upper μπες obtained at offsets of +12” ffrom the centro are consistent with the (1312) line intensity micasured towards the (0.0) position and the source cianeter estimated above.," No size estimate can be derived from the (13--12) map because emission was detected only towards the central position: however, the upper limits obtained at offsets of $\pm$ from the centre are consistent with the (13–12) line intensity measured towards the (0,0) position and the source diameter estimated above."
 We cau also compare our results with those derived frou CO. (Iofuer et al., We can also compare our results with those derived from $^{17}$ O (Hofner et al.
 2000) and CUS (Cesaroni et al., 2000) and $^{34}$ S (Cesaroni et al.
 1991): iu the former. the angular diameters are slightly ereater (~20% )) than those estimated by us. with the oulv ↸∖⊼∏∖↻↑↕∪∐∪↕≯≼∶∐∣∙↓⊤∙↖↖⇁↕∐↸⊳∐↕↴∖↴↑↖↖↽∪↑↕⋯↸∖↴∖↴↕⋜∐⋅∶↴∙⊾↸∖↥⋅↕∐≼⊲↓⊤≼≓≽∶↕∐ ↑∐↸∖↕⋜↧↑↑↸∖↥⋅⊓⋯⊳↸∖↥⋅∙↕∐↴∖↴↑↸∖⋜∥↧∙↑∐↸∖⋜↧∐∶↴∙⊾∏↕⋜∐⋅↴∖↴↕∑↸∖↴∖↴⋜∐⋅↸∖∿⋅↱↗∩↖⋰∣⋰⊲∓↙ ↴∖↴," 1991): in the former, the angular diameters are slightly greater $\sim$ ) than those estimated by us, with the only exception of G10.47, which is two times larger in $^{17}$ O; in the latter tracer, instead, the angular sizes are $\sim$ smaller with respect to."
⋯⋜↧∐↸∖↥⋅↖↖↽↕↑↕⊔⋅↸∖↴∖↴⋉∖↸⊳↑↑∪≼⊲∐∶⋝≼⊲⊐∐∙∙∖↖⊽↸∖↴∖↴∐⋜↧∐↸⊳∪↕⋯∖↴⋝⋯⊳↨↘↽ to this poiut iu Sect. 1.2.., We shall come back to this point in Sect. \ref{sint}.
 From the aneular diameters obtained from Eq. (3)).," From the angular diameters obtained from Eq. \ref{eth}) ),"
 we derived the rotation temperature aud total column density of the nunolecules by meaus of the population diagram method (see e.g. Hollis 1982. Olani et al.," we derived the rotation temperature and total column density of the molecules by means of the population diagram method (see e.g. Hollis 1982, Olmi et al."
 1993). which assuines the eas to be in local thermodvuamicalequilibriuu (LTE).," 1993), which assumes the gas to be in local thermodynamicalequilibrium (LTE)."
 Such an assuniptiou is believed to work verv well for, Such an assumption is believed to work very well for
Lacy 2001). TORS (Willott ct al.,"Lacy 2001), 7CRS (Willott et al."
 2008: Laev et al., 2003; Lacy et al.
 1999) and TexOx-1000: hereafter POOL (Lll Rawlings 2003)., 1999) and TexOx-1000; hereafter TOOT (Hill Rawlings 2003).
 The locations of all four radio surveys on the radio redshift plane are shown in Fig 1.., The locations of all four radio surveys on the radio $~-~$ redshift plane are shown in Fig \ref{fig1}.
 Details of the ZP5 sample can be found in Table 1., Details of the ZP5 sample can be found in Table 1.
 Actlitionally. Table 2 [ists those objects which satisfied the redshift and. racio luminosity criteria for the ZP5 sample. but were excluded due to their broad-emission line spectra.," Additionally, Table 2 lists those objects which satisfied the redshift and radio luminosity criteria for the ZP5 sample, but were excluded due to their broad-emission line spectra."
 The TOOT objects were selected. from. a preliminary version of the survey., The TOOT objects were selected from a preliminary version of the survey.
 They are therefore a subset of all the TOOT sources meeting the radio [ux density and sky. area selection criteria., They are therefore a subset of all the TOOT sources meeting the radio flux density and sky area selection criteria.
 Broad-line objects were excluded. in the case of POOT 125213310 alter LIST imaging and during," Broad-line objects were excluded, in the case of TOOT 1252+3310 after HST imaging and during"
cach other at all energy rauges. with lobes exteud aloug he magnetic field lines.,"each other at all energy ranges, with lobes extend along the magnetic field lines."
 The density of the accelerated articles at the connection-point separating region (in he middle of the plane) is clearly much smaller. although here is still a concentration of low-energy accelerated articles there since the acceleration of low-cucrey articles is rapid aud effieieut at perpendicular shocks.," The density of the accelerated particles at the connection-point separating region (in the middle of the plane) is clearly much smaller, although there is still a concentration of low-energy accelerated particles there since the acceleration of low-energy particles is rapid and efficient at perpendicular shocks."
 At higher cucrev ranges (uiddle and bottom). the lack of accelerated particles may be interpreted as due to the act that the acceleration to high energies takes time.," At higher energy ranges (middle and bottom), the lack of accelerated particles may be interpreted as due to the fact that the acceleration to high energies takes time."
 Figure 23 illustrates the profiles of the density of accelerated particles for differcut energy ranges at 2=0 (top) aud :=x (bottom)., Figure 3 illustrates the profiles of the density of accelerated particles for different energy ranges at $z = 0 $ (top) and $z=\pi $ (bottom).
 Iu each panel. the black solic lines show the density of low cnerey particlesy. (3.0)<pipy< LO) the blue dashed lines show the density of intermediate euergev particles (8.0<p/pg 10.0). and red dot dashed lines show the density of particles witli ligh energies (15.0<p/py 30.0).," In each panel, the black solid lines show the density of low energy particles $3.0<p/p_0<4.0$ ), the blue dashed lines show the density of intermediate energy particles $8.0<p/p_0<10.0$ ), and red dot dashed lines show the density of particles with high energies $15.0<p/p_0<30.0$ )."
 In counectiou-poin separating regious τ=0 (top). it can be seen that while the downstream distribution of low cucrev particles is roughly a conustaut. the deusitv of particles with higher energies mnerease as a function of distance downstream from the shock.," In connection-point separating regions $z = 0 $ (top), it can be seen that while the downstream distribution of low energy particles is roughly a constant, the density of particles with higher energies increase as a function of distance downstream from the shock."
" These particles are uot accelerated at the shock laver in the ceuter of the plane but iu the ""hot spots”."," These particles are not accelerated at the shock layer in the center of the plane but in the “hot spots""."
" At 2=x (bottom). the density of particles of all energies decreases as a function of distance. which indicates the accelerated particles diffusive away frou the ""hot spots”."," At $z = \pi $ (bottom), the density of particles of all energies decreases as a function of distance, which indicates the accelerated particles diffusive away from the “hot spots""."
 Since the lich energy particles have larger ciffision cocticicnts than the particles with low euerev. it is easier for them to transport to the middle of the plane.," Since the high energy particles have larger diffusion coefficients than the particles with low energy, it is easier for them to transport to the middle of the plane."
 The profile at +=0 is similar to Voyagers observation of anomalous cosuuic ravs (ACRs) at the termination shock and the Weliosheath (Stoneetal.2005:Ciiuinesetal.2008) which shows the intensity of the ACRs is still increasing aud the energy spectrum is uufoldiug over a large distance after entering the Ieliosheath.," The profile at $z = 0$ is similar to 's observation of anomalous cosmic rays (ACRs) at the termination shock and the Heliosheath \citep{Stone2005,Cummings2008} which shows the intensity of the ACRs is still increasing and the energy spectrum is unfolding over a large distance after entering the Heliosheath."
 The sale plysics has discussed by Jokipi&νότα(2008). where “hot spot” of energetic particles is produced by the spatial variation of tle injection of the source particles.," The same physics has discussed by \citet{Jokipii2008AIP}, where “hot spot"" of energetic particles is produced by the spatial variation of the injection of the source particles."
 Iu our curreut work. the concentration of energetic particles are a consequence of particle accelerated in a shock containing large-scale magnetic variation.," In our current work, the concentration of energetic particles are a consequence of particle accelerated in a shock containing large-scale magnetic variation."
 The top panel iu Figure L| represeuts the positions in + direction and the times as 8001 as the particles reached a certain momentum p.—3py., The top panel in Figure $4$ represents the positions in $z$ direction and the times as soon as the particles reached a certain momentum $p_c = 3p_0$.
 We show that particles are accelerated mainly at the connection-point couvereiue reeion., We show that particles are accelerated mainly at the connection-point converging region.
 There are also particles accelerated at middle of he plane because the particles can eau cucrev rapidly at perpendicular or highly oblique shock due to the sanallucss of perpendicular diffusion cocficient (Jokipiü 1987). however. the further acceleration is suppressed x the effect that the charged particles travel away from he connection-poiut separating region. see also the top xumel in Fieure 5.," There are also particles accelerated at middle of the plane because the particles can gain energy rapidly at perpendicular or highly oblique shock due to the smallness of perpendicular diffusion coefficient \citep{Jokipii1987ApJ}, however, the further acceleration is suppressed by the effect that the charged particles travel away from the connection-point separating region, see also the top panel in Figure 5."
 It is clear that since the particles ead to follow the naenetic fiek lines. wheu the field Ine conuection points separate from caci other as field convects through the shock. the particles travel mainly along magnetic field and away from the iniddle of the aue.," It is clear that since the particles tend to follow the magnetic field lines, when the field line connection points separate from each other as field convects through the shock, the particles travel mainly along magnetic field and away from the middle of the plane."
 The characteristic time for a fied line convect roni upstream to downstream 7.=D/U-~1. therefore here is no significant acceleration iu tlic! quiddle of the aue after f=ΤΠ.," The characteristic time for a field line convect from upstream to downstream $\tau_c = D/U_1 \sim 1$, therefore there is no significant acceleration in the middle of the plane after $t = \tau_c$."
" Some of the particles can eget more acceleration traveling from other region o ""hot spots”."," Some of the particles can get more acceleration traveling from other region to “hot spots""."
 Figure | bottom shows the distance partices traveled in z direction from its original places |::g| versus time when particle ect accelerated at a certain αιαον (p.=3py)., Figure 4 $bottom$ shows the distance particles traveled in $z$ direction from its original places $|z-z_0|$ versus time when particle get accelerated at a certain energy $p_c = 3p_0$ ).
" It shows many particles are accelerated close to their original position. which is related to the acceleration in the ""hot spot”."," It shows many particles are accelerated close to their original position, which is related to the acceleration in the “hot spot""."
" Nevertheless. there are also a number of particles travel from the commection point separating reeion to ""hot spot” aud ect further acceleration. which is represented by the particles that travel a large distance iu z direction."," Nevertheless, there are also a number of particles travel from the connection point separating region to “hot spot"" and get further acceleration, which is represented by the particles that travel a large distance in z direction."
 Figure 5 shows the same plot as Figure L. except here the critical momentum is p.=10.099.," Figure 5 shows the same plot as Figure 4, except here the critical momentum is $p_c = 10.0p_0$."
 It is shown again in Figure 5 top that most of particles are accelerated to hielt enerev are im the hot spot., It is shown again in Figure 5 $top$ that most of particles are accelerated to high energy are in the hot spot.
 IToxcever. as opposite to Figure lfop. there are very few particles accelerated at the ceuter of plane since energetie particles iiore transport away frou the middle region aud the time available is not long enough.," However, as opposite to Figure 4 $top$, there are very few particles accelerated at the center of plane since energetic particles more transport away from the middle region and the time available is not long enough."
 For a quick estimate. the acceleration time 1s approximately. Therefore for most of particles. they do uot have sufficient time to be accelerated to high cnereics at the center.," For a quick estimate, the acceleration time is approximately, Therefore for most of particles, they do not have sufficient time to be accelerated to high energies at the center."
 A nunber of particles accelerated at the ceuter will travel to the “hot spot” aud eet more acceleration. as shown in Figure 5 botftoin.," A number of particles accelerated at the center will travel to the “hot spot"" and get more acceleration, as shown in Figure 5 $bottom$."
 Clearly. this preseuts different pictures of particle acceleration by the shock contain 2-D spatial maguetic feld variations. indicates the resulting distribution function is spatially dependent.," Clearly, this presents different pictures of particle acceleration by the shock contain 2-D spatial magnetic field variations, indicates the resulting distribution function is spatially dependent."
 In Figure 6 we show the steady state ehnereyv spectra obtained im the regionstop: [Ul<r<OB m02«oIxc gx] (black solid line). and [0.1<r<(0.3. 0.41<2 OL (ereen dashed line) audboffon:: xoax1.0. π002<2< x] (black solid line). and[0.8 [0.8<r<1.0. πμ... 0.1] (green. dashed line).," In Figure 6 we show the steady state energy spectra obtained in the regions: $0.1<x<0.3$, $\pi-0.2<z<\pi$ ] (black solid line), and $0.1<x<0.3$, $-0.1<z<0.1$ ] (green dashed line) and: $0.8<x<1.0$, $\pi-0.2<z<\pi$ ] (black solid line), and $0.8<x<1.0$, $-0.1<z<0.1$ ] (green dashed line)."
 It is shown that the spatial difference among distribution functions at differeut locations caused by large-scale magnetic feld variation is considerable., It is shown that the spatial difference among distribution functions at different locations caused by large-scale magnetic field variation is considerable.
" The black lines in both top plot and bottom plot. which correspoud to the ""hot spots”. show power-luv like distributious except at high energies."," The black lines in both top plot and bottom plot, which correspond to the “hot spots"", show power-law like distributions except at high energies."
 At high euergies. the particles will leave the simulation domain before gain chough cucerey which causes the roll over im distribution function. this roll over is mainly caused by a finite distance to upstreani boundary.," At high energies, the particles will leave the simulation domain before gain enough energy which causes the roll over in distribution function, this roll over is mainly caused by a finite distance to upstream boundary."
 For other locations. the 2-D effect we discussed will produce the modification im distribution functions.," For other locations, the 2-D effect we discussed will produce the modification in distribution functions."
 The most pronounced effect cam be found at the nose ofthe shock (exeen lines). iu the top panel the distribution of which shows a suppression of acceleration at all the euergies.," The most pronounced effect can be found at the nose of the shock (green lines), in the top panel the distribution of which shows a suppression of acceleration at all the energies."
 This insufficient acceleration is most promünent iu the ranee of 6/—12py., This insufficient acceleration is most prominent in the range of $6-12 p_0$.
 At these energies the acceleration time scales are' longer than the time for the field. liue convection swi»e the particles away from the counection-poiut separatiis reedon. as we discussed above.," At these energies the acceleration time scales are longer than the time for the field line convection swipe the particles away from the connection-point separating region, as we discussed above."
 The bottom plot srow that deep downstream the spectrin of accelerated ouwticles is simular at lich energies since the iobilitv o these particles., The bottom plot show that deep downstream the spectrum of accelerated particles is similar at high energies since the mobility of these particles.
 The previous discussion has established the effect of a spatially varvius upstream magnetic field on the, The previous discussion has established the effect of a spatially varying upstream magnetic field on the
An interesting comparison can be made with the velocity distribution of the peak of the C IV line. studied in higher redshift SDSS quasars by. Richardsetal...(2002).,"An interesting comparison can be made with the velocity distribution of the peak of the C IV line, studied in higher redshift SDSS quasars by \citet{richardsetal02}."
. Working with composite spectra generated [rom large samples of objects divided by C IV blieshilt relative to the Mg II line. these authors found that more blueshifted CIV lines occurred as a result of the red wing of the line being obsceured.," Working with composite spectra generated from large samples of objects divided by C IV blueshift relative to the Mg II line, these authors found that more blueshifted C IV lines occurred as a result of the red wing of the line being obscured."
 Thev suggested that this obscuration is due to a central screen of finite geometrical Chickuess. which is optically thin seen [ace-on but becomes thicker with increasing angle.," They suggested that this obscuration is due to a central screen of finite geometrical thickness, which is optically thin seen face-on but becomes thicker with increasing angle."
 Note that (his is. in some sense. opposite to the scheme proposed here. in which the objects with the largest blueshifts are those seen closest to [ace-on.," Note that this is, in some sense, opposite to the scheme proposed here, in which the objects with the largest blueshifts are those seen closest to face-on."
 In any. case. the geometry ancl kinematics of the C IV-emitting clouds and the ο THIJ|-emitting clouds may be different. and so the explanations may not be inconsistent.," In any case, the geometry and kinematics of the C IV-emitting clouds and the [O III]-emitting clouds may be different, and so the explanations may not be inconsistent."
 Characteristics of AGNs with blueshifted [O IL] lines have been reported previously., Characteristics of AGNs with blueshifted [O III] lines have been reported previously.
 llowever. conclusions have been based ou small samples. with heterogeneous data. or requiring dubious assumptions.," However, conclusions have been based on small samples, with heterogeneous data, or requiring dubious assumptions."
 In this study. a large. uniform sample of AGNs [rom the SDSS DRI have been analyzed.," In this study, a large, uniform sample of AGNs from the SDSS DR1 have been analyzed."
 Objects with discrepant |O LI} redshifts have been identified and subsamples constructed to explore the properties of objects populating different regions in the [O III] relative velocity distribution., Objects with discrepant [O III] redshifts have been identified and subsamples constructed to explore the properties of objects populating different regions in the [O III] relative velocity distribution.
 Analvsis of these samples vields the following conclusions., Analysis of these samples yields the following conclusions.
 1) A significant fraction. as many as half. of all AGNs show |O III] emission Chat is blueshifted to the point that the line peak is shifted by tens to hundreds of kins /.," 1) A significant fraction, as many as half, of all AGNs show [O III] emission that is blueshifted to the point that the line peak is shifted by tens to hundreds of km $^{-1}$."
 Ie This shift is a true shift relative to the svstemic velocity. as determined from the low ionization narrow [orbidden lines.," 2) This shift is a true shift relative to the systemic velocity, as determined from the low ionization narrow forbidden lines."
 ALA The AGNs with the largest bIueshifted |O LU] lines tend to have high Τομ. using black hole masses determined from their luminosities and IL? widths.," 3) The AGNs with the largest blueshifted [O III] lines tend to have high $_{Edd}$, using black hole masses determined from their luminosities and $\beta$ widths."
 IIowever. this is not a light correlation: there are high L/Lyegy objects Chat do not show blueshifts. aud lower L/Lgg objects Chat clo.," However, this is not a tight correlation; there are high $_{Edd}$ objects that do not show blueshifts, and lower $_{Edd}$ objects that do."
 4) The single anomalous property common to all the objects with highly blueshifted [O III] emission is the large width of the |O III] lines., 4) The single anomalous property common to all the objects with highly blueshifted [O III] emission is the large width of the [O III] lines.
 These average more than broader than those in similar objects that have [O HI] close to the svstemic velocity., These average more than broader than those in similar objects that have [O III] close to the systemic velocity.
 5) Conversely. the blueshifted |O III] lines do not tend to be any more asymmetric or anv weaker in strength than the non-blueshifted ones.," 5) Conversely, the blueshifted [O III] lines do not tend to be any more asymmetric or any weaker in strength than the non-blueshifted ones."
 All the subsamples show a similar tendency (to have a sharp red edge to the line ancl a blue edge that is shallow. or has a wing," All the subsamples show a similar tendency to have a sharp red edge to the line and a blue edge that is shallow, or has a wing"
of three dillerent bases: Ανατ diffusion map with Av —45. and diffusion map with A—150.,"of three different bases: Asa07, diffusion map with $K$ =45, and diffusion map with $K$ =150."
 We also compare parameter estimates to those estimated with the MPAJZJIIU data base., We also compare parameter estimates to those estimated with the MPA/JHU data base.
 Our goal in this section is to study how the choice of basis alfects the final parameter estimates for a large set of real galaxy spectra., Our goal in this section is to study how the choice of basis affects the final parameter estimates for a large set of real galaxy spectra.
 Our data sample consists of spectra from. ten arbitrarily chosen spectroscopic plates of SDSS DRG 0274 inclusive. ancl 0286: AXdelman-MeCarthyetal. 2008)) that are classified. as galaxy spectra.," Our data sample consists of spectra from ten arbitrarily chosen spectroscopic plates of SDSS DR6 $-$ 0274 inclusive, and 0286; \citealt{Adelman2008}) ) that are classified as galaxy spectra."
 The goal is to test. our methods on a sample that is large enough that we include ealaxies with a broad range of star formation and metallicity histories but not so large that analysis is computationally cumbersome., The goal is to test our methods on a sample that is large enough that we include galaxies with a broad range of star formation and metallicity histories but not so large that analysis is computationally cumbersome.
 In a future work. we will present results [or the more than T00k galaxy spectra in SDSS DIRT.," In a future work, we will present results for the more than 700k galaxy spectra in SDSS DR7."
 We remove spectra from this sample by applying three cuts., We remove spectra from this sample by applying three cuts.
 Phe first. motivated by aperture considerations. is to analyse only spectra whose SDSS redshift estimates = 0.05.," The first, motivated by aperture considerations, is to analyse only spectra whose SDSS redshift estimates $\geq$ 0.05."
 Second. we determine the proportion of the 3850 wavelength bins that are Hagged as bad.," Second, we determine the proportion of the 3850 wavelength bins that are flagged as bad."
 LÉthis proportion exceedsLOM... we remove the spectrum from the sample: if not. we retain the speetrum for further analysis.," If this proportion exceeds, we remove the spectrum from the sample; if not, we retain the spectrum for further analysis."
 Third. we select. galaxy spectra with a SDSS redshift confidence level : 0.35.," Third, we select galaxy spectra with a SDSS redshift confidence level $\geq$ 0.35."
 These cuts leave us with a sample of 3046 ealaxy spectra., These cuts leave us with a sample of 3046 galaxy spectra.
 We bring all spectra to rest. [rame using the SDSS redshift estimates., We bring all spectra to rest frame using the SDSS redshift estimates.
 In the fitting routines. we exclude any spectral bins with SDSS Lag : 2.," In the fitting routines, we exclude any spectral bins with SDSS flag $\geq$ 2."
 This eliminates any sky residuals. bad. pixels. ancl artefacts from the data reduction.," This eliminates any sky residuals, bad pixels, and artefacts from the data reduction."
 We additionally mask the pixels in the regions within and around emission lines as in CidFernandesetal.(2005)., We additionally mask the pixels in the regions within and around emission lines as in \citet{CF2005}.
. Results of the S'EARLIGILUFE spectral fits give a mean N2/N of 1.03 for each of the three bases used. close to a value of 1 that would. be expected if wavelength bin [luxes were independently distributed Gaussian random variables.," Results of the STARLIGHT spectral fits give a mean $\chi^2/N_{\lambda}$ of 1.03 for each of the three bases used, close to a value of 1 that would be expected if wavelength bin fluxes were independently distributed Gaussian random variables."
 Note that this value varies considerably from the mean value of 0.78 found in the analysis of 50362 SDSS spectra by CidFernandesetal. (2005)., Note that this value varies considerably from the mean value of 0.78 found in the analysis of 50362 SDSS spectra by \citet{CF2005}.
. This cdüllerence can be attributed to our careful handling of spectral bin error estimates in our rebinning of the spectra to à dispersion of 1 measurement perA., This difference can be attributed to our careful handling of spectral bin error estimates in our rebinning of the spectra to a dispersion of 1 measurement per.
. The SPARLIGIUT fitting routine is used to [fit all 3046 SDSS spectra with each of the three bases., The STARLIGHT fitting routine is used to fit all 3046 SDSS spectra with each of the three bases.
 Each basis vields parameter estimates that are substantially different., Each basis yields parameter estimates that are substantially different.
 In Fig., In Fig.
 10 we plot cach galaxy's logiZ.32 versus (log/.). estimate for each basis.," \ref{sdss:tZ} we plot each galaxy's $\log \langle Z_* \rangle_L$ versus $\langle
\log t_* \rangle_L$ estimate for each basis."
" There are several notable cdilferences in the lowZahnlogfo, plane for each basis."," There are several notable differences in the $\log \langle Z_* \rangle_L-\langle
\log t_* \rangle_L$ plane for each basis."
 First. both diffusion map bases produce estimates that are tightly centered around an increasing linear trend while the Asa07 estimates are dilfusely: spread: around. such a trend.," First, both diffusion map bases produce estimates that are tightly centered around an increasing linear trend while the Asa07 estimates are diffusely spread around such a trend."
 Moreover. the direction of discrepancy in the Ανατ estimates from. the linear trend. corresponds. exactly with the direction. of degeneracy between old. metal-poor and. voung. metal-rich ealaxies.," Moreover, the direction of discrepancy in the Asa07 estimates from the linear trend corresponds exactly with the direction of degeneracy between old, metal-poor and young, metal-rich galaxies."
 This suggests that the observed variability along this direction is not due to the physics of these galaxies. but rather is caused by confusion stemming from the choice of basis.," This suggests that the observed variability along this direction is not due to the physics of these galaxies, but rather is caused by confusion stemming from the choice of basis."
 secondly. the slopes of the estimated trends. produced bv the diffusion map bases (0.146. for A—45. ancl 0.180 [or Av —150) are considerably smaller than the slope of the trend in the Asa07 estimates (0.250).," Secondly, the slopes of the estimated trends produced by the diffusion map bases (0.146 for $K$ =45 and 0.180 for $K$ =150) are considerably smaller than the slope of the trend in the Asa07 estimates (0.250)."
 These estimates have implications for the physical models that govern. galaxy evolution., These estimates have implications for the physical models that govern galaxy evolution.
 Finally. the A —45 cilfusion map basis estimates no voung. metal-poor galaxies. showing a sharp decline from denselv-populated regions of the parameter space to vacant regions.," Finally, the $K$ =45 diffusion map basis estimates no young, metal-poor galaxies, showing a sharp decline from densely-populated regions of the parameter space to vacant regions."
 ‘This suggests that this small number of prototypes is not sullicient to cover the parameter space: particularly. voung. metal-poor SSP's have been neglected in the basis.," This suggests that this small number of prototypes is not sufficient to cover the parameter space; particularly, young, metal-poor SSPs have been neglected in the basis."
 Next we compare kincmatic parameter estimation., Next we compare kinematic parameter estimation.
 Fig., Fig.
 1l shows that the Asa07 basis tends to consistently estimate slightlv larger values of fy than either. diffusion map basis.," \ref{sdss:kin}
 shows that the Asa07 basis tends to consistently estimate slightly larger values of $A_V$ than either diffusion map basis."
 On average. AsaQ7T estimates of chy are 0.045 larger than dillusion map A —45 estimates and 0.024 larger than clilfusion map A —150 estimates.," On average, Asa07 estimates of $A_V$ are 0.045 larger than diffusion map $K$ =45 estimates and 0.024 larger than diffusion map $K$ =150 estimates."
" Estimates of a, are consistent. between all three bases.", Estimates of $\sigma_*$ are consistent between all three bases.
 Finally. we compare age-binned SEL estimates found by each basis.," Finally, we compare age-binned SFH estimates found by each basis."
" Like CidFernandesetal.(2005)... we condense the SELL to three parameters: old. ro (6j>10"" vr) intermediate. 4 (10xfj10(0 vr) and voung. ay (£j<109 vr)."," Like \citet{CF2005}, we condense the SFH to three parameters: old, $x_{\textrm o}$ $t_j>10^9$ yr), intermediate, $x_{\textrm i}$ $10^8\le t_j \le 10^9$ yr), and young, $x_{\textrm y}$ $t_j<10^8$ yr)."
 Plots of diffusion map estimates of cach component versus Asaü7 estimates are in Fig. 12.., Plots of diffusion map estimates of each component versus Asa07 estimates are in Fig. \ref{sdss:sfh}.
 Phe estimated SEL show a high degree of correspondence between the bases., The estimated SFHs show a high degree of correspondence between the bases.
 On average. each diffusion map basis obtains slightly higher estimates of ro and slightly lower estimates of both «5 and Jue ," On average, each diffusion map basis obtains slightly higher estimates of $x_{\textrm o}$ and slightly lower estimates of both $x_{\textrm i}$ and $x_{\textrm y}$."
We compare the SDSS parameters estimated with the three different choices of ΛΙΙΙ basis with parameters, We compare the SDSS parameters estimated with the three different choices of STARLIGHT basis with parameters
The radio profile of a pulsar may include the precursor - a peculiar Component preceding the main pulse by up to a few tens degrees in longitude.,The radio profile of a pulsar may include the precursor - a peculiar component preceding the main pulse by up to a few tens degrees in longitude.
 “Phe presence of such a component is more or less firmly. ascertained for the Crab »ulsar (Campbell.Lleiles&Rankin 1970).. PSR D1055-52 (MeCulloch.ctal.1976)... PSR. Bis22-09 1981).. and the Vela pulsar. (INrishnamohan&Downs 1983).," The presence of such a component is more or less firmly ascertained for the Crab pulsar \citep*{c70}, , PSR B1055-52 \citep{m76}, PSR B1822-09 \citep*{f81}, and the Vela pulsar \citep{kd83}."
 The precursor dillers substantially from he components of the main pulse by its spectral anc polarization properties., The precursor differs substantially from the components of the main pulse by its spectral and polarization properties.
 In the main pulse. the componen widths ancl separations generally. increase with wavelength. signifving the overall broadening of the emission cone.," In the main pulse, the component widths and separations generally increase with wavelength, signifying the overall broadening of the emission cone."
 A he same time. the width of the precursor and its separation rom the main pulse remains unchanged over a broa requency range.," At the same time, the width of the precursor and its separation from the main pulse remains unchanged over a broad frequency range."
 The spectrum of the precursor is. also distinct., The spectrum of the precursor is also distinct.
 In the pulsar DIS22-09. it is unusually Dat. (Fowleretal.1981:Gil 1994)... whereas in the Crab pulsar i is extremely steep (Manchester1971).," In the pulsar B1822-09, it is unusually flat \citep{f81,g94}, , whereas in the Crab pulsar it is extremely steep \citep{m71}."
. Phe most distinctive feature of the precursor is its complete linear. polarization. in contrast to the main pulse emission. which is typically somewhat depolarized due to simultaneous presence of the two orthogonally polarized modes.," The most distinctive feature of the precursor is its complete linear polarization, in contrast to the main pulse emission, which is typically somewhat depolarized due to simultaneous presence of the two orthogonally polarized modes."
 The single-pulse studies have further revealed some fascinating features of the precursor emission., The single-pulse studies have further revealed some fascinating features of the precursor emission.
 Lhe precursor intensity shows strong pulse-to-pulse Ductuations., The precursor intensity shows strong pulse-to-pulse fluctuations.
 In. the Vela pulsar. the intensity variations allect the longitudinal location of the precursor: the stronger the precursor. the larger is its separation from the main pulse (Ixrishnamohan&Downs 1983).," In the Vela pulsar, the intensity variations affect the longitudinal location of the precursor: the stronger the precursor, the larger is its separation from the main pulse \citep{kd83}."
. In PSR. DIS22-09. the precursor appears pronounced only in strong enough pulses: weak pulses. instead. include the interpulse component. which laes the main pulse by about 180 in longitude (Fowleretal.1981:Fowler&Wright1982:Giletal. 1994).," In PSR B1822-09, the precursor appears pronounced only in strong enough pulses; weak pulses, instead, include the interpulse component, which lags the main pulse by about $180^\circ$ in longitude \citep{f81,f82,g94}."
 Because of sporadic character of the precursor emission. it does not necessarily form a component in the average profile.," Because of sporadic character of the precursor emission, it does not necessarily form a component in the average profile."
 For example. the pulsars BOO50|OS and. D1656|14 do not exhibit a precursor in the average profile. but occasional pulses do incorporate strong subpulses at. the extreme leading edge of the pulse. (Llankins&Corces1981:Weltevredeetal. 2006).," For example, the pulsars B0950+08 and B1656+14 do not exhibit a precursor in the average profile, but occasional pulses do incorporate strong subpulses at the extreme leading edge of the pulse \citep{hc81,welt06}."
.. Thus. in a broad. sense. the precursor phenomenon can be defined as a sporadic activity in the longitudinal region preceding the main pulse.," Thus, in a broad sense, the precursor phenomenon can be defined as a sporadic activity in the longitudinal region preceding the main pulse."
 One can expect that the precursors defined in this way are much more tvpical of pulsars than is usually believed., One can expect that the precursors defined in this way are much more typical of pulsars than is usually believed.
 ]t is interesting to note that the precursor phenomenon appears related. το other manifestations of intensity modulation in pulsar radio emission., It is interesting to note that the precursor phenomenon appears related to other manifestations of intensity modulation in pulsar radio emission.
 ltecent single-pulse observations of PSR. 1326-6700. (Wang.Manchester.&Johnston2007) reveal the precursor component arising exceptionally during the nulls of the main pulse. when the intensity of the latter drops below the detection level.," Recent single-pulse observations of PSR J1326-6700 \citep*{w07} reveal the precursor component arising exceptionally during the nulls of the main pulse, when the intensity of the latter drops below the detection level."
 Furthermore. several other pulsars of the above survey exhibit occasional alternation between the two forms of the average profile. (mode changing phenomenon). the mocal profiles being mainlydillerentin the intensity of the leading component relatively to that of the rest of the profile.," Furthermore, several other pulsars of the above survey exhibit occasional alternation between the two forms of the average profile (mode changing phenomenon), the modal profiles being mainlydifferentin the intensity of the leading component relatively to that of the rest of the profile."
as long as the conditions are stable during both the visibility and the photometry measurement.,as long as the conditions are stable during both the visibility and the photometry measurement.
 Since at the different wavelengths of our two VLTI datasets different temperatures. radii and presumably different types of emitting matter dominate the observed flux. we split the following discussion according to these wavelength bands.," Since at the different wavelengths of our two VLTI datasets different temperatures, radii and presumably different types of emitting matter dominate the observed flux, we split the following discussion according to these wavelength bands."
 Our data suggest that IRS 7 could be resolved (re. has a visibility of less than unity) in the A-band at the short VLTI baseline used., Our data suggest that IRS 7 could be resolved (i.e. has a visibility of less than unity) in the $K$ -band at the short VLTI baseline used.
 We fitted à wavelength-independent diameter of a uniform-dise model to the NIR-data., We fitted a wavelength-independent diameter of a uniform-disc model to the NIR-data.
 This model. adequate for the given accuracy and size of the data-set. minimizes the y7-metric Qu= 0.9) at (2.6+0.4) mas. which is a remarkable result. because such a best-fit diameter is larger than expected.," This model, adequate for the given accuracy and size of the data-set, minimizes the $\chi ^2$ -metric $\chi^2_{\rm red} \approx 0.9$ ) at $(2.6\,\pm\,0.4)$ mas, which is a remarkable result, because such a best-fit diameter is larger than expected."
 However. the total error including systematics like the variation of the interferometric transfer function and the small number of interferograms can increase the uncertainty on the derived diameter up to the order of 1.5 mas (AMBER team. private communication).," However, the total error including systematics like the variation of the interferometric transfer function and the small number of interferograms can increase the uncertainty on the derived diameter up to the order of $\pm$ 1.5 mas (AMBER team, private communication)."
 Repeated measurements at a similar setup. seeing. and instrument performance are required to further investigate in detail the systematics of the here used AMBER setup.," Repeated measurements at a similar setup, seeing, and instrument performance are required to further investigate in detail the systematics of the here used AMBER setup."
 To calculate the diameter of the photosphere of an IRS 7- supergiant of early MI spectral type at the distance to the GC (~ 7.6 Κρο). we assume Tey=3400 K. and a bolometric correction BCK=2.7 (??)..," To calculate the diameter of the photosphere of an IRS 7-like supergiant of early MI spectral type at the distance to the GC $\sim$ 7.6 kpc), we assume $T_{\rm eff}\approx\,3400$ K, and a bolometric correction $BC_{\rm K}\,=2.7$ \citep{1996AJ....112.1988B,2003ApJ...597..323B}."
 Recent PSF-fitted VLT photometry and extinction estimations are K=7.4 and Ax=3.7 for a 2005 dataset of ours.," Recent PSF-fitted VLT photometry and extinction estimations are $K\,=\,7.4$ and $A_{\rm K}\,=\,3.7$ for a 2005 dataset of ours."
 This is about a magnitude fainter than the Blum values based on 1997 data., This is about a magnitude fainter than the Blum values based on 1997 data.
 Since the typical precison for these estimates is about 0.1 mag for photometry and extinction. this discrepancy points to a significant photometric variability. and follows the trend reported by ?..," Since the typical precison for these estimates is about 0.1 mag for photometry and extinction, this discrepancy points to a significant photometric variability, and follows the trend reported by \citet{1999ApJ...523..248O}."
 Therefore we use our recent photometry measurements here. being relatively close in time to our AMBER measurement.," Therefore we use our recent photometry measurements here, being relatively close in time to our AMBER measurement."
 We derive a stellar radius of about (1000x150) ΑΟ. or an angular diameter of + 0.2) mas at the GC distance.," We derive a stellar radius of about $\,\pm\,150)$ $R_\odot$ or an angular diameter of $\,\pm\,0.2$ ) mas at the GC distance."
 Recent interferometric studies of a Ori. the nearby red supergiant of spectral type MI-21Ia-Ibe similar to IRS 7. showed a larger measured radius at NIR (and MIR) wavelengths than the expected stellar photosphere due to a surrounding molecular gas shell of significantly lower temperature (about 2000 K) and a radius of about 1.4 times the radius of the stellar photosphere (??)..," Recent interferometric studies of $\alpha$ Ori, the nearby red supergiant of spectral type M1-2Ia-Ibe similar to IRS 7, showed a larger measured radius at NIR (and MIR) wavelengths than the expected stellar photosphere due to a surrounding molecular gas shell of significantly lower temperature (about 2000 K) and a radius of about 1.4 times the radius of the stellar photosphere \citep{2004A&A...421.1149O,2007A&A...474..599P}."
 The increased — 1.6€0.2 mas diameter of such an « Ori-like. warm molecular gas shell around the photosphere of IRS 7 would still be significantly smaller than the uniform-dise. diameter derived. here. from the AMBER data. but the respective theoretical visibility of (0.96+ 0.01) lies within the total error of our observation.," The increased $\sim$ $\,\pm\,0.2$ mas diameter of such an $\alpha$ Ori-like, warm molecular gas shell around the photosphere of IRS 7 would still be significantly smaller than the uniform-disc diameter derived here from the AMBER data, but the respective theoretical visibility of $0.96\,\pm\,0.01$ ) lies within the total error of our observation."
 Without a more precise dataset of repeated AMBER measurements allowing for cross-calibration to minimize this total error of about 1.5 mas we cannot determine the significance of contributions of other (and larger) shells than the photosphere to the NIR flux of IRS 7., Without a more precise dataset of repeated AMBER measurements allowing for cross-calibration to minimize this total error of about 1.5 mas we cannot determine the significance of contributions of other (and larger) shells than the photosphere to the NIR flux of IRS 7.
 However. astrophysics also can be responsible for intrinsically lower thar expected visibilities.," However, astrophysics also can be responsible for intrinsically lower than expected visibilities."
 The visibility drops. if in addition to the flux of a putative circumstellar molecular shell the radiatior of more extended warm dust has been resolved out by the interferometer (e.g.observedinthesupergiantIRC+10420..?).," The visibility drops, if in addition to the flux of a putative circumstellar molecular shell the radiation of more extended warm dust has been resolved out by the interferometer \citep[e.g. observed in the supergiant \object{IRC~+10420},."
 Indeed. a significant flux contribution of cooler. extended dust is seen in the MIDI data discussed below.," Indeed, a significant flux contribution of cooler, extended dust is seen in the MIDI data discussed below."
 Furthermore. a change in optical depth due to molecular band-heads betweer 2.2 and 2.4 jm can contribute to an apparent size increase at these wavelengths.," Furthermore, a change in optical depth due to molecular band-heads between 2.2 and 2.4 $\mu$ m can contribute to an apparent size increase at these wavelengths."
 In terms of phase-referencing several aspects have to be considered., In terms of phase-referencing several aspects have to be considered.
 As long as the visibility is high enough the SNR of the correlated flux is high and a stable phase-reference i5 provided., As long as the visibility is high enough the SNR of the correlated flux is high and a stable phase-reference is provided.
 But here we show data on the shortest VLTI baseline only., But here we show data on the shortest VLTI baseline only.
 The uniform-dise model (2.4 mas diameter) predicts a visibility of 0.45 at the longest UT-baseline (130 m)., The uniform-disc model (2.4 mas diameter) predicts a visibility of 0.45 at the longest UT-baseline (130 m).
 That means. only half of the correlated flux will be seen at such long baselines reducing the SNR. if the model is applicable.," That means, only half of the correlated flux will be seen at such long baselines reducing the SNR, if the model is applicable."
 Furthermore. any resolvable asymmetry in the brightness distribution of IRS 7 would lead to non-zero closure-phases and à complex visibility function.," Furthermore, any resolvable asymmetry in the brightness distribution of IRS 7 would lead to non-zero closure-phases and a complex visibility function."
 This hampers the usage IRS 7 as phase-reference unless the position-angle dependence of this phase is known., This hampers the usage IRS 7 as phase-reference unless the position-angle dependence of this phase is known.
 Furthermore if 1deed warm molecular gas and dust shells make up the NIR-visibility of IRS 7. temporal variations of optical depth and radial size in such shell can result m significant visibility changes and would have to be know! if IRS 7 shall be used as visibility calibrator in a dual- experiment.," Furthermore if indeed warm molecular gas and dust shells make up the NIR-visibility of IRS 7, temporal variations of optical depth and radial size in such shell can result in significant visibility changes and would have to be known if IRS 7 shall be used as visibility calibrator in a dual-field experiment."
 More observational data similar to the one presented here is needed to answer these questions in detail., More observational data similar to the one presented here is needed to answer these questions in detail.
" But since IRS 7 is by far the brightest star in the NIR. located within the central 5 "". and according to our results compact enough to give a strong interferometric signal on a 50 m baseline. we can confirm it to be the prime candidate for future dual-star phase-referencing experiments in the GC."," But since IRS 7 is by far the brightest star in the NIR, located within the central 5 $\arcsec$, and according to our results compact enough to give a strong interferometric signal on a 50 m baseline, we can confirm it to be the prime candidate for future dual-star phase-referencing experiments in the GC."
 As suggested by previous VLT/VISIR imaging and mentioned in the introduction. IRS 7 surrounded by significant amounts of warm dust. radiating in the MIR.," As suggested by previous VLT/VISIR imaging and mentioned in the introduction, IRS 7 surrounded by significant amounts of warm dust, radiating in the MIR."
 It i5 however surprising that our MIDI experiment revealed average N-band visibilities as low as 0.2., It is however surprising that our MIDI experiment revealed average $N$ -band visibilities as low as 0.2.
 Lacking detailed a priori knowledge about the dust morphology of IRS 7. observed at a nominal interferometric angular resolution of about 45 mas. such visibility amplitudes can be interpreted in two related ways focusing on the flux measurement and on the spatial scales probed. (," Lacking detailed a priori knowledge about the dust morphology of IRS 7, observed at a nominal interferometric angular resolution of about 45 mas, such visibility amplitudes can be interpreted in two related ways focusing on the flux measurement and on the spatial scales probed. ("
1) A flat visibility spectrum as in Fig.,1) A flat visibility spectrum as in Fig.
 2 is created by an unresolved. (cireum-)stellar point source radiating of the total flux plus a more extended and smooth brightness distribution the flux of which is completely resolved out by tbe interferometer. and appears only in the total flux spectrum (upper panel in Fig. 2)).," \ref{fig:2} is created by an unresolved, (circum-)stellar point source radiating of the total flux plus a more extended and smooth brightness distribution the flux of which is completely resolved out by tbe interferometer, and appears only in the total flux spectrum (upper panel in Fig. \ref{fig:2}) )."
 Assuming a Gaussian intensity profile for the extended flux with the constraint of contributing less than of its flux to the visibility measurement leads to a, Assuming a Gaussian intensity profile for the extended flux with the constraint of contributing less than of its flux to the visibility measurement leads to a
ie. orbital migration inwards. ancl svstems will be broken-up.,"i.e. orbital migration inwards, and systems will be broken-up."
 The hard/soft limit [or binaries in our cluster simulations is roughlv 60 AU and for the planetary systems it is more like 0.1 AU.," The hard/soft limit for binaries in our cluster simulations is roughly $60\,$ AU and for the planetary systems it is more like $0.1\,$ AU."
 Considering this in conjunction with the relatively low munber density. of stars in the simulations performed so far it is not surprising (hat we have vet to observe hardening of close planetary orbits., Considering this in conjunction with the relatively low number density of stars in the simulations performed so far it is not surprising that we have yet to observe hardening of close planetary orbits.
 Exchange interactions alter the observed. distribution of orbital characteristics in a fairly random manner although it is more likely for a wide svstem to be involved in such an event., Exchange interactions alter the observed distribution of orbital characteristics in a fairly random manner although it is more likely for a wide system to be involved in such an event.
 Contrary (o recent claims (Bonnelletal.2001:Smith&Bonnell2001). we find that Iree-[loating planets can form a significant population in stellar clusters.," Contrary to recent claims \citep{bon01,smi01} we find that free-floating planets can form a significant population in stellar clusters."
 This is based on the results of open cluster size N-body simulations but is expected to be even more likely in the case of elobular clusters., This is based on the results of open cluster size $N$ -body simulations but is expected to be even more likely in the case of globular clusters.
 While it should be stressed (hat the detection of free-floating planets in M22. is preliminary. and also speculative. il suggests that at least 100. planets were formed for every star.," While it should be stressed that the detection of free-floating planets in M22 is preliminary, and also speculative, it suggests that at least 100 planets were formed for every star."
 This may sound implausible but is in fact supported by recent simulations., This may sound implausible but is in fact supported by recent simulations.
 Ida&Ixokubo(2001) have shown that in a protoplanetary disk where the surface densitv of the solid component is low. the isolation mass of planets is small ancl many (erresüal planets can form.," \citet{ida01} have shown that in a protoplanetary disk where the surface density of the solid component is low, the isolation mass of planets is small and many terrestial planets can form."
 It is also possible that protoplanetary disks having lower metalliitv than solar would form many earth-like planets - perhaps 50-100 per star (Shigeru Ida. private communication).," It is also possible that protoplanetary disks having lower metallicity than solar would form many earth-like planets - perhaps 50-100 per star (Shigeru Ida, private communication)."
 A population of free-floating sub-stellar objects has also been detected in (he voung cluster σ Orionis (Zapatero-Osorioetal...2000)., A population of free-floating sub-stellar objects has also been detected in the young cluster $\sigma$ Orionis \citep{zap00}.
. The possibility. has been raised (hat these may. be formed as such (Boss2001).. i.e. not attached to a parent star.," The possibility has been raised that these may be formed as such \citep{bos01}, i.e. not attached to a parent star."
 We agree wilh Davies&Sietrdsson(2001) Chat subsequent survevs for planetary svstems should be conducted in clusters less dense that 47 Tuc. such as metal-rich. open clusters.," We agree with \citet{dav01} that subsequent surveys for planetary systems should be conducted in clusters less dense that 47 Tuc, such as metal-rich open clusters."
 Observations of a metal-rich. globular cluster should help determine whether the lack of planetary svstems in 47 Tuc is due to the metallicity of the cluster or dvnamieal interactions., Observations of a metal-rich globular cluster should help determine whether the lack of planetary systems in 47 Tuc is due to the metallicity of the cluster or dynamical interactions.
 We note (hat a planet has been detected within a binary pulsar svstem in AI (Thorset(etal.1999) which is metal-poor compared to 47 Tuc (Ilarris.1996)., We note that a planet has been detected within a binary pulsar system in M4 \citep{tho99} which is metal-poor compared to 47 Tuc \citep{har96}.
. As we expand the parameter space of our N-bocly study many of the interesting issues regarding planetary svstems in star clusters will be addressed., As we expand the parameter space of our $N$ -body study many of the interesting issues regarding planetary systems in star clusters will be addressed.
 Of particular importance will be the inclusion of svstems with multiple planets per star (Murray&Holman2001)., Of particular importance will be the inclusion of systems with multiple planets per star \citep{mur01}.
. Full realisation of the capabilities of the GRAPE-6 hardware when the 1 Tílop board becomes available will allow larger particle numbers. and consequently more planetary systems. to be studied per simulation.," Full realisation of the capabilities of the GRAPE-6 hardware when the $1\,$ Tflop board becomes available will allow larger particle numbers, and consequently more planetary systems, to be studied per simulation."
 This will improve (he statistical significance of our results considerably., This will improve the statistical significance of our results considerably.
from Fig. 21..,"from Fig. \ref{fit3198},"
 which shows the best-fit self-consistent disk-halo decomposition together with the observed rotation curve., which shows the best-fit self-consistent disk-halo decomposition together with the observed rotation curve.
 However. the model has a certain difficulty in fitting the second and third data-points. which remain higher than the best-fit self-consistent rotation curve.," However, the model has a certain difficulty in fitting the second and third data-points, which remain higher than the best-fit self-consistent rotation curve."
 Clearly. this could be ascribed to the exponential modeling of the density profile of the visible matter. which. as noticed before. does not take into account the small bulge and the gas present in NGC 3198.," Clearly, this could be ascribed to the exponential modeling of the density profile of the visible matter, which, as noticed before, does not take into account the small bulge and the gas present in NGC 3198."
 Since these two data-points are those that define the value of the ratio Ro//r for NGC 3198. Fig.," Since these two data-points are those that define the value of the ratio $R_{\Omega}/h$ for NGC 3198, Fig."
 7 confirms that the best-fit self-consistent model has a slightly higher value for this ratio., \ref{figromega} confirms that the best-fit self-consistent model has a slightly higher value for this ratio.
 Note also that the properties of the best-fit self-consistent decomposition are quite different from those found in the parametric analysis. with the best-fit model characterized by a disk of intermediate weight.," Note also that the properties of the best-fit self-consistent decomposition are quite different from those found in the parametric analysis, with the best-fit model characterized by a disk of intermediate weight."
 As is evident from Fig. 21..," As is evident from Fig. \ref{fit3198},"
 the disk contribution to the rotation curve is Important in the inner parts of the system., the disk contribution to the rotation curve is important in the inner parts of the system.
 However. with its 66. the best-fit self-consistent model remains below the classical maximum-disk solutions that van Albada et al. (," However, with its $\beta\approx 6$, the best-fit self-consistent model remains below the classical maximum-disk solutions that van Albada et al. ("
1985). for example. place at59.,"1985), for example, place at $\beta\gtrapprox 9$."
 This paper has addressed the construction of self-consistent models for a dark matter distribution assumed to be isothermal. in the presence of a zero-thickness disk.," This paper has addressed the construction of self-consistent models for a dark matter distribution assumed to be isothermal, in the presence of a zero-thickness disk."
" The models have then been applied to interpret the properties of observed rotation curves. with special attention to the issues of conspiracy and degeneracy that are known to affect their disk-halo decomposition,"," The models have then been applied to interpret the properties of observed rotation curves, with special attention to the issues of conspiracy and degeneracy that are known to affect their disk-halo decomposition."
 We argue that what has been learned from the study of the strictly isothermal case should be applicable to the case of dark matter distributions characterized by a quasi-isothermal inner region (as is the case for the results of collisionless violent relaxation)., We argue that what has been learned from the study of the strictly isothermal case should be applicable to the case of dark matter distributions characterized by a quasi-isothermal inner region (as is the case for the results of collisionless violent relaxation).
 It would be interesting to test the results on the dark matter οistributions predicted by current cosmological models. which οefinitely favor a density profile asymptotic to ο).," It would be interesting to test the results on the dark matter distributions predicted by current cosmological models, which definitely favor a density profile asymptotic to $r^{-3}$."
 This test οould be performed with an approach similar to the one adopted —n this paper. provided that we had a physically justified οistribution function to start from.," This test could be performed with an approach similar to the one adopted in this paper, provided that we had a physically justified distribution function to start from."
 In particular. it would be —nteresting to test to what extent the cosmologically predicted distributions could be reconciled with the existence of cases. such as that of NGC 3198. in which the rotation curve remains very flat in a wide radial range.," In particular, it would be interesting to test to what extent the cosmologically predicted distributions could be reconciled with the existence of cases, such as that of NGC 3198, in which the rotation curve remains very flat in a wide radial range."
 Note that this paper has considered the impact of a visible matter distribution on the distribution of dark matter., Note that this paper has considered the impact of a visible matter distribution on the distribution of dark matter.
 A study of the dynamical role of the dark halo in shaping the distribution of the visible matter would require considering a formation scenario that we do not wish to address here., A study of the dynamical role of the dark halo in shaping the distribution of the visible matter would require considering a formation scenario that we do not wish to address here.
 The main results obtained in this paper are the following:, The main results obtained in this paper are the following:
"The Oklo constraints on the variation of fine-structure constant have null results 20].. therefore Combining Eq.(13)). Eq.(15)) aud Eq.(16)). we obtain Comparing theoretical calculation Eq.(11)) with the result from experimental data Eq.(17)). we cau have the conclusion preliminarily that SR, cau indeed settle the iuconsistence between the Oklo aud the QSO observational results.","The Oklo constraints on the variation of fine-structure constant have null results \cite{Oklo1,Oklo2,Oklo3,Oklo4,Oklo5,Oklo6}, therefore Combining \ref{QSO-1}) ), \ref{equal}) ) and \ref{oklo-var}) ), we obtain Comparing theoretical calculation \ref{Oklo-trans}) ) with the result from experimental data \ref{result-1}) ), we can have the conclusion preliminarily that ${\cal SR}_{c,R}$ can indeed settle the inconsistence between the Oklo and the QSO observational results."
 Cio a step further. we cau estimate tlie radius of the Universe from the coutrast between Eq.(11)) aud Eq.(17)) roughly Here Ry~10! Mpe is the radius (or horizou) of present observable Uuiverse.," Go a step further, we can estimate the radius of the Universe from the contrast between \ref{Oklo-trans}) ) and \ref{result-1}) ) roughly Here $R_0\sim 10^4$ Mpc is the radius (or horizon) of present observable Universe."
" It is wort! ioticiug that Eq.(18)) shows SR, is Cousistent with the available cosmological observations ou the Ly."," It is worth noticing that \ref{R}) ) shows ${\cal SR}_{c,R}$ is consistent with the available cosmological observations on the $R_0$."
" Iu couclusiou. S,5 is really a candidate of the solution to the inconsistence betweel he observational results of the QSO absorption lines aud ofthe Oklo natural reactor ou the variation of the fiue-structure constant. which is very dillerent. Crom the Einsteins Specia Relativity."," In conclusion, ${\cal SR}_{c,R}$ is really a candidate of the solution to the inconsistence between the observational results of the QSO absorption lines and of the Oklo natural reactor on the variation of the fine-structure constant, which is very different from the Einstein's Special Relativity."
" Furthermore. we obtain a favorable evidence to SR, from the coutrast of the heoretical assessinent. with the observational data. that is. the radius of the Universe. I. is ereater than the radius (horizon) of the observable Universe. Ry."," Furthermore, we obtain a favorable evidence to ${\cal SR}_{c,R}$ from the contrast of the theoretical assessment with the observational data, that is, the radius of the Universe, $R$, is greater than the radius (horizon) of the observable Universe, $R_0$ ."
" It is auticipated that as uore experimental methods are applied aud more precise observational data are obtainect. SR,p wil be confronted with wore stringent tests. even be proved or disproved."," It is anticipated that as more experimental methods are applied and more precise observational data are obtained, ${\cal SR}_{c,R}$ will be confronted with more stringent tests, even be proved or disproved."
 Similarly. as SA. develops. we will have deeper insight into its application to various experiments. inclucling the experiments ou the variation of the fine-structure coustaut.," Similarly, as ${\cal
SR}_{c,R}$ develops, we will have deeper insight into its application to various experiments, including the experiments on the variation of the fine-structure constant."
 We would like to thank Professor Hau-Yiu Cuo. Chao-Guane Huaug. Zhan Xu. and Xiug-Clhiaug Song for {μοι helpful diseussious aud suggestions.," We would like to thank Professor Han-Yin Guo, Chao-Guang Huang, Zhan Xu, and Xing-Chang Song for their helpful discussions and suggestions."
 Oue of us (MLY) wishes to ackuowledge Professor Huan-Wu Peng for introducing the Dirac large numbers hypothesis to us., One of us (MLY) wishes to acknowledge Professor Huan-Wu Peng for introducing the Dirac large numbers hypothesis to us.
 The work is supported iu part by National Natural Science Fouudation of China uuder Grant Numbers 90103021. and by the PhD ProgramFuuds of the Education Ministry of China under Grant Number 200203580I0.," The work is supported in part by National Natural Science Foundation of China under Grant Numbers 90403021, and by the PhD ProgramFunds of the Education Ministry of China under Grant Number 20020358040."
corona is more extended.,corona is more extended.
 The best fit solution to the X-ray data in the ultra-soft state corresponds to a corona of radius Κ.Ξ8x10' em =30ry (for a 20 bblack hole)., The best fit solution to the X-ray data in the ultra-soft state corresponds to a corona of radius $R_{\rm{c}}=8\times 10^{7}$ cm $\approx 30~r_{\rm{g}}$ (for a 20 black hole).
 By keeping the total bolometric luminosity constant (Lpot=3.6x10? ere sv). the level of emission and the spectrum in the energy band can be reproduced if the radius of the corona Αι>10!em (Fig. 7)).," By keeping the total bolometric luminosity constant $L_{\rm{bol}}=3.6\times 10^{38}$ erg $^{-1}$ ), the level of emission and the spectrum in the energy band can be reproduced if the radius of the corona $R_{\rm{c}}\gtrsim 10^{10}~\rm{cm}$ (Fig. \ref{sp_corona}) )."
 These results are consistent with the detailed calculation of gamma-ray absorption above the disk inhomogeneous in the full isotropization limit. see Sect. 22)).," These results are consistent with the detailed calculation of gamma-ray absorption above the disk inhomogeneous in the full isotropization limit, see Sect. \ref{sect_wind}) )."
 Some spectral changes appear in X-rays because of the reduction in the compactness of the corona., Some spectral changes appear in X-rays because of the reduction in the compactness of the corona.
 Fig., Fig.
 7. shows it will be difficult to reconcile the flat X-ray spectrum at 100 keV seen in very soft states (produced by electrons when the compactness 1s high) with significant gamma-ray emission (which requires low compactness to avoid gamma-ray attenuation. by pair production)., \ref{sp_corona} shows it will be difficult to reconcile the flat X-ray spectrum at 100 keV seen in very soft states (produced by electrons when the compactness is high) with significant gamma-ray emission (which requires low compactness to avoid gamma-ray attenuation by pair production).
 Note also that the spectrum could be changed due to anisotropic effects and inhomogeneities not taken into account in this model., Note also that the spectrum could be changed due to anisotropic effects and inhomogeneities not taken into account in this model.
 It is difficult to imagine a very extended corona since most of the gravitational potential energy (90%)) remains in the region within 30r. around the compact object., It is difficult to imagine a very extended corona since most of the gravitational potential energy ) remains in the region within $30~r_{\rm{g}}$ around the compact object.
 The simulations in Fig., The simulations in Fig.
 7. assumes no magnetic field., \ref{sp_corona} assumes no magnetic field.
" For magnetic energy density at equipartition with the radiation in the corona. the magnetic field is about Ba,~5x10° G (for R.=8x10 em)."," For magnetic energy density at equipartition with the radiation in the corona, the magnetic field is about $B_{\rm{eq}}\sim 5\times 10^6~$ G (for $R_{\rm{c}}=8\times 10^7~$ cm)."
 Synchrotron radiation becomes the dominant processes at high energies. but the shape of the escaping high-energy spectrum changes only slightly.," Synchrotron radiation becomes the dominant processes at high energies, but the shape of the escaping high-energy spectrum changes only slightly."
 The energy of the absorption cut-off remains magnetic field independent. hence the constraints on the size of the corona are unchanged.," The energy of the absorption cut-off remains magnetic field independent, hence the constraints on the size of the corona are unchanged."
 In addition. the high-energy cut-off of the intrinsic synchrotron spectrum cannot exceed c/o=70 MeV (where ay is the fine structure constant. see ?)) due to synchrotro losses. hence too low to account for the high-energy emission.," In addition, the high-energy cut-off of the intrinsic synchrotron spectrum cannot exceed $m_{\rm{e}}c^2/\alpha_{\rm F}\approx 70~$ MeV (where $\alpha_{\rm F}$ is the fine structure constant, see \citealt{1983MNRAS.205..593G}) ) due to synchrotron losses, hence too low to account for the high-energy emission."
 This limit is calculated assuming no relativistic Doppler boosting and that the cooling timescale synchrotron emission faa equals the acceleration timescale of particles in the corona which cannot be shorter than the Larmor timescale 5j. assumption usually made in diffuse shock acceleration.," This limit is calculated assuming no relativistic Doppler boosting and that the cooling timescale synchrotron emission $t_{\rm{syn}}$ equals the acceleration timescale of particles in the corona which cannot be shorter than the Larmor timescale $t_{\rm{L}}$, assumption usually made in diffuse shock acceleration."
 This balance between acceleration and cooling implies also that it is very difficult to accelerate particles at high energies 2?)).," This balance between acceleration and cooling implies also that it is very difficult to accelerate particles at high energies \citealt{1984ARA&A..22..425H,2002PhRvD..66b3005A}) )."
" For the equipartition magnetic field strength. the condition f,=face SIVES Vinay5(9mizc[AeBog)7=5x 10"". allowing gamma-ray emission to a few tens of GeV only."," For the equipartition magnetic field strength, the condition $t_{\rm{syn}}\geq t_{\rm{acc}}$ gives $\gamma_{\rm{max}}\leq (9 m^2_{\rm{e}}c^4/4e^3 B_{\rm{eq}})^{1/2}= 5\times 10^4$ , allowing gamma-ray emission to a few tens of GeV only."
" To accelerate particles to Ya,=2x10°. the magnetic fielc should not exceed ~3x10° G. These estimates are basec on the optimistic assumption that the acceleration efficiency defined as jj=E,/eBe equals | (where Ες is the synchrotror energy losses and e is the charge of the electron)."," To accelerate particles to $\gamma_{\rm{max}}=2\times 10^5$, the magnetic field should not exceed $\sim 3\times 10^5~$ G. These estimates are based on the optimistic assumption that the acceleration efficiency defined as $\eta=\dot{E_{\rm s}}/eBc$ equals 1 (where $\dot{E_{\rm s}}$ is the synchrotron energy losses and $e$ is the charge of the electron)."
 The constraint on the magnetic field strength in the corona could be ever more stringent than what is given here., The constraint on the magnetic field strength in the corona could be even more stringent than what is given here.
 The magnetic fielc strength at equipartition is also sufficiently high to quench the development of pair cascade., The magnetic field strength at equipartition is also sufficiently high to quench the development of pair cascade.
 We conclude that the gamma-ray emission measured by has probably not a coronal origin., We conclude that the gamma-ray emission measured by has probably not a coronal origin.
 High-energy gamma-ray emission in Cygnus X-3 seems to be related to the soft X-ray state. when the X-ray spectrum is dominated by a bright accretion disk component.," High-energy gamma-ray emission in Cygnus X-3 seems to be related to the soft X-ray state, when the X-ray spectrum is dominated by a bright accretion disk component."
 Gamma rays should be significantly absorbed by soft X-rays emitted by the inner (hottest) parts of the accretion disk. unless the gamma-ray source lies far enough from the disk.," Gamma rays should be significantly absorbed by soft X-rays emitted by the inner (hottest) parts of the accretion disk, unless the gamma-ray source lies far enough from the disk."
 The apparent lack of absorption feature in the spectrum measured by indicates that high-energy gamma rays should be located atleast ~105-10? em away from the acereting star. depending on the inclination of the system.," The apparent lack of absorption feature in the spectrum measured by indicates that high-energy gamma rays should be located at least $\sim 10^8$ $10^{10}~$ cm away from the accreting star, depending on the inclination of the system."
 These conclusions are not affected by absorption of X-rays in the stellar wind. since this process becomes significant at larger distances >10'° em.," These conclusions are not affected by absorption of X-rays in the stellar wind, since this process becomes significant at larger distances $\gtrsim 10^{10}~$ cm."
 Thomson seattering with free electrons in the wind could redistribute and isotropize the X-ray emission above the disk and affect the gamma-ray optical depth map above the aceretion disk., Thomson scattering with free electrons in the wind could redistribute and isotropize the X-ray emission above the disk and affect the gamma-ray optical depth map above the accretion disk.
 In the limit where X-rays from the disk are fully isotropized. the gamma-ray photosphere is quasi-spherical and is located at about 10! em from the compact object.," In the limit where X-rays from the disk are fully isotropized, the gamma-ray photosphere is quasi-spherical and is located at about $10^{10}$ cm from the compact object."
 A more detailed treatment of this effect would require for instance Monte Carlo techniques to follow the multiple elastic scattering of X-rays in the wind., A more detailed treatment of this effect would require for instance Monte Carlo techniques to follow the multiple elastic scattering of X-rays in the wind.
 In addition to the bright black body emission from the aceretion disk. the X-ray spectrum contains a non-thermal tail in hard X-rays probably related to a corona above the disk.," In addition to the bright black body emission from the accretion disk, the X-ray spectrum contains a non-thermal tail in hard X-rays probably related to a corona above the disk."
 We modeled the corona as a spherical. isotropic and homogeneous cloud around the compact object.," We modeled the corona as a spherical, isotropic and homogeneous cloud around the compact object."
 We showed that gamma-ray absorption with non-thermal hard X-rays from the corona is too small compared with the contribution from the disk., We showed that gamma-ray absorption with non-thermal hard X-rays from the corona is too small compared with the contribution from the disk.
 In this article. we present also a more precise modeling of the non-thermal radiation from the corona in Cygnus X-3 withBELM.," In this article, we present also a more precise modeling of the non-thermal radiation from the corona in Cygnus X-3 with."
 This code enables to extend the energy of the electrons in the high-energy domain., This code enables to extend the energy of the electrons in the high-energy domain.
 Using the best fit solution to X-ray data of ?.. we found that gamma rays produced in the corona suffer from strong absorption by non-comptonized photons from the disk before they escape to the observer.," Using the best fit solution to X-ray data of \citet{2009MNRAS.392..251H}, we found that gamma rays produced in the corona suffer from strong absorption by non-comptonized photons from the disk before they escape to the observer."
" The gamma-ray flux seen by could be reproduced if the corona ts unrealistically extended (R.=10!"" cm).", The gamma-ray flux seen by could be reproduced if the corona is unrealistically extended $R_{\rm{c}}\gtrsim 10^{10}~\rm{cm}$ ).
 This study does not favor a coronal origin of the observed gamma-ray emission., This study does not favor a coronal origin of the observed gamma-ray emission.
 At distances comparable to the orbital separation. the Wolf-Rayet star photon density dominates over the accretion disk X-ray density.," At distances comparable to the orbital separation, the Wolf-Rayet star photon density dominates over the accretion disk X-ray density."
 The gamma-ray emission and the modulation are likely to be produced by energetic electron-positron pairs possibly located in the jet. upscattering stellar radiation inverse Compton scattering.," The gamma-ray emission and the modulation are likely to be produced by energetic electron-positron pairs possibly located in the jet, upscattering stellar radiation inverse Compton scattering."
 In this case. the spectrum is Well fitted if pairs are injected with a power-law energy distribution of index 4.4.," In this case, the spectrum is well fitted if pairs are injected with a power-law energy distribution of index 4.4."
 The power-law cannot extend below Ynin250 (assuming no Doppler boosting) or the observed hard X-ray flux below 100 keV would be overestimated., The power-law cannot extend below $\gamma_{\rm{min}}\gtrsim 50$ (assuming no Doppler boosting) or the observed hard X-ray flux below 100 keV would be overestimated.
 Alternatively. the inverse Compton emission from the jet could also be responsible for the hard X-ray emission (instead of the corona).," Alternatively, the inverse Compton emission from the jet could also be responsible for the hard X-ray emission (instead of the corona)."
 This would requirea spectral break in the electron energy distribution below ypu∖tA10° with a harder power-law of index close to 34 with yiieA10 (in order to obtain a flat, This would requirea spectral break in the electron energy distribution below $\gamma_{\rm{brk}}\lesssim 10^3$ with a harder power-law of index close to 3 with $\gamma_{\rm min}\lesssim 10$ (in order to obtain a flat
 Understanding the stellar populations of galaxies is kev (ο untangling the mysteries of their formation and evolution.,} Understanding the stellar populations of galaxies is key to untangling the mysteries of their formation and evolution.
 Because of our location in the Milky Way. getting an overall picture of the stellar populations is difficult.," Because of our location in the Milky Way, getting an overall picture of the stellar populations is difficult."
 The nearby spiral ewlaxy MIOL (NGC 5457) is the closest [ace-0n spiral (IIubbletypeSÀADBD(s)ed:deVaucouleursetal.1991). and provides an excellent opportunity for resolution of stellar population details., The nearby spiral galaxy M101 (NGC 5457) is the closest face-on spiral \citep[Hubble type SAB(rs)cd;][]{rc3} and provides an excellent opportunity for resolution of stellar population details.
 Previous studies of stellar populations in MIOI include work on the Cepheid variable stars (Ixelsonetal.etal. 1993).. Xrav binaries (Ixuntzetal.2005:Mukai2003).. and novae 2000).. among many others.," Previous studies of stellar populations in M101 include work on the Cepheid variable stars \citep{kel96,ste98}, X–ray binaries \citep{kdk05,mukai03}, and novae \citep{scp00}, among many others."
 Star clusters are excellent. (racers of stellar populations: (μον are much brighter than single stars and usually have small internal spreads in age and metallicity., Star clusters are excellent tracers of stellar populations: they are much brighter than single stars and usually have small internal spreads in age and metallicity.
 Globular clusters iΕν particular are believed to be indicators of galaxy history (e.g..Straderοἱal.2005).," Globular clusters in particular are believed to be indicators of galaxy history \citep[e.g.,][]{str05}."
. Globular cluster systems (GC'Ss) in spirals have been studied much less (han their counterparts iΕν elliplicals: spirals have fewer clusters per unit of galaxy light. aud their irregular background light makes detection of clusters more challenging.," Globular cluster systems (GCSs) in spirals have been studied much less than their counterparts in ellipticals: spirals have fewer clusters per unit of galaxy light, and their irregular background light makes detection of clusters more challenging."
 The Milkv Way GCS is the gold standard for comparison to all others. but it is difficult to sav whether it is a truly (vpical GCS since the sample of spiral galaxy GCSs available for comparison is small.," The Milky Way GCS is the `gold standard' for comparison to all others, but it is difficult to say whether it is a truly typical GCS since the sample of spiral galaxy GCSs available for comparison is small."
 Younger star cluster populations are better-stucdied in other galaxies (e.g..Larsen&Richtler1999) than in the Milky Way: due to extinction. the census of voung cluster populations in the Galaxy. is [ar," Younger star cluster populations are better-studied in other galaxies \citep[e.g.,][]{lr99} than in the Milky Way; due to extinction, the census of young cluster populations in the Galaxy is far"
different environments in the RR svstem.,different environments in the RR system.
 Phe STIS Lla emission. seen in Fig. S..," The STIS $\alpha$ emission, seen in Fig. \ref{fig8},"
 can be traced to roughly north and south of the central source., can be traced to roughly north and south of the central source.
 The Ha has a smaller spatial extent and is seen primarily through scattering. (indirect line-ofl-sight)., The $\alpha$ has a smaller spatial extent and is seen primarily through scattering (indirect line-of-sight).
 Phe D-line emission can be traced. to north and south of the central source in the STIS spectra., The D-line emission can be traced to north and south of the central source in the STIS spectra.
 The Iarge spatial extent of the D-lines allows them to be seen both clireethy (at larecr istances [rom the central source) and. incürectlv via scattering., The large spatial extent of the D-lines allows them to be seen both directly (at larger distances from the central source) and indirectly via scattering.
 The single-peaked La emission is only seen indirectly and. therefore. is arising only [rom the inner regions of the RAR.," The single-peaked $\alpha$ emission is only seen indirectly and, therefore, is arising only from the inner regions of the RR."
 The single-peaked emission lines of Hobbsetal.(2004) and Wittetal.(2009) most likely. originate from the region as mentioned. by Jura.Turner.&Balm OOT)., The single-peaked emission lines of \citet{hobbs2004} and \citet{witt2009} most likely originate from the region as mentioned by \citet{jura1997}.
. In table 2 of Hobbsctal.(2004). they classify S4 emission lines from 12 atomic species based on the shape ( “their profile., In table 2 of \citet{hobbs2004} they classify 84 emission lines from 12 atomic species based on the shape of their profile.
" They list 24 “narrow. 12 ""broad! and. 4s ouble-peaked? atomic lines."," They list 24 `narrow', 12 `broad' and 48 `double-peaked' atomic lines."
 The ‘narrow or single-peaked emission spectra include the extscii] 7291.47A lines., The `narrow' or single-peaked emission spectra include the ] 7291.47 lines.
 The 3933.66A Ix-line is also among the lines classified as single-peaked. though upon close inspection an asymmetry can be seen in the line.," The 3933.66 K-line is also among the lines classified as single-peaked, though upon close inspection an asymmetry can be seen in the line."
 The spectra of Whiteoak(1983) reveal that. at higher-resolution. the Weline is in fact. clouble-peakecl with a separation )etween peaks similar to that of the D-lines.," The spectra of \citet{whiteoak1983} reveal that, at higher-resolution, the K-line is in fact double-peaked with a separation between peaks similar to that of the D-lines."
 Close examination of the cdouble-peaked oofiles reveals that the relative height. of the blue-shifted auc red-shifted emission peaks vary [rom species to species. or example the D-lines and Ix-line.," Close examination of the double-peaked profiles reveals that the relative height of the blue-shifted and red-shifted emission peaks vary from species to species, for example the D-lines and K-line."
 Most of these. however have near-equal [ux or the two components (Hobbsetal.2004).," Most of these, however have near-equal flux for the two components \citep{hobbs2004}."
. Phe W-line spectra of Whiteoak&Gardner(1983). shows a weaker bluc-shiftecl emission. component relative το the stronger red-shifted emission component. opposite to what is seen intextsci.," The K-line spectra of \citet{whiteoak1983} shows a weaker blue-shifted emission component relative to the stronger red-shifted emission component, opposite to what is seen in."
. Phe exact reason for this is unclear., The exact reason for this is unclear.
 “Phe present work did not look at the orbital phase-cdependence of the other emission lines in the svstem., The present work did not look at the orbital phase-dependence of the other emission lines in the system.
 Future work will look at how the V-height anc R-height ratios of other multiplet lines behave as a function of the orbital period., Future work will look at how the V-height and R-height ratios of other multiplet lines behave as a function of the orbital period.
 This could also be done with single lines in. principle: however. with multiplet lines one assumes that each component line should be equally allected: by scattering.," This could also be done with single lines in principle; however, with multiplet lines one assumes that each component line should be equally affected by scattering."
 One also knows what the Hux ratios between line components should. be and also that the lines arise from the same atom: therefore. the environmental conditions giving rise to the lines are the same.," One also knows what the flux ratios between line components should be and also that the lines arise from the same atom; therefore, the environmental conditions giving rise to the lines are the same."
 Hence. any discrepancy in such measurements. may reveal more about how this complex svstem behaves.," Hence, any discrepancy in such measurements may reveal more about how this complex system behaves."
 The complex profiles of the D-lines in LID 44179. perioclically varving in intensity and shape with the orbital period. as the photomoetric primary post-AGB component of the binary moves through its eccentric orbit. reveal detailed information about the varving mass-oss from the primary.," The complex profiles of the D-lines in HD 44179, periodically varying in intensity and shape with the orbital period as the photometric primary post-AGB component of the binary moves through its eccentric orbit, reveal detailed information about the varying mass-loss from the primary."
 Peak mass-loss occurs during the orbital phases around. periastron. to be replaced by partial re-acecretion during the phases near apastron.," Peak mass-loss occurs during the orbital phases around periastron, to be replaced by partial re-accretion during the phases near apastron."
 The primary conclusions are: Lt is clear that the cause of the broadened. photospheric absorption lines is of great importance for understanding and interpreting the spectra of LID 44179., The primary conclusions are: It is clear that the cause of the broadened photospheric absorption lines is of great importance for understanding and interpreting the spectra of HD 44179.
 With current observations. some ambiguities cannot be resolved.," With current observations, some ambiguities cannot be resolved."
 The broadening mechanisms investigated in this paper are either unlikely or cannot Lully explain the observed [ine-profiles., The broadening mechanisms investigated in this paper are either unlikely or cannot fully explain the observed line-profiles.
 Lt is likely that there may be a superposition of mechanisms at play in shaping these spectral features., It is likely that there may be a superposition of mechanisms at play in shaping these spectral features.
 “Phe inclirect ine-of-sight adds to the complication of interpreting the spectra., The indirect line-of-sight adds to the complication of interpreting the spectra.
 The elfective inclination angle used. here may in act be somewhat cillerent., The effective inclination angle used here may in fact be somewhat different.
 Lt is more likely that we see WD 44179 under a small range of angles. of which the ellective inclination angle is the mean.," It is more likely that we see HD 44179 under a small range of angles, of which the effective inclination angle is the mean."
 Lis likely the case hat the spread of viewing angles leads to broadened profiles., It is likely the case that the spread of viewing angles leads to broadened profiles.
 In addition. there is a slightly dilferent viewing geometry for he north and south ends of the nebula.," In addition, there is a slightly different viewing geometry for the north and south ends of the nebula."
 Spatiallv-resolved. ugher-resolution spectra of the photospheric lines could help resolve some of these remaining puzzles.," Spatially-resolved, higher-resolution spectra of the photospheric lines could help resolve some of these remaining puzzles."
 A full 3-D. mocel is called for in order to understand our complex view of the jnary deep inside the cieeumbinary disc., A full 3-D model is called for in order to understand our complex view of the binary deep inside the circumbinary disc.
 We would like to thank the anonvmous referee for the constructive comments. that. greatly improved. this paper., We would like to thank the anonymous referee for the constructive comments that greatly improved this paper.
 JDP would like to thank llans van Winckel, JDT would like to thank Hans van Winckel
Binarity VENis à veryMM common stellar. mEproperty.-- which. coversm a very wide range of separations. from two stellar radii to housands of astronomical units.,"Binarity is a very common stellar property, which covers a very wide range of separations, from two stellar radii to thousands of astronomical units."
 Close binaries have short orbital periods (from a few hours to a few vears). and they are easily. detected from variations in their racial velocities (RV).," Close binaries have short orbital periods (from a few hours to a few years), and they are easily detected from variations in their radial velocities (RV)."
 For that reason. they are the most commonly stucied of this class of stars (see. eg. Llalbwachsetal. 2003)).," For that reason, they are the most commonly studied of this class of stars (see, eg, \citealt{Halbwachs03}) )."
 Dinaries with periods around a few centuries are also rather well known: the components are sullicientIy separated to be detected: visually (in the past) or on images. and they are still close enough to avoid the risk of confusing a field star and a binary component: they may be discarded by applving a statistical criterion almost as old as the discovery of double stars (Struve1852).," Binaries with periods around a few centuries are also rather well known: the components are sufficiently separated to be detected visually (in the past) or on images, and they are still close enough to avoid the risk of confusing a field star and a binary component: they may be discarded by applying a statistical criterion almost as old as the discovery of double stars \citep{Struve52}."
. Very wide binaries are particularly interesting. since the distribution of their separations is a clue to the gravitational perturbers which made the gravity field of the Cialaxy (seo Jiang&‘Tremaine2010— and references thercin).," Very wide binaries are particularly interesting, since the distribution of their separations is a clue to the gravitational perturbers which made the gravity field of the Galaxy (see \citealt{Jiang10} and references therein)."
 llowever. the selection of binaries with separations of thousands of astronomical units is dillieult: the components have also wide apparent separations. and it is necessary to use additional criteria in order to discard the optical companions.," However, the selection of binaries with separations of thousands of astronomical units is difficult: the components have also wide apparent separations, and it is necessary to use additional criteria in order to discard the optical companions."
 “Lrigonometric parallax. or another estimation of the distance. is sometimes used. but the most ellicient. and the most employed. criterion is proper motion: when the semi-major axis of the orbit is large. the orbital motion of the stars around the barvcentre of the system generates a dillerence in proper motion which is negligihle. and. the components must have similar apparent displacements.," Trigonometric parallax, or another estimation of the distance, is sometimes used, but the most efficient, and the most employed criterion is proper motion: when the semi-major axis of the orbit is large, the orbital motion of the stars around the barycentre of the system generates a difference in proper motion which is negligible, and the components must have similar apparent displacements."
 Such binaries are called common proper motion (CDM) stars., Such binaries are called common proper motion (CPM) stars.
"than the critical mass above which centrifugal effects become important in slowing the collapse of the gas in the halo. given bv Clarke DBromnm (2003) as We here assume that the spin parameter has the fiducial value of Ay, = 1.","than the critical mass above which centrifugal effects become important in slowing the collapse of the gas in the halo, given by Clarke Bromm (2003) as We here assume that the spin parameter has the fiducial value of $\lambda_{0.1}$ = 1."
 Again. we have that μις ο = 2.7 2).," Again, we have that $T_{\rmn final}$ = $T_{\rmn CMB}$ = $~{\rmn K}$ $z$ )."
" Thus. the density of the gas when the temperature has dropped to μμ is given by Using these values for the final temperature and density in equation (23). we obtain the characteristic stellar mass for the case of stars formed in collapsing DM haloes as where we have again usec M,oaMppg. with a= 0.3."," Thus, the density of the gas when the temperature has dropped to $T_{\rm final}$ is given by Using these values for the final temperature and density in equation (23), we obtain the characteristic stellar mass for the case of stars formed in collapsing DM haloes as where we have again used $M_{\rmn char} \simeq \alpha M_{\rmn BE}$, with $\alpha = 0.3$ ."
 The characteristic mass of stars formed in the assembly of DM haloes with masses z107 AL. depends only on the halo mass., The characteristic mass of stars formed in the assembly of DM haloes with masses $\ga 10^8$ $_{\odot}$ depends only on the halo mass.
 Thus. stars formed in this process are expected to have characteristic masses of the order of LO ΝΕ. comparable to the SN-shocked. case.," Thus, stars formed in this process are expected to have characteristic masses of the order of 10 $_{\odot}$, comparable to the SN-shocked case."
 We have investigated the importance of HD as a coolant of the primordial gas in four distinct. cases: the evolution of supernova-shocked. gas. with shock velocities < 100 kni 5: the evolution of gas shocked during DM halo collapse. with shock velocities < 100 km s freely collapsing unshocked. un-ionized. gas clouds within minihaloes: and freely collapsing clouds of ionized gas within τοις 11 regions.," We have investigated the importance of HD as a coolant of the primordial gas in four distinct cases: the evolution of supernova-shocked gas, with shock velocities $\ga$ 100 km $^{-1}$; the evolution of gas shocked during DM halo collapse, with shock velocities $\la$ 100 km $^{-1}$; freely collapsing unshocked, un-ionized gas clouds within minihaloes; and freely collapsing clouds of ionized gas within relic H II regions."
 In the cases where the primordial gas is ionized. LID is an important coolant.," In the cases where the primordial gas is ionized, HD is an important coolant."
 Thus. behind strong shocks nd in velic LE LE regions. the primordial gas is able to cool w HD line emission to temperatures & LOO Ix. In the case of strong shocks. LLD cooling can lower the temperature of the »wimorcdial gas to the temperature of the CALB in a fraction X the age of the Universe at redshifts 2 & 10.," Thus, behind strong shocks and in relic H II regions, the primordial gas is able to cool by HD line emission to temperatures $\la$ 100 K. In the case of strong shocks, HD cooling can lower the temperature of the primordial gas to the temperature of the CMB in a fraction of the age of the Universe at redshifts $z$ $\ga$ 10."
 In much of 1e literature. it is assumed that metals are required to lower 1o temperature of interstellar gas to the CMD temperature (c.c. Dromm et al.," In much of the literature, it is assumed that metals are required to lower the temperature of interstellar gas to the CMB temperature (e.g. Bromm et al."
 2001: Schneider ct al., 2001; Schneider et al.
 2002: Clarke Dromm 2003)., 2002; Clarke Bromm 2003).
 We emphasize that through LLD coolingfemperatiurc. the lowest temperature attainable w radiative cooling.," We emphasize that through HD cooling, the lowest temperature attainable by radiative cooling."
 All that is recquirect is for a large enough abundance of LID to be produced. which we have shown can be done under stronely-shocked conditions in which the »imorcdial gas is ionized anc evolves isobarically.," All that is required is for a large enough abundance of HD to be produced, which we have shown can be done under strongly-shocked conditions in which the primordial gas is ionized and evolves isobarically."
 We have calculated the characteristic mass of primorclial stars formed from eas that has cooled to the CAB emperature Door., We have calculated the characteristic mass of primordial stars formed from gas that has cooled to the CMB temperature floor.
 We estimate that Pop 15 stars. formed rom gas shocked either through SN. explosions or during he assembly of the first cbwarf galaxies. have characteristic masses that are redshift dependent ancl of the order of 10 M.," We estimate that Pop II.5 stars, formed from gas shocked either through SN explosions or during the assembly of the first dwarf galaxies, have characteristic masses that are redshift dependent and of the order of 10 $_{\odot}$."
 The implications of this ability of the primordial gas to ellectively cool to low temperatures are numerous., The implications of this ability of the primordial gas to effectively cool to low temperatures are numerous.
 LID cooling ollers a mechanism by which low mass metal-poor stars can be formed very early in the history of the Universe. at redshifts z 2 10.," HD cooling offers a mechanism by which low mass metal-poor stars can be formed very early in the history of the Universe, at redshifts $z$ $\ga$ 10."
 TFhus. LID cooling may play a role in the formation of the most metal-poor stars that have been observed.," Thus, HD cooling may play a role in the formation of the most metal-poor stars that have been observed."
 In particular. it has been suggested that the metal abundance patterns of two recently discovered: extremely metal poor halo stars. LLEOLOT-5240 and 11327-2326. can be explained by these stars having formed from gas enriched by the elements released in the tvpe HE supernova explosion of a 20-25 M. star (Christlich et al.," In particular, it has been suggested that the metal abundance patterns of two recently discovered extremely metal poor halo stars, HE0107-5240 and HE1327-2326, can be explained by these stars having formed from gas enriched by the elements released in the type II supernova explosion of a 20-25 $_{\odot}$ star (Christlieb et al."
 2002: Frebel οἱ al., 2002; Frebel et al.
 2005)., 2005).
 While the first generation of stars which formed in minihaloes of mass 10° AL. would likely have been far more massive than this CZ;100 AL. ). the characteristic mass that we calculate for Pop 11.5 stars falls just in this mass range.," While the first generation of stars which formed in minihaloes of mass $10^6$ $_{\odot}$ would likely have been far more massive than this $\ga 100$ $_{\odot}$ ), the characteristic mass that we calculate for Pop II.5 stars falls just in this mass range."
 Therefore. it may. have been the supernova explosions of Pop IL5 stars that dispersed. metals into the primorclial eas that later formed the most metal poor stars that are observed toclay.," Therefore, it may have been the supernova explosions of Pop II.5 stars that dispersed metals into the primordial gas that later formed the most metal poor stars that are observed today."
 As we have shown. the evolution of the primordial gas following the DM halo collapse that formed the first dwarl galaxies may have allowed for the formation of primorclial stars with masses of the order of LO M...," As we have shown, the evolution of the primordial gas following the DM halo collapse that formed the first dwarf galaxies may have allowed for the formation of primordial stars with masses of the order of 10 $_{\odot}$."
 The formation of the oldest globular clusters. which formed within ~ LO° vr alter the big bane. must have required the presence of metal coolants to account for the observed abuncanee of low-mass stars in them (see Ashman Zepf 1992: Kane ct al.," The formation of the oldest globular clusters, which formed within $\sim$ $^9$ yr after the big bang, must have required the presence of metal coolants to account for the observed abundance of low-mass stars in them (see Ashman Zepf 1992; Kang et al."
 1990: ΡΩΜΗ Clarke 2002)., 1990; Bromm Clarke 2002).
 Overall. the fact that. primordial gas can cool to," Overall, the fact that primordial gas can cool to"
ambipolar diffusiou. simulatiousce. of more generalized cases are required to support the scenario of prompt supercritical core formation in shocks.,"ambipolar diffusion, simulations of more generalized cases are required to support the scenario of prompt supercritical core formation in shocks."
 Three-cimensional simulatious of systems with oblique shocks. including self-gravity of the gas. would be inumediately helpful.," Three-dimensional simulations of systems with oblique shocks, including self-gravity of the gas, would be immediately helpful."
 ln addition. a more realistic core-Lorming environment cau be exaumiued by adding nonlinear turbuleuce to the iullow velocity field.," In addition, a more realistic core-forming environment can be examined by adding nonlinear turbulence to the inflow velocity field."
 Further simulatious along these lines. together with observations probing deusity aud inagnetic structtT iu filaments aud cores at differeut stages. will improve uuclerstauding of what precipitates star formation.," Further simulations along these lines, together with observations probing density and magnetic structure in filaments and cores at different stages, will improve understanding of what precipitates star formation."
 We are eerateful to the referee for a very thoroughOm aid helpful report., We are grateful to the referee for a very thorough and helpful report.
 This work was supported by NASA under grant NNX10AFO60C. The main text cousiders a 1-D system with velocities auc magnetic fields perpendicular to each other. for simplicity.," This work was supported by NASA under grant NNX10AF60G. The main text considers a 1-D system with velocities and magnetic fields perpendicular to each other, for simplicity."
 We expect that our results will qualitatively hold for more general geometry., We expect that our results will qualitatively hold for more general geometry.
 Here. we show that under certain couditious. our results can quantitatively be applied to oblique C-type shocks.," Here, we show that under certain conditions, our results can quantitatively be applied to oblique C-type shocks."
 Iu the following. we shall consider a plane-parallel shock iu the standard shock frame. using the same coordiuate system as before.," In the following, we shall consider a plane-parallel shock in the standard shock frame, using the same coordinate system as before."
" The shock [ront is in the y-z plane. the upstream [low is along the w-clirection (vy= vox). aud the upstream maguetic fell is now in the κ plane (Bua=Brox+By oy). at an angle 0 to the inflow (CE,o/B,o= tan)."," The shock front is in the $y$ $z$ plane, the upstream flow is along the $x$ -direction $\mathbf{v}_{0} = v_{0}\hat{\mathbf{x}}$ ), and the upstream magnetic field is now in the $x$ $y$ plane $\mathbf{B}_\mathrm{cloud} = B_{x,0} \hat{\mathbf{x}} + B_{y,0} \hat{\mathbf{y}}$ ), at an angle $\theta$ to the inflow $B_{y,0}/B_{x,0} = \tan\theta $ )."
" For steady. plane-parallel shocks. OQ;=0,0.0."," For steady, plane-parallel shocks, $\partial_t = \partial_y = \partial_z = 0$."
" From tlie nass and momentum conservation equations for neutrals (Equations (1a))—-(1b))). we have Similarly. the momentuui equation for ious and the magnetic induction equation (Equatious (2a))—(3b))) are (with the strouee couplingOm approximation) Note that B,=const.9in plane-parallel shocks. since V:B= 0."," From the mass and momentum conservation equations for neutrals (Equations \ref{mCon}) $-$ \ref{NeuMom}) )), we have Similarly, the momentum equation for ions and the magnetic induction equation (Equations \ref{IonMom}) $-$ \ref{induc}) )) are (with the strong coupling approximation) Note that $B_x = const. = B_{x,0}$in plane-parallel shocks, since $\nabla\cdot\mathbf{B} = 0$ ."
power al &o>405Mpe. + compared to the fits to the power spectrum.,power at $k>40h$ $^{-1}$ compared to the fits to the power spectrum.
 However. the direct fits are not reliable in this regime. since the N-body simulations become unreliable for A>40h n. which. is. why the fits⋅ presented above only use information [rom &«40hAIpe 7.," However, the direct fits are not reliable in this regime, since the $N$ -body simulations become unreliable for $k>40h$ $^{-1}$, which is why the fits presented above only use information from $k<40h$ $^{-1}$."
 The conclusion from the above comparison is that on small scales there is disagreement between analytic formulae for non-linear power spectrum and the halo model., The conclusion from the above comparison is that on small scales there is disagreement between analytic formulae for non-linear power spectrum and the halo model.
 Since the analvtic models have not been calibrated with simulations in this regime it is possible that they are unreliable ancl so the halo model should be used instead. (indeed. the analytic models of 2 do not even predict the power spectrum. for kcI005Mpe Ly," Since the analytic models have not been calibrated with simulations in this regime it is possible that they are unreliable and so the halo model should be used instead (indeed, the analytic models of \citealt{2002astro.ph..7664S} do not even predict the power spectrum for $k>100h$ $^{-1}$ )."
 Nevertheless. since non-linear predictions at high. & have been used. in the literature. especially for predicting the lensine cllects on small scales (e.g. 2)). it is important to recognize their possible limitations when using them outside the regime of applicability.," Nevertheless, since non-linear predictions at high $k$ have been used in the literature, especially for predicting the lensing effects on small scales (e.g. \citealt{1999MNRAS.305..746M}) ), it is important to recognize their possible limitations when using them outside the regime of applicability."
 lt is unlikely that the cliscrepancy can be resolved bv modifving the mass function., It is unlikely that the discrepancy can be resolved by modifying the mass function.
 The existing simulations resolve the mass function down to LOMAL. which is the mass that dominates the power spectrum at &~I0005Mpe. 5.," The existing simulations resolve the mass function down to $10^{11}M_{\sun}$, which is the mass that dominates the power spectrum at $k\sim 1000h$ $^{-1}$."
 Substructure could boost the amount of power. since in the mass function one counts only isolated haloes. not those that are within larger haloes.," Substructure could boost the amount of power, since in the mass function one counts only isolated haloes, not those that are within larger haloes."
 Subhaloes within haloes contribute to the clustering in the same wav as isolated haloes on scales that are comparable to the scale radius., Subhaloes within haloes contribute to the clustering in the same way as isolated haloes on scales that are comparable to the scale radius.
 However. the abundance of subhaloes is small compared to the abundance of isolated haloes even at small halo masses. so it is unlikely that this is a significant correction (2)..," However, the abundance of subhaloes is small compared to the abundance of isolated haloes even at small halo masses, so it is unlikely that this is a significant correction \citep{2001MNRAS.321..559B}."
 Similarly. while the scatter in the mass concentration relation boosts the amount of power. we find the effect is relatively small for the scatter suggested from simulations (77) and again cannot resolve the discrepancy.," Similarly, while the scatter in the mass concentration relation boosts the amount of power, we find the effect is relatively small for the scatter suggested from simulations \citep{2001MNRAS.321..559B,2001ApJ...554...56C} and again cannot resolve the discrepancy."
 For ey versus Qu and mar our fit to 2? produces very similar trends to that in 2. and 7.., For $c_0$ versus $\Omega_0$ and $n_{\rm eff}$ our fit to \citet{2002astro.ph..7664S} produces very similar trends to that in \citet{2001ApJ...554..114E} and \citet{2001MNRAS.321..559B}.
 Phis comparison should be reliable. since the haloes that dominate are around 1055.10HAL. which are abundant aad well resolved in the simulations.," This comparison should be reliable, since the haloes that dominate are around $10^{13}-10^{14}M_{\sun}$, which are abundant and well resolved in the simulations."
 For : we also find broad agreement. although the errors from the power spectrum method are very large.," For $\beta$ we also find broad agreement, although the errors from the power spectrum method are very large."
 We have used the halo model and the non-linear evolution of dark matter power spectrum (as given by the fitting formula of ?)) to probe the dependence of halo concentration on cosmological parameters., We have used the halo model and the non-linear evolution of dark matter power spectrum (as given by the fitting formula of \citealt{2002astro.ph..7664S}) ) to probe the dependence of halo concentration on cosmological parameters.
 The most important. parameters or the concentration are the matter density and the cllective 4ope of the linear power spectrum at the non-linear scale., The most important parameters for the concentration are the matter density and the effective slope of the linear power spectrum at the non-linear scale.
 _Ve present analytical expressions which give concetration at 16 non-linear scale as a function of these two parameters., We present analytical expressions which give concetration at the non-linear scale as a function of these two parameters.
 We examined. our result. against the mocdels for halo 'oncentration of 2? and ?.., We examined our result against the models for halo concentration of \citet{2001ApJ...554..114E} and \citet{2001MNRAS.321..559B}.
 We found. broad agreement with 1o trends presented there in that we also find that spectra with lower elfective slope mar have lower concentration at 1e non-linear mass., We found broad agreement with the trends presented there in that we also find that spectra with lower effective slope $n_{\rm eff}$ have lower concentration at the non-linear mass.
 Although there is some cillerence in 10 mass-concentration dependence between ο and. 2. we ind no compelling reason to prefer one mocel to the other xeed on the power spectrum.," Although there is some difference in the mass-concentration dependence between \citet{2001ApJ...554..114E} and \citet{2001MNRAS.321..559B}, we find no compelling reason to prefer one model to the other based on the power spectrum."
 This is because the dynamic range covered by the power spectrum analysis is too narrow o obtain a reliable mass dependence of the concentration over a wide range of masses., This is because the dynamic range covered by the power spectrum analysis is too narrow to obtain a reliable mass dependence of the concentration over a wide range of masses.
 We have found that using these models to predict the non-linear power spectrum results in a significantly lower power spectrum on small scales compared to ? and ?.., We have found that using these models to predict the non-linear power spectrum results in a significantly lower power spectrum on small scales compared to \citet{1996MNRAS.280L..19P} and \citet{2002astro.ph..7664S}.
 Fhis suggests that care must be exercised when using these models in the range where they have not been calibrated and may indicate that the amount of clark matter power on small scales is smaller than predictions from these models., This suggests that care must be exercised when using these models in the range where they have not been calibrated and may indicate that the amount of dark matter power on small scales is smaller than predictions from these models.
 For mildly non-linear &. even the best fitted halo mocels show discrepancies from the 7? power spectrum at the level. both for the self-similar and CDM models.," For mildly non-linear $k$, even the best fitted halo models show discrepancies from the \citet{2002astro.ph..7664S} power spectrum at the level, both for the self-similar and CDM models."
 Some of this discrepancy. arises from the fits in 2.. which are only accurate at. Level.," Some of this discrepancy arises from the fits in \citet{2002astro.ph..7664S}, which are only accurate at level."
 Llowever. direct. comparison of the ido model to the IN-body. simulations of ? also reveals discrepancies at the similar level.," However, direct comparison of the halo model to the $N$ -body simulations of \citet{1998ApJ...499...20J} also reveals discrepancies at the similar level."
 Phis is not surprising given he approximate nature of the halo model and argues that it cannot be a full replacement. for N-body simulations in he era of high precision cosmology., This is not surprising given the approximate nature of the halo model and argues that it cannot be a full replacement for $N$ -body simulations in the era of high precision cosmology.
 However. using the xwameters derived. in this paper. the halo model can be used. for qualitative predictions of the dark matter. power spectrum over much wider range of models and scales than weviously available.," However, using the parameters derived in this paper, the halo model can be used for qualitative predictions of the dark matter power spectrum over much wider range of models and scales than previously available."
 We thank J. Bullock. V. Eke. J. X. Peacock and I. E. Smith for making their codes available.," We thank J. Bullock, V. Eke, J. A. Peacock and R. E. Smith for making their codes available."
 ILL is supported bv an NSE Graduate Research Fellowship., KH is supported by an NSF Graduate Research Fellowship.
 US is supportccl by NASA. NSE. Sloan and Packard Foundations.," US is supported by NASA, NSF, Sloan and Packard Foundations."
The faint eendssiou (Lyx~Lo? 109?eres 1) of transiently accreting low-nass bbiuaries m quiesceut state (qELMXDs) was historically interpreted as a thermal blackbody with cuission area sanaller than that expected for a 10 kan neutron star (NS).,The faint emission $L_{\rm X}\sim10^{32}$ $10^{33}\cgslum$ ) of transiently accreting low-mass binaries in quiescent state (qLMXBs) was historically interpreted as a thermal blackbody with emission area smaller than that expected for a 10 km neutron star (NS).
 It was later claimed that the observed luminosity was not due to low accretion rate onto the NS surface. as initially sugeested (2).. but due to heat from the NS crust vacating through the upper lavers of the NS atinosphliere (2)..," It was later claimed that the observed luminosity was not due to low accretion rate onto the NS surface, as initially suggested \citep{vanparadijs87}, but due to heat from the NS crust radiating through the upper layers of the NS atmosphere \citep{brown98}."
 Tn this interpretation. called Deep Crustal Hoatiug. the enerey is deposited iu the NS crust bv pressure-sensitive nuclear reactions (electron captures. neutrou Cluissions and pyenonuclear reactions. ?77]). as matter accumulates on the surface duriug episodes of rapid accretion.," In this interpretation, called Deep Crustal Heating, the energy is deposited in the NS crust by pressure-sensitive nuclear reactions (electron captures, neutron emissions and pycnonuclear reactions, \citealt{gupta07, haensel08}) ), as matter accumulates on the surface during episodes of rapid accretion."
" This chain of reactions. from the NS surface to depths with the density of uudiffereutiated οὐαυτπα, releases ~1.5MeV. per accreted nucleon in the crust."," This chain of reactions, from the NS surface to depths with the density of undifferentiated equilibrium, releases $\sim 1.5\MeV$ per accreted nucleon in the crust."
 Ina steady state. these reactions eive rise to a time-averaged huninosity. which is directly proportional to the mass accretion rate (2): where Q is the average heat deposited in the NS crust oor accreted nucleon.," In a steady state, these reactions give rise to a time-averaged luminosity, which is directly proportional to the mass accretion rate \citep{brown98}: where $Q$ is the average heat deposited in the NS crust per accreted nucleon."
 The resulting thermal spectrum is described by a realistic NS atmosphere composed exclusively of wdrogen., The resulting thermal spectrum is described by a realistic NS atmosphere composed exclusively of hydrogen.
 Tndeed. the gravitational setthue of the accreted material from the low-mass companion star lappens on time scales of seconds (7).. resulting ij a pure ILatmiosphere around the NS.," Indeed, the gravitational settling of the accreted material from the low-mass companion star happens on time scales of $\sim$ seconds \citep{bildsten92}, resulting in a pure H-atmosphere around the NS."
 The current uodels of NS IL-atmosphere. (277) show that the observed cluission is consistent with that from the eutire surface area of a ~ LO km NS (?)..," The current models of NS H-atmosphere \citep{zavlin96, mcclintock04,
 heinke06a} show that the observed emission is consistent with that from the entire surface area of a $\sim$ 10 km NS \citep{rutledge99}. ."
 The I-atinosphere interpretation allows observers to determine the plysical radius Rys (or the projected radius Ry=Rxs(1|2). with 11:2(12GMxs/Rsc2)7 ) using spectral fitting iu the soft range. where the thermal spectra of q(LAINBs peaks.," The H-atmosphere interpretation allows observers to determine the physical radius $R_{\rm NS}$ (or the projected radius $\rinfty =
R_{\rm NS} \left(1+z\right)$, with $1+z=\left(1-2G\mns/\rns
c^{2}\right)^{-1/2}$ ) using spectral fitting in the soft range, where the thermal spectrum of qLMXBs peaks."
 The radius nieasureiieut of NSs using thethermal spectru of qLAINBs is one wav to place coustraits, The radius measurement of NSs using thethermal spectrum of qLMXBs is one way to place constraints
seen in (—D). Our CTIO final optical photometric catalogs consist of 4432. 8485. 12464. 1163. and 3892 entries having measurements down to V—22 mag for ESOI31SCO9. NGC 3284. VdB-Hagen 164. NGC 6268. and Czernik 38. respectively.,"seen in $(U-B)$ Our CTIO final optical photometric catalogs consist of 4432, 8485, 12464, 1163, and 3892 entries having measurements down to $\sim$ 22 mag for ESO131SC09, NGC 5284, VdB-Hagen 164, NGC 6268, and Czernik 38, respectively."
 As for LCO. the catalogs for IC 2714. NGC 4052. NGC 5316 and NGC 5715 report 2756. 6650. 2524. and 4105 entries.," As for LCO, the catalogs for IC 2714, NGC 4052, NGC 5316 and NGC 5715 report 2756, 6650, 2524, and 4105 entries."
 These catalogs will be made available at the data-base maintained by E. Paunzen at Vienna University. Austria.," These catalogs will be made available at the data-base maintained by E. Paunzen at Vienna University, Austria."
 Completeness corrections were determined by running artificial star experiments on the data., Completeness corrections were determined by running artificial star experiments on the data.
 Basically. we created several artificial images by adding artificial stars to the original frames.," Basically, we created several artificial images by adding artificial stars to the original frames."
 These stars were added at random positions. and had the same colour and luminosity distribution of the true sample.," These stars were added at random positions, and had the same colour and luminosity distribution of the true sample."
 To avoid generating overcrowding. in each experiment we added up to of the original number of stars.," To avoid generating overcrowding, in each experiment we added up to of the original number of stars."
 Depending on the frame. between 1000 and 3000 stars were added.," Depending on the frame, between 1000 and 5000 stars were added."
 In this way we have estimated that the completeness level of our photometry is better than down to 1-19.5. Each optical catalog was then cross-correlated with 2MASS. which resulted in a final catalog including and magnitudes.," In this way we have estimated that the completeness level of our photometry is better than down to $V = 19.5$ Each optical catalog was then cross-correlated with 2MASS, which resulted in a final catalog including and magnitudes."
 As a by-product. pixel (i.e.. detector) coordinates were converted to RA and DEC for J2000.0 equinox. thus providing 2MASS-based astrometry. useful for spectroscopic The only cluster in our sample having previous CCD photometry is Czernik 38. for which BV photometry was provided by Maciejewski (2008).," As a by-product, pixel (i.e., detector) coordinates were converted to RA and DEC for J2000.0 equinox, thus providing 2MASS-based astrometry, useful for spectroscopic The only cluster in our sample having previous CCD photometry is Czernik 38, for which BV photometry was provided by Maciejewski (2008)."
 We can only compare BV. since Maciejewski did not observe in I. We found 425 stars in common. and the results are shown in Fig 3. in the sense of our photometry minus Maciejewski.," We can only compare BV, since Maciejewski did not observe in I. We found 425 stars in common, and the results are shown in Fig 3, in the sense of our photometry minus Maciejewski."
 We found that the two studies are very different both in V and in B mag., We found that the two studies are very different both in V and in B mag.
 The mean differences are reported in the top left corners of the various panels in Fig., The mean differences are reported in the top left corners of the various panels in Fig.
 3., 3.
 The reasons for such important zero point differences can be various., The reasons for such important zero point differences can be various.
 We remind the reader that Maciejewski observed in very poor seeing conditions (~ 4 arcsec) and with a Schmidt camera having a scale as large as 1.08 aresec/pixel., We remind the reader that Maciejewski observed in very poor seeing conditions $\sim$ 4 arcsec) and with a Schmidt camera having a scale as large as 1.08 arcsec/pixel.
 Besides. the color range of the standard stars is limited between 0.3 and 1.3 in B-V. while all Main Sequence stars in Czernik 38 have redder colors.," Besides, the color range of the standard stars is limited between 0.3 and 1.3 in B-V, while all Main Sequence stars in Czernik 38 have redder colors."
 This implied he had to extrapolate colors when calibrating., This implied he had to extrapolate colors when calibrating.
 Besides. with such a poor detector scale. the seeing conditions and moderated crowding of the field (see Fig.," Besides, with such a poor detector scale, the seeing conditions and moderated crowding of the field (see Fig."
 |) easily produce blends. and stars tend. on the average. to be brighter.," 1) easily produce blends, and stars tend, on the average, to be brighter."
 This is exactly what the positive residuals in Fig., This is exactly what the positive residuals in Fig.
 3 indicate., 3 indicate.
 For all these reasons we believe our photometry is more solid and precise (note the scatter in the residual in Fig 3 for V larger than  17.0 To further check the quality of our data. we compared our UBV photometry for IC 2714 with the higher quality photoelectric study by Clarida et al. (," For all these reasons we believe our photometry is more solid and precise (note the scatter in the residual in Fig 3 for V larger than $\sim$ 17.0 To further check the quality of our data, we compared our UBV photometry for IC 2714 with the higher quality photoelectric study by Clariá et al. ("
1994).,1994).
 This is shown in Fig., This is shown in Fig.
 4., 4.
 The comparison is done for 90 common stars and it is in the sense of our photometry minus Clariá et al. (, The comparison is done for 90 common stars and it is in the sense of our photometry minus Clariá et al. (
1994).,1994).
 The results are quite good for V and B-V. as indicated in Fig.," The results are quite good for V and B-V, as indicated in Fig."
 +. down to V — 14.0.," 4, down to V $\sim$ 14.0."
 However. we found some discrepancy for U-B. in the form of a un-accounted color term.," However, we found some discrepancy for U-B, in the form of a un-accounted color term."
work with larger samples (Ilui ct al. 19953).,"work with larger samples (Hui et al. \cite{hui95}) ),"
 one solves the Jeans equations in the equatorial plane aud obtains the mass distribution i some analytical form., one solves the Jeans equations in the equatorial plane and obtains the mass distribution in some analytical form.
 NCC1399 is a nearly round (EO-E1) galaxy., NGC1399 is a nearly round (E0-E1) galaxy.
 Its dynamics depeuds ou the ellipticity of the potential. which is wich rounder than its density distribution (eq€{2 Binney Tremaine 1987)).," Its dynamics depends on the ellipticity of the potential, which is much rounder than its density distribution $\epsilon_{\Phi}\sim\epsilon_{\rho}/3$; Binney Tremaine \cite{bintr}) )."
 Therefore. spjerical svuuuetry is adopte for this Ssvsteni.," Therefore, spherical symmetry is adopted for this system."
 For sake of simplicity. we assune isotropy for the velocity ellipsoid iu the Jeaus equations. accordingly with previous works based on discrete radial velocity fields in different carly-ty20 systeius (Caillimair et al. 199 L..," For sake of simplicity, we assume isotropy for the velocity ellipsoid in the Jeans equations, accordingly with previous works based on discrete radial velocity fields in different early-type systems (Grillmair et al. \cite{grill94}, ,"
 ITui et al. 1995..," Hui et al. \cite{hui95},"
 Arnaho die al. 1998..," Arnaboldi et al. \cite{arn98},"
 Iissler-Patie et al. 1999)., Kissler-Patig et al. \cite{kisl99}) ).
 ludeed. isotropy is not excluded by previous dynamical studies. based ou integrated lelt data: 1) Bielkuell et al. (1989))," Indeed, isotropy is not excluded by previous dynamical studies, based on integrated light data: i) Bicknell et al. \cite{bick89}) )"
" fouxd a variable anisotropy paraicter witlin 100"" around a central null value for a constant mass-to-helto ratio. ALLy=lb d) Saslia ct al. (2000))"," found a variable anisotropy parameter within $100''$ around a central null value for a constant mass-to-light ratio, $M/L_\mathrm{B}=14$; ii) Saglia et al. \cite{sagl00}) )"
" found that a wide raice of anisotropy parameter. iucludiug the Isotropic case. are compatible with the dispersion profiles from PNe aud GCs,"," found that a wide range of anisotropy parameter, including the isotropic case, are compatible with the dispersion profiles from PNe and GCs."
 On the equaorial plane (2= 0). the Isotropic axisvunmoetrie Jeans equation is equivalent to the Isotropic Radial Jeans Equation (IRJE) in spherical coordinates.," On the equatorial plane $z=0$ ), the isotropic axisymmetric Jeans equation is equivalent to the Isotropic Radial Jeans Equation (IRJE) in spherical coordinates."
 Using eCR.0)—ptr) from the light profile with a fixed M/L. Ver from the observations and adopting an aualytical form for the potential. Eq. (13) ," Using $\rho(R,0)=\rho(r)$ from the light profile with a fixed M/L, $V_\mathrm{rot}$ from the observations and adopting an analytical form for the potential, Eq. \ref{axJ1}) )"
can be solved aud the mass distribution derived frou the velocity dispersion data., can be solved and the mass distribution derived from the velocity dispersion data.
 Iu more 1) under spherical svuiuuetry. we compute ptr) by deprojecting the Willeen Bickucll’s (1988)) surface brightuess profile with Xy=16.7340.05 magy 2. RL=λα... and a=172cx0.05 aud the imassto-lieht ratio. AMíLy=121.ει. (we adjust the M/L frou the same authors to our adopted distance).," In more 1) under spherical symmetry, we compute $\rho(r)$ by deprojecting the Killeen Bicknell's \cite{kill88}) ) surface brightness profile with $\Sigma_\mathrm{0}=16.73\pm 0.05$ $_\mathrm{B}$ $^{-2}$, $R_\mathrm{s}=3.0''\pm 0.2''$ and $\alpha=1.72\pm0.05$ and the mass-to-light ratio, $M/L_\mathrm{B}=12M_{\odot}/L_{\odot}$ (we adjust the M/L from the same authors to our adopted distance)."
 This profile is consisteut with the PNe uumuber density distribution (see Fig. 3))., This profile is consistent with the PNe number density distribution (see Fig. \ref{hist}) ).
 Saglia et al. (2000)), Saglia et al. \cite{sagl00}) )
" performed an accurate ceprojectiou of the light distribution aud a dynamical moceling for NGC 1399, obtaining a AM/Ly=10AJ../L. for the huninous component inside R=60"". where the influence of the dark halo starts."," performed an accurate deprojection of the light distribution and a dynamical modeling for NGC 1399, obtaining a $M/L_\mathrm{B}=10M_{\odot}/L_{\odot}$ for the luminous component inside $R=60''$, where the influence of the dark halo starts."
 Since they do not provide us with the stellar deusitv distribution i au analytical form. we prefer to use the analytical expression frou Eq. (2)) (," Since they do not provide us with the stellar density distribution in an analytical form, we prefer to use the analytical expression from Eq. \ref{SBKB}) ) ("
as was doue wi Isissler-Patig et al. 1999..,"as was done by Kissler-Patig et al. \cite{kisl99},"
 for 2) Due to the lack of detailed data. a siuplifed model of VííGCR) as assined: we have a linear regnue out to Rocilo”. t101 Vua drops to zero.," for 2) Due to the lack of detailed data, a simplified model of $V_\mathrm{rot}(R)$ is assumed: we have a linear regime out to $R\approx140''$, then $V_\mathrm{rot}$ drops to zero."
 This artificial model is deprojected assuming circular orbits auk no correction is adopted for inclination (the reason is that the peals velocity is already large enough to accomuodate a high 3) We consider a dark mass contribution to the potential by a simple pseudo-isothermal sphere: where o4 and rg are free paraneters., This artificial model is deprojected assuming circular orbits and no correction is adopted for inclination (the reason is that the peak velocity is already large enough to accommodate a high 3) We consider a dark mass contribution to the potential by a simple pseudo-isothermal sphere: where $\sigma_\mathrm{d}$ and $r_\mathrm{d}$ are free parameters.
" In the IRJE: where 5=ALE, and j(r) is the deprojected huninosity profile: 1) oq aud rq are assigned by matching the velocitydispersion solution of the IRJE. once projected along the"," In the IRJE: where $\gamma=M/L_\mathrm{B}$ and $j(r)$ is the deprojected luminosity profile; 4) $\sigma_\mathrm{d}$ and $r_\mathrm{d}$ are assigned by matching the velocitydispersion solution of the IRJE, once projected along the"
and the components where &=νο.,and the components where $k=\sqrt{6}/2$.
 A condition in 3D for isentropic overturning can he derived from. considering when the racial gradient of the entropy s=b|(12)7 becomes negative. Le. when (1/r).b«l.," A condition in 3D for isentropic overturning can be derived from considering when the radial gradient of the entropy $s = b +
(1/2)r^{2}$ becomes negative, i.e., when $(1/r)\partial_{r} b < -1$."
 This is equivalent to the criterion. that IGr)9G6]z[m]. which can be shown by using Eq. 13..," This is equivalent to the criterion that $|(1/r)\partial_{r} (r u_{r})| > |m|$, which can be shown by using Eq. \ref{3deqs4}."
 Yo correlate our notation with the appendix of OLOT. we define the dimensionless nonlinearity parameter 21. such that Ooverturning occurs if Ajc1.," To correlate our notation with the appendix of OL07, we define the dimensionless nonlinearity parameter $A$ , such that overturning occurs if $|A|>1$."
 This is defined such that the radial velocity is the real part of in the dimensionless units that we have been. using in this section (this is equivalent to Eq. 29))., This is defined such that the radial velocity is the real part of in the dimensionless units that we have been using in this section (this is equivalent to Eq. \ref{lm2wave}) ).
" Overturning is achieved at the centre when the radial velocity in the wave takes a maximum value s,=1.27 at its innermost peak at r=2.04."," Overturning is achieved at the centre when the radial velocity in the wave takes a maximum value $u_{r} = 1.27
$ at its innermost peak at $r=2.04$."
 This value is used to compare it to the magnitude of the radial velocity achieved in numerical simulations at the onset of wave breaking., This value is used to compare it to the magnitude of the radial velocity achieved in numerical simulations at the onset of wave breaking.
 In these dimensionless units. we similarly require 0.99 or b0.38.," In these dimensionless units, we similarly require $u_{\phi} \gtrsim 0.99$ or $b \gtrsim 0.38$."
" Note that there is not such a simple interpretation of the criterion on iw, às in 2D. though the value is quantitatively verysimilar?."," Note that there is not such a simple interpretation of the criterion on $u_{\phi}$ as in 2D, though the value is quantitatively very."
. From the results of the 2D simulations in BOLO. we expect the waves to undergo instability ancl break within several wave periods after these criteria begin to be satisfied.," From the results of the 2D simulations in BO10, we expect the waves to undergo instability and break within several wave periods after these criteria begin to be satisfied."
 The linear solution written down in Eqs. 18-, The linear solution written down in Eqs. \ref{linearsoln3D}-
" 21 ids not a nonlinear solution. unlike the equivalent. in 2D. ""This can be shown by computing the nonlinear terms in the full Boussines¢-tvpe system. using the linear solution. in Alathematica. for example."," \ref{linearsoln3D1} is not a nonlinear solution, unlike the equivalent in 2D. This can be shown by computing the nonlinear terms in the full Boussinesq-type system using the linear solution, in Mathematica, for example."
 We find that u-Vb=0. in general. and similarly for the nonlinear terms in the momentum equation.," We find that $\mathbf{u} \cdot \nabla b
\ne0$, in general, and similarly for the nonlinear terms in the momentum equation."
 This means that the reflection of the waves from the centre could. be different than in 2D. since nonlinearities do not vanish for this wave.," This means that the reflection of the waves from the centre could be different than in 2D, since nonlinearities do not vanish for this wave."
 In this section we perform a weakly nonlinear analysis to determine the dominant nonlinear effects for small amplitudes., In this section we perform a weakly nonlinear analysis to determine the dominant nonlinear effects for small amplitudes.
 Since these nonlinearities do not vanish. this highlights the importance of numerical simulations for these waves approaching the centre.," Since these nonlinearities do not vanish, this highlights the importance of numerical simulations for these waves approaching the centre."
 We describe the results of such simulations in 5., We describe the results of such simulations in \ref{3dresults}.
 We propose a weakly nonlinear solution of the form and similarly for the other variables. where e<1.," We propose a weakly nonlinear solution of the form and similarly for the other variables, where $\epsilon \ll
1$."
 This [orm is adopted. because we are interested in. calculating whether the incoming wave generates harmonics through the quadratic. (self-)nonlinearities., This form is adopted because we are interested in calculating whether the incoming wave generates harmonics through the quadratic (self-)nonlinearities.
 These. additional waves (other than m=0) will escape to infinity ancl carry away a portion of the energy flux., These additional waves (other than $m=0$ ) will escape to infinity and carry away a portion of the energy flux.
 Here we write in4(r.8)c/=mre8.8) from Iq. 29..," Here we write $u_{r1}(r,\theta)e^{i\xi} = u_{r}(r,\theta,\xi)$ from Eq. \ref{lm2wave},"
 for the f=m=2 wave above. and similarly for other variables.," for the $l=m=2$ wave above, and similarly for other variables."
 We substitute these expansions into the Boussinesqetype svstem ancl equate powers of €., We substitute these expansions into the Boussinesq-type system and equate powers of $\epsilon$.
 At each order we also equate coetlicients of οὃς, At each order we also equate coefficients of $e^{in\xi}$.
 At Leading order only one mode is present. and we obtain the previously derived linear solution.," At leading order only one mode is present, and we obtain the previously derived linear solution."
 After some algebra the solution at O(c) can be computed to give which is an /=m=4 wave with complex amplitude dos. which has been computed using Mathematica and given in terms of cA.," After some algebra the solution at $O(\epsilon^{2})$ can be computed to give which is an $l=m=4$ wave with complex amplitude $A_{22}$, which has been computed using Mathematica and given in terms of $A$."
 For the wave described by Eq. 35.," For the wave described by Eq. \ref{leq4meq4wave},"
 £ can be computed., $F$ can be computed.
 The ratio of the οποίον [lux in the outgoing /=m4 wave to the ingoing |—m=2 wave can be shown to be approximatelv 1.210LAP.," The ratio of the energy flux in the outgoing $l=m=4$ wave to the ingoing $l=m=2$ wave can be shown to be approximately $1.2
\times 10^{-5}|A|^{2}$."
 We deline a rellection coelTicient which measures the amplitude: decav for ai wave travelling from a radius r to the centre. and back to r.," We define a reflection coefficient which measures the amplitude decay for a wave travelling from a radius $r$ to the centre, and back to $r$."
 For perfect rellection from the centre R=1. whereas complete absorption means that R=0.," For perfect reflection from the centre $\mathcal{R} = 1$, whereas complete absorption means that $\mathcal{R} = 0$."
 Phe reflection coellicient. for reflection from the centre. for a weakly nonlinear /=m2 wave. can be computed [rom This means that à weakly nonlinear primary wave (with Al< 1). will reflect approximately perfectly from the centre. with a rellection coellicicnt that is close to unity.," The reflection coefficient for reflection from the centre, for a weakly nonlinear $l=m=2$ wave, can be computed from This means that a weakly nonlinear primary wave (with $|A| \ll
1$ ), will reflect approximately perfectly from the centre, with a reflection coefficient that is close to unity."
 However. a small fraction of the IW energy flux is transferred to waveswith higher / and. m-values. reinforcing the fact that Eqs. 18-," However, a small fraction of the IW energy flux is transferred to waveswith higher $l$ and $m$ -values, reinforcing the fact that Eqs. \ref{linearsoln3D}-"
 210 is not an exact solution. contrary to the analogous solution in 2D. We solve the Doussinesqetvpe svstem in three dimensions using the Cartesian pseudospectral code SNOOPY," \ref{linearsoln3D1} is not an exact solution, contrary to the analogous solution in 2D. We solve the Boussinesq-type system in three dimensions using the Cartesian pseudospectral code SNOOPY"
properties of the models. since each real object is viewed [rom only one direction.,"properties of the models, since each real object is viewed from only one direction."
 The density structure of the ISM is often described as “fractal”. meaning; sell-similar on all size scales.," The density structure of the ISM is often described as “fractal"", meaning self-similar on all size scales."
 We will consider models (hat are hierarchically clumpecl instead. meaning that they are sell-similar over a limited range (about a [actor of ten) in sizes.," We will consider models that are hierarchically clumped instead, meaning that they are self-similar over a limited range (about a factor of ten) in sizes."
" We use a procedure similar to (hat in Elhmnegreen (1997): (a) Consider a ""supercube'. a portion of which will represent a spherical reflection nebula."," We use a procedure similar to that in Elmegreen (1997): (a) Consider a “supercube"", a portion of which will represent a spherical reflection nebula."
 The supercube of size L on a side consists ol 64 cubical cells stacked along each dimension., The supercube of size L on a side consists of 64 cubical cells stacked along each dimension.
 For each cell we determine the local density of dust. as explained below. (," For each cell we determine the local density of dust, as explained below. ("
b) Place .N. points randomly within the supercube.,b) Place $N$ points randomly within the supercube.
 We used Vv = 32. (, We used $N$ = 32. (
c) Randomly cast another NV points. all within a distance L/(2.N) in each Cartesian axis from each of the points east in the preceding round.,"c) Randomly cast another $N$ points, all within a distance $L/(2\Delta)$ in each Cartesian axis from each of the points cast in the preceding round."
" Here the distance A is related to the ""fractal dimension. D. bv D=log(CN)/log(.N)."," Here the distance $\Delta$ is related to the “fractal dimension”, $D$, by $D\equiv\log(N)/\log(\Delta)$."
 Allow anv of the points that fall outside of (he supercube to remain there. (, Allow any of the points that fall outside of the supercube to remain there. (
d) Repeat procedure (c). above. twice more. so thatthe total number of points cast is V4. (,"d) Repeat procedure (c), above, twice more, so thatthe total number of points cast is $N^4$. ("
e) Shift the points outside of the supercube to within it by translating each Cartesian coordinate outside of the supercube by £ until it lies within.,e) Shift the points outside of the supercube to within it by translating each Cartesian coordinate outside of the supercube by $L$ until it lies within.
 This procedure reflects the points so (hat if Chev originally fall olf the left side of the supercube they reappear (he same distance from the right within the supercube. and correspondingly for up/down and [ront/back.," This procedure reflects the points so that if they originally fall off the left side of the supercube they reappear the same distance from the right within the supercube, and correspondingly for up/down and front/back."
 The density within the supercube is then proportional to the number of points within each cell. (, The density within the supercube is then proportional to the number of points within each cell. (
£) Inscribe a sphere within the supercube ancl place a point source of radiation at its center.,f) Inscribe a sphere within the supercube and place a point source of radiation at its center.
" The constant of proportionalitv between (he number of points in each cell and (he optical depth within (he cell is chosen to make the radial optical depth. averaged over all directions. be7,."," The constant of proportionality between the number of points in each cell and the optical depth within the cell is chosen to make the radial optical depth, averaged over all directions, be."
. The main parameter of this procedure is D. which describes the degree of clumping.," The main parameter of this procedure is $D$, which describes the degree of clumping."
 We considered. D) = 2.3 and 2.6. in the range observed in actual clouds.," We considered $D$ = 2.3 and 2.6, in the range observed in actual clouds."
 Another observable parameter is 2. (he exponent of the power of (he projection of the density within the supercube onto the plane of theskv!.. so that P(A)xhhà. where & is thewavenunmber.," Another observable parameter is $\beta$, the exponent of the power of the projection of the density within the supercube onto the plane of the, so that $P(k)\propto k^{-\beta}$, where $k$ is thewavenumber."
 Observations (e.g. Stanimirovié et al., Observations (e.g. Stanimirović et al.
 1999) show 9~3., 1999) show $\beta\sim3$.
 With our recipe we find 9=2.5 with D = 2.6 and 9~2.3 with D = 2.3., With our recipe we find $\beta=2.8$ with $D$ = 2.6 and $\beta\sim2.3$ with $D$ = 2.3.
 However. none of the conclusions in this paper depend upon which set of hierarchical models we consider.," However, none of the conclusions in this paper depend upon which set of hierarchical models we consider."
 Many different models can have the same 2., Many different models can have the same $\beta$ .
 No one parameter. either D or 9. can completely describe even the projection," No one parameter, either $D$ or $\beta$ , can completely describe even the projection"
Studies in near-Hi. where the extinction is lower than in visual wavelengths ancl majority of ight comes from the old. scllar population. have shown tiu about of all spiral galaxies have a large scale stellar bar (?????)..,"Studies in near-IR, where the extinction is lower than in visual wavelengths and majority of light comes from the old stellar population, have shown that about of all spiral galaxies have a large scale stellar bar \citep{eskridge2000,whyte2002,laurikainen2004,menendez2007,marinova2007}."
 According to recent analysis of over 2000 spiral galaxies (?).. he bar fraction decreases from arout in the local universe to about at redshift zO.S4 (seealso2?7??)..," According to recent analysis of over 2000 spiral galaxies \citep{sheth2008}, the bar fraction decreases from about in the local universe to about at redshift $z=0.84$ \citep[see
 also][]{abraham99,elmegreen2004,jogee2004,menendez2007}."
 Anvhow. bars are so common that they are either very robust or they represent a recurrent pienomenon in the life ofa spiral galaxy (7)..," Anyhow, bars are so common that they are either very robust or they represent a recurrent phenomenon in the life of a spiral galaxy \citep{bournaud2005}."
 In contrast wit1 some earlier stucdes (??). ? claim the bar frequency. is roughlv the same in dilferent environments modest interactions do not seem to play a major role in bar formation and destruction.," In contrast with some earlier studies \citep{thompson81,elmegreen90c}, \citet{hernandeztoledo2007} claim the bar frequency is roughly the same in different environments – modest interactions do not seem to play a major role in bar formation and destruction."
 Jars can be roughly divided into two classes based on their light distribution: flat and. exponential bars (??)," Bars can be roughly divided into two classes based on their light distribution: flat and exponential bars \citep{elmegreen85,elmegreen96b}."
 In the first twpe. which is more typical to carly type barred ealaxies. the racial surface brightness profile along the bar major axis is Matter than in the surrounding disc. whereas in the exponential bars the profile is quite similar to the surrounding disc.," In the first type, which is more typical to early type barred galaxies, the radial surface brightness profile along the bar major axis is flatter than in the surrounding disc, whereas in the exponential bars the profile is quite similar to the surrounding disc."
 Furthermore. the flat. bars can display twisting of isophotes (2)..," Furthermore, the flat bars can display twisting of isophotes \citep{elmegreen96a}."
 Bar morphology can also be either classical or of ansae-tvpe. characterized by blops at the both ends of tyw bar (?7)," Bar morphology can also be either classical or of ansae-type, characterized by blops at the both ends of the bar \citep{laurikainen2007,martinez2007}."
 Anoher approach to characterize a bar is its strength., Another approach to characterize a bar is its strength.
 Some atempts have based on the cllipticity of the deprojectecd bar. (e.g.22?)," Some attempts have based on the ellipticity of the deprojected bar \citep[e.g. ][]{martin95b,whyte2002,laurikainen2002b}."
 lecentlv. there have been attempts to estimate the actual gravitational perturbation of the bar by. using near-IHt photometry (?22?2?2)..," Recently, there have been attempts to estimate the actual gravitational perturbation of the bar by using near-IR photometry \citep{buta2001b,laurikainen2002b,laurikainen2004,laurikainen2005,buta2005}."
 Phere is also another bar strength estimate. namely the 2d3o-Fourier amplitudes of density (22).. which is an approximation of the relative mass of the bar.," There is also another bar strength estimate, namely the $A_2$ -Fourier amplitudes of density \citep{laurikainen2004,laurikainen2005}, which is an approximation of the relative mass of the bar."
 All these bar strength estimates are discussed with respect to the Hubble sequence by. 2.., All these bar strength estimates are discussed with respect to the Hubble sequence by \citet{laurikainen2007}.
 Perhaps the most important. parameter defining a bar is its pattern speed. Ono. or how Last the xw rotates.," Perhaps the most important parameter defining a bar is its pattern speed, $\Omega_{bar}$, or how fast the bar rotates."
 In principle. this determines how far the orbits of stars and gas clouds are allected by the bar.," In principle, this determines how far the orbits of stars and gas clouds are affected by the bar."
 Phe pattern speed has, The pattern speed has
impact on the cluster velocity dispersion and hence the mass estimate.,impact on the cluster velocity dispersion and hence the mass estimate.
" At the high mass range cluster velocity dispersions should be more reliable, but there are very few objects that contribute to the average mass estimate."," At the high mass range cluster velocity dispersions should be more reliable, but there are very few objects that contribute to the average mass estimate."
" In addition to this, in the high mass range, when all the galaxies in an individual mock halo have been detected perfectly by the DFoF code, the cluster mass from the velocity dispersion tends to be overestimated by around 10°*Mo."," In addition to this, in the high mass range, when all the galaxies in an individual mock halo have been detected perfectly by the DFoF code, the cluster mass from the velocity dispersion tends to be overestimated by around $10^{0.4}\textrm{M}_\odot$."
" This is, however, comparable with the size of the error bars in the high mass range of fig.12.."," This is, however, comparable with the size of the error bars in the high mass range of \ref{fig:mass_v_n}."
 'The range of cluster masses is a good match to known masses of massive clusters., The range of cluster masses is a good match to known masses of massive clusters.
" Therefore, from this analysis we can assume that mass estimates made with the real 2SLAQ cluster velocity dispersions will be approximately representative of their true physical masses with a large amount of uncertainty, particularly in the low mass range."," Therefore, from this analysis we can assume that mass estimates made with the real 2SLAQ cluster velocity dispersions will be approximately representative of their true physical masses with a large amount of uncertainty, particularly in the low mass range."
" This uncertainty could be reduced with a larger sample of clusters and by including all cluster galaxies, rather than just the LRGs, to calculate the velocity dispersions."," This uncertainty could be reduced with a larger sample of clusters and by including all cluster galaxies, rather than just the LRGs, to calculate the velocity dispersions."
" In section 5.1 we chose to produce a catalogue that optimised the completeness, while maintaining the highest possible"," In section 5.1 we chose to produce a catalogue that optimised the completeness, while maintaining the highest possible"
uncorrelated with location of the bright sources. with an RMS noise of 0.15 mJy/beam.,"uncorrelated with location of the bright sources, with an RMS noise of $0.15$ mJy/beam."
 Convergence of the deconvolution iterations is judged by the statistics in the residual image at convergence., Convergence of the deconvolution iterations is judged by the statistics in the residual image at convergence.
" Errors in the final residual image purely due to primary beam (PB) effects (within the main-lobe) can be expressed as: where ""x represents the convolution operator. v is the feed Parallactic Angle. APB(w) is the error between the true and the assumed primary beam model at PA=w. É is the true sky distribution and PSF(w) is the instantaneous (snapshot) PSF."," Errors in the final residual image purely due to primary beam (PB) effects (within the main-lobe) can be expressed as: where $\star$ ' represents the convolution operator, $\psi$ is the feed Parallactic Angle, $\Delta PB(\psi)$ is the error between the true and the assumed primary beam model at $=\psi$, $\vec{I^\circ}$ is the true sky distribution and $PSF(\psi)$ is the instantaneous (snapshot) PSF."
 When imaging using an azimuthally symmetric PB model. the PB error pattern is given by APB(W)=PB-PB) where PB is the azimuthally averaged PB.," When imaging using an azimuthally symmetric PB model, the PB error pattern is given by $\Delta PB(\psi) = \overline{PB} - PB(\psi)$ where $\overline{PB}$ is the azimuthally averaged PB."
 Rotation of this error pattern on the sky contributes the dominant systematic errors in the residual image (and consequently in the final deconvolved image)., Rotation of this error pattern on the sky contributes the dominant systematic errors in the residual image (and consequently in the final deconvolved image).
 The peak residual can be estimated for a point source of flux density S located at the position of the peak of the error pattern multiplied by the maximum sidelobe of the instantaneous PSF at PA=wW;: Instantaneous Stokes-[ and -V VLA antenna power patterns at 1.4. GHz are shown in Fig. 7.., The peak residual can be estimated for a point source of flux density $S$ located at the position of the peak of the error pattern multiplied by the maximum sidelobe of the instantaneous PSF at $\psi_i$: Instantaneous Stokes-I and -V VLA antenna power patterns at 1.4 GHz are shown in Fig. \ref{PB}.
 The patterns rotate on the sky with PA which results in. time-varying. position-dependent gain across the field of view.," The patterns rotate on the sky with PA which results in time-varying, position-dependent gain across the field of view."
 The APB and an azimuthal cut through this error pattern. at 50%. 10% and 1% point of PB are shown in Figs.," The $\Delta PB$ and an azimuthal cut through this error pattern at $50\%$ , $10\%$ and $1\%$ point of $\overline{PB}$ are shown in Figs."
 5 and 9 respectively., \ref{dPB-I} and \ref{dPBCut-I} respectively.
" The contours correspond to PB,,,, |. "," The contours correspond to $\overline{PB}_{max}\times
[0.01,0.05,0.07,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,0.95]$ ."
Within the main-lobe of the Stokes-I beam. the peak of the error pattern is where PB is between |—10%.," Within the main-lobe of the Stokes-I beam, the peak of the error pattern is where $\overline{PB}$ is between $1-10\%$."
 For $=1 Jy. PSFidetobedWe|mac=305€ (measured for the test 1.4 GHz. C-array data) ard APBNg»=0.005. the peak residual will be about 2 mJy in Stokes-L. Peak residuals in Stokes-V would be at the level of about 10 mJy.," For $S=1$ Jy, $\left.PSF_{sidelobe}(\psi_\circ)\right|_{max}=40\%$ (measured for the test 1.4 GHz, C-array data) and $\left.\Delta
PB(\psi_\circ)\right|_{max}=0.005$, the peak residual will be about $2$ mJy in Stokes-I. Peak residuals in Stokes-V would be at the level of about $10$ mJy."
 The decon‘olution algorithm described above consists essentiallyof approximating the function shown in Fig. 9(, The deconvolution algorithm described above consists essentiallyof approximating the function shown in Fig. \ref{dPBCut-I} (
or,or
If this behaviour occurs only in a significant fraction of the intermediate and low luminosity objects. then it could reproduce the observed change in quasar fraction.,"If this behaviour occurs only in a significant fraction of the intermediate and low luminosity objects, then it could reproduce the observed change in quasar fraction."
 Essentially this mocel is a slightly. more complicated version of the two-population model considered. in Section 4.5. with the two populations being unified. along a time rather than a jet orientation axis.," Essentially this model is a slightly more complicated version of the two-population model considered in Section 4.5, with the two populations being unified along a time rather than a jet orientation axis."
 Ht is important to stress that there is as vet no. firm evidence for the type of time variability required., It is important to stress that there is as yet no firm evidence for the type of time variability required.
 However. the few long-term time variability stucies that there may be some interesting ellects: the BLRG3€ -s390.3 was found to undergo a sustaine decrease of 1.5 mags the optical over zSO vears (Cannon. Penston Penston LOGS): however. Angione (1973) used archiva plates to study the variability. of 23 quasars over =08 vears finding no evidence for long-term sustained increases or decreases.," However, the few long-term time variability studies hint that there may be some interesting effects: the BLRG 3C 390.3 was found to undergo a sustained decrease of 1.5 mags in the optical over $\approx 80$ years (Cannon, Penston Penston 1968); however, Angione (1973) used archival plates to study the variability of 23 quasars over $\approx 60$ years finding no evidence for long-term sustained increases or decreases."
 A separate issue related to time variability is whether the probability of individual radio sources being observed to be quasars varies systematically throughout their lifetimes., A separate issue related to time variability is whether the probability of individual radio sources being observed to be quasars varies systematically throughout their lifetimes.
 Because flus-limitecl samples. introduce inevitable biases into the age distributions of the sources they contain (c.g. DBlundell. Rawlings Willott 1999). this can lead to subtle ollects.," Because flux-limited samples introduce inevitable biases into the age distributions of the sources they contain (e.g. Blundell, Rawlings Willott 1999), this can lead to subtle effects."
 Using complete. low-Lrequeney selected: samples. of radio-loud AGN we have investigated the Lraction of observed broad line objects — the quasar fraction as a function of redshift. ane radio ancl emission line. luminosity.," Using complete, low-frequency selected samples of radio-loud AGN we have investigated the fraction of observed broad line objects – the quasar fraction – as a function of redshift, and radio and emission line luminosity."
 Our findings are interpreted in terms of orientation-based unified schemes., Our findings are interpreted in terms of orientation-based unified schemes.
" We find that We have [found evidence which supports at least wo probable physical causes [or the drop in quasar raction at [low luminositv: (i) a gradual decrease in uus, and/or a gradual increase in the fraction of lishtlv-reddened (OS2A,2: 5) lines-of-sight with decreasing quasar unilnosity and (ii) the emergence ofa second population of ow Luminosity racio sources which. like AIST. lack a well-fed quasar nucleus. and may well lack a thick obscuring torus."," We find that We have found evidence which supports at least two probable physical causes for the drop in quasar fraction at low luminosity: (i) a gradual decrease in $\theta_{\rm trans}$ and/or a gradual increase in the fraction of lightly-reddened $0 \ltsimeq A_{V} \ltsimeq 5$ ) lines-of-sight with decreasing quasar luminosity; and (ii) the emergence of a second population of low luminosity radio sources which, like M87, lack a well-fed quasar nucleus, and may well lack a thick obscuring torus."
 We would like to thank Steve Eales. Gary Hill. Julia Γον and David Rossitter for important. contributions to the τς Redshift Survey.," We would like to thank Steve Eales, Gary Hill, Julia Riley and David Rossitter for important contributions to the 7C Redshift Survey."
 Thanks also to Robert Laing ancl Chris Simpson for some very useful cliscussions. and to the referee lan Browne for useful suggestions.," Thanks also to Robert Laing and Chris Simpson for some very useful discussions, and to the referee Ian Browne for useful suggestions."
 This research has mace use of the NASA/IPAC. Extra-ealactic Database. which is operated. by the Jet Propulsion Laboratory. Caltech. under contract with the National Acronautics ancl Space Administration.," This research has made use of the NASA/IPAC Extra-galactic Database, which is operated by the Jet Propulsion Laboratory, Caltech, under contract with the National Aeronautics and Space Administration."
 CJW thanks PPARC for support., CJW thanks PPARC for support.
common flat field.,common flat field.
 An average extinelion curve was used to reduce the data., An average extinction curve was used to reduce the data.
" For the skv brightness data we used an extraction aperture of either 40 pixels (30.6"") or 60 pixels (45.97) depending upon the decker usec.", For the sky brightness data we used an extraction aperture of either 40 pixels $\arcsec$ ) or 60 pixels $\arcsec$ ) depending upon the decker used.
 Errors for our data can be estimated as the equacdrature sum of the individual uncertainties., Errors for our data can be estimated as the quadrature sum of the individual uncertainties.
 The plate scale is well determined (<1%)). as described previously.," The plate scale is well determined $<$ ), as described previously."
" Nevertheless. in setting the slit width to 395 jan (5.00"") we relied upon our ability to read the micrometer setting bv eve. a process which was reproducible only at the 3 jam level."," Nevertheless, in setting the slit width to 395 $\mu$ m $\arcsec$ ) we relied upon our ability to read the micrometer setting by eye, a process which was reproducible only at the 3 $\mu$ m level."
 In addition. there was the question of whether the slit was exactly Παν closed when the micrometer read 0.," In addition, there was the question of whether the slit was exactly fully closed when the micrometer read 0."
 We measured (his repeatedly using exposures of an internal quartz lamp. varvine the slit width. and found that the zero-point was no larger than 3 jam. Thus. our slit setting is probably uncertain by about 4 san. or (0.02 magnitudes).," We measured this repeatedly using exposures of an internal quartz lamp, varying the slit width, and found that the zero-point was no larger than 3 $\mu$ m. Thus, our slit setting is probably uncertain by about 4 $\mu$ m, or (0.02 magnitudes)."
 As described previously. the uncertainty in the plate scale at the detector is known to better than1%.," As described previously, the uncertainty in the plate scale at the detector is known to better than."
. The adoption of a mean extinction curve was estimated by Alassev Γο (2000) to add another 0.01 magnitude error. since (his affects only the wavelength dependent part of the extinction.," The adoption of a mean extinction curve was estimated by Massey Foltz (2000) to add another 0.01 magnitude error, since this affects only the wavelength dependent part of the extinction."
 The mean errors from the spectrophotometrie standards adds another 0.03 magnitudes. a combination both of the uncertainty in the absolute calibration ancl probably variable slit losses.," The mean errors from the spectrophotometric standards adds another 0.03 magnitudes, a combination both of the uncertainty in the absolute calibration and probably variable slit losses."
 So in total. we estimate (he uncertainty in our spectrophotometry as 0.04 magnitudes.," So in total, we estimate the uncertainty in our spectrophotometry as 0.04 magnitudes."
 Although our goal was to obtain moderate resolution spectrophotometry. it is also useful to describe the data in terms of broad- and πατονρα indices. to facilitate comparison wilh the previous (wo decades.," Although our goal was to obtain moderate resolution spectrophotometry, it is also useful to describe the data in terms of broad- and narrow-band indices, to facilitate comparison with the previous two decades."
 The synthetic V and 2 magnitudes presented in Tables 1. and 2 were computed using the filter Functions determined by Bessell (1990)., The synthetic $V$ and $B$ magnitudes presented in Tables \ref{tab:AllMags} and \ref{tab:CompMags} were computed using the filter functions determined by Bessell (1990).
 The convolutions for both the broadband anc narrowband magnitudes were performed on Vega using STIS speclrophotometry (Bohlin Gilliland 2004) to determine the zero-points assuming (hat Vega has a D and V magnitude of 0.03 (Bessell et 11988)., The convolutions for both the broadband and narrowband magnitudes were performed on Vega using STIS spectrophotometry (Bohlin Gilliland 2004) to determine the zero-points assuming that Vega has a $B$ and $V$ magnitude of 0.03 (Bessell et 1988).
 The broadband magnitudes were then computed after replacing 17 oon both sice of the hiehly variable OI 5577 atmospheric line by an averaged value., The broadband magnitudes were then computed after replacing 17 on both side of the highly variable OI 5577 atmospheric line by an averaged value.
 The zurowband magnitudes were computed using a constant response over a LOO interval centered al either A4250. A4550. or A5150.," The narrowband magnitudes were computed using a constant response over a 100 interval centered at either $\lambda$ 4250, $\lambda$ 4550, or $\lambda$ 5150."
 The 1988 and 1999 magnitudes presented in Tables 1 and 2. do not perfectly match those of Massey et ((1990) ancl Massey Foltz (2000). as there was an error made in (he conversion (to (he standard svstem in (he previous studies.," The 1988 and 1999 magnitudes presented in Tables \ref{tab:AllMags} and \ref{tab:CompMags} do not perfectly match those of Massey et (1990) and Massey Foltz (2000), as there was an error made in the conversion to the standard system in the previous studies."
 The values given here are correct. and agree much better with other broadband neasurements of the night skv brightness of itt Peak. e.g.. Pilachowski et ((1939).," The values given here are correct, and agree much better with other broadband measurements of the night sky brightness of Kitt Peak, e.g., Pilachowski et (1989)."
 since all of our 2009/10 data were taken on all-sky photometric nights. we were especially," Since all of our 2009/10 data were taken on all-sky photometric nights, we were especially"
age of the population or the fraction of voung stars as the radio power increases (Fig. 3)).,age of the population or the fraction of young stars as the radio power increases (Fig. \ref{fig:Pfits}) ).
 The only exception is that the very highest power sources (the D4 composite. consisting of the 11 sources with logP?z 26: Table 12) appear to have a substantially vounger population (100. Myr). as well as strong 33727 emission (which was not included in the fit).," The only exception is that the very highest power sources (the D4 composite, consisting of the 11 sources with $\log P > 26$ ; Table \ref{tab:composites}) ) appear to have a substantially younger population (100 Myr), as well as strong 3727 emission (which was not included in the fit)."
 This difference is not seen in the matching sample of racdio-quiet sources. suggesting that the voung stars are in some wav associated with the active nucleus.," This difference is not seen in the matching sample of radio-quiet sources, suggesting that the young stars are in some way associated with the active nucleus."
 Reeall that this was Ίο only composite showing a simple X7 dillerence with the ther composites 3.1))., Recall that this was the only composite showing a simple $\chi^2$ difference with the other composites \ref{sec:differences}) ).
 We checked the eleven individual Esvectra which went into the D4 composite. in case the 'omposite was being skewed by a single peculiar object.," We checked the eleven individual spectra which went into the D4 composite, in case the composite was being skewed by a single peculiar object."
 No individual spectrum. appeared to be peculiar: 6 of the 11 gaiowed strong emission lines., No individual spectrum appeared to be peculiar; 6 of the 11 showed strong emission lines.
 The D-composites and their rest-Litting models are shown in Fig. 5.., The D-composites and their best-fitting models are shown in Fig. \ref{fig:modelD}.
 We tried splitting re second-highest power bin. (D3). to see if there was a continuous trend: both sub-bins had similar ages. of ~1000 and ~700 Myr. quite dilferent from the 100 Myr population ound in the D4 bin.," We tried splitting the second-highest power bin (D3), to see if there was a continuous trend; both sub-bins had similar ages, of $\sim 1000$ and $\sim 700$ Myr, quite different from the 100 Myr population found in the D4 bin."
 Thus the dilference. appears to. be confined to the very highest radio-power sources., Thus the difference appears to be confined to the very highest radio-power sources.
 In Figure 6 we plot the ratio of these models., In Figure \ref{fig:modelD-comp} we plot the ratio of these models.
 The igure shows there are small changes to spectral lines. but he principal dilference is a change in slope in the mocel fit o the D4 composite.," The figure shows there are small changes to spectral lines, but the principal difference is a change in slope in the model fit to the D4 composite."
 We investigated whether the young population in the lighest-power radio sources could in [act be due to emission rom the central AGN. which would also produce excess blue ight.," We investigated whether the young population in the highest-power radio sources could in fact be due to emission from the central AGN, which would also produce excess blue light."
" We tried replacing the second. voung population in our fits with a power-law continuum of the form fyxA"". where à wavas allowed to vary between 5 aand 0."," We tried replacing the second, young population in our fits with a power-law continuum of the form $f_\lambda \propto \lambda^\alpha$, where $\alpha$ was allowed to vary between $-5$ and 0."
 The fit was significantly. poorer than the best-fitting model with a voung stellar population: the bbreak was not well reproduced., The fit was significantly poorer than the best-fitting model with a young stellar population: the break was not well reproduced.
 Thus we conclude that the highest power radio sources do show evidence of association with a population of voung stars., Thus we conclude that the highest power radio sources do show evidence of association with a population of young stars.
 Emission lines were present in many of the spectra. mostly‘Ouj.. and occasionally aand citepseeTable3of]Jsem 107..," Emission lines were present in many of the spectra, mostly, and occasionally and \\citep[see Table~3 of][]{scm+07}."
 Phe 44958.5007 pair was seen in only a single galaxy. J100322.41-000137.8. but was redshifted bevond the wavelength range of most of our sources.," The 4958,5007 pair was seen in only a single galaxy, J100322.41-000137.8, but was redshifted beyond the wavelength range of most of our sources."
 Sadleretal.(2007) found that the fraction of 28LAQ radio galaxies which show cemission is higher (QJ) than the overall 28LAQ spectroscopic sample (17.7Roseboometal.2006)., \citet{scm+07} found that the fraction of 2SLAQ radio galaxies which show emission is higher ) than the overall 2SLAQ spectroscopic sample \citep[17.7\%;][]{rpd+06}.
. llowever. since more Luminous galaxies are more likely to show emission. this result. needs to be approached with caution.," However, since more luminous galaxies are more likely to show emission, this result needs to be approached with caution."
 In any case. most of the radio galaxies in 28LO would not have been recognised as GN on the basis of their optical spectra. alone.," In any case, most of the radio galaxies in 2SLAQ would not have been recognised as AGN on the basis of their optical spectra alone."
 This agrees well with several other studies. which found little evidence of correlation between radio power and emission line strength. in nearby. racio ealaxies (ltixonctal.1991:Owenet1995).," This agrees well with several other studies, which found little evidence of correlation between radio power and emission line strength in nearby radio galaxies \citep{rwb91,olk95}."
 ὃν using a comparison sample of radio-quiet. galaxies. matched. in redshift and luminositv. we are able. to investigate this cllect.," By using a comparison sample of radio-quiet galaxies, matched in redshift and luminosity, we are able to investigate this effect."
 Comparison of the emission-line properties of our radio-loud sources with the matched sample of racio-quict galaxies reveals clillercnees between the two groups., Comparison of the emission-line properties of our radio-loud sources with the matched sample of radio-quiet galaxies reveals differences between the two groups.
 We can examine the emission lines in two wavs: finding the number of individual galaxies which show emission lines as a function of various parameters. and investigating the properties of the emission lines in the composite spectra.," We can examine the emission lines in two ways: finding the number of individual galaxies which show emission lines as a function of various parameters, and investigating the properties of the emission lines in the composite spectra."
 The equivalent widths ofthe line in the individual spectra were measured: using the, The equivalent widths ofthe line in the individual spectra were measured using the
the eccentricity is e then the equation of the orbit is given by where 8 is the phase angle and @= 276.0<6< Lis orbital phase.,"the eccentricity is $e$ then the equation of the orbit is given by where $\theta$ is the phase angle and $\theta\,=\,2\pi \phi$, $0\leq\phi\leq1$ is orbital phase."
 From Figure 2.. using simple gcometry. one can write If the radio emitting region is located at à height z from the base of the jet then In Figure 2. zO'PC'= υπο Using equations (2)) and (4)) equation (5)) can be written Expressing all distances in the units of e. equation (6)) can be rewritten as where p= 2.2 cor Using the gcometry of Figure 2 one can finally write where %=2cos?(0)sn; and .4=zsni| cosi.," From Figure \ref{orbit}, using simple geometry, one can write If the radio emitting region is located at a height $z$ from the base of the jet then In Figure \ref{orbit} $\angle O^{\prime}FC\, =\, (\frac{\pi}{2}-\chi)$ , so Using equations \ref{eq1}) ) and \ref{eq3}) ) equation \ref{eq4}) ) can be written as Expressing all distances in the units of $a$, equation \ref{eq5}) ) can be rewritten as where ${\bar r}=\frac{r}{a}$ , ${\bar z}=\frac{z}{a}$, ${\bar x}=\frac{x}{a}$ and Using the geometry of Figure \ref{orbit} one can finally write where $\mathscr{Z} = \bar z \, \cos i \, - \, \bar K(\theta) \, \sin{i}$ and $\mathscr{B} = \bar z\, \sin{i} \,+\, \bar K(\theta) \, \cos{i}$ ."
 For an aligned. jet. where ὁ=0. %=2 and A=(0).," For an aligned jet, where $i=0$, $\mathscr{Z} = \bar z$ and $\mathscr{B} = \bar K(\theta)$."
" For a spherical wind the wind density at a distance r from star is given by (?)). llere AZ is the mass loss rate of the wind. Z2, is the radius of the star. e is the terminal velocity of the wind at far away distance."," For a spherical wind the wind density at a distance $r$ from star is given by \cite{puls96}) ), Here $\dot M$ is the mass loss rate of the wind, $R_{\star}$ is the radius of the star, $v_{\infty}$ is the terminal velocity of the wind at far away distance."
" The frec-[ree absorption optical depth is given by As rcHi so with the approximation that 2). the optical depth is given by For LS 5039. the parameter values are Z7=375001lx . M-10A. tia =20H... ο, 24"" and ος=240 km s.1(2?21."," The free-free absorption optical depth is given by As $r > R_{\star}$, so with the approximation that $(1-\frac{\bar R_{\star}}{\bar r})^{-2} \approx (1+\frac{2\bar R_{\star}}{\bar r})$ , the optical depth is given by For LS 5039, the parameter values are $T\,=\,37500$ K, $\dot M\,=\,10^{-7}\,M_{\odot}$ $^{-1}$, $a\,=\,20\,R_{\odot}$, $e\,=\,0.24$, $R_{\star}\,=\,9.5\,R_{\odot}$, $i\,=\,24^o$ and $v_{\infty}\,=\,2440$ km $^{-1}$ \cite{swain04, cas05, swain11}) )."
 The variation of optical depth with orbital phase for three different locations of the radio emitting regions are shown in Figure 3. for frequencies 1280 and 605 Mllz., The variation of optical depth with orbital phase for three different locations of the radio emitting regions are shown in Figure \ref{optdep1} for frequencies 1280 and 605 MHz.
 For the inner jet it is evident that he optical depth varies periodically., For the inner jet it is evident that the optical depth varies periodically.
 It is maximum during he periastron passage (ὁ=0) and is minimum curing apastron passage (6.= 0.5).," It is maximum during the periastron passage $\phi\,=\,0$ ) and is minimum during apastron passage $\phi\,=\,0.5$ )."
 Ehis is true for both O° and 24° inclination angle of the jet the inclination of orbital ane with respect to the sky. plane., This is true for both $0^o$ and $24^o$ inclination angle of the jet the inclination of orbital plane with respect to the sky plane.
 As the height of the radio emission zone increases the periodic variation of the optical depth diminishes ancl essentially the optical depth comes almost independent of the orbital phase for z217 =ΊταL6 AU).," As the height of the radio emission zone increases the periodic variation of the optical depth diminishes and essentially the optical depth becomes almost independent of the orbital phase for $\bar z \approx 17$ $z\,=\,17a = 1.6$ AU)."
 For z1.6 AU. the optical depth or 1280. MllIz. τν=1280MIIZ)| for the inclination angle 24°.," For $z \approx 1.6$ AU, the optical depth for 1280 MHz, $\tau_{ff}(\nu=1280 \text{MHz}) \approx 1$ for the inclination angle $^o$."
 As the spectral turnover is found to be around 1000 Mllz.so rrr& Lis the necessary condition to constrain he emission height for the given physical condition.," As the spectral turnover is found to be around 1000 MHz, so $\tau_{ff} \approx 1$ is the necessary condition to constrain the emission height for the given physical condition."
 Since he optical depth at this height becomes independent of the orbital phase so the emitted radio Εαν densities will also be ohase-independent., Since the optical depth at this height becomes independent of the orbital phase so the emitted radio flux densities will also be phase-independent.
 Phe approximately: constant observed lux during periastron and apastron passages reported here does not contradict the present. absorption mocdel., The approximately constant observed flux during periastron and apastron passages reported here does not contradict the present absorption model.
 For an alignedjet (/= 0). the estimated height of the radio emission zone will be little less than 1.6 AU.," For an aligned jet $i=0$ ), the estimated height of the radio emission zone will be little less than 1.6 AU."
 These estimates indeed assume that the basic emission process remains unchanged [or all orbital phases., These estimates indeed assume that the basic emission process remains unchanged for all orbital phases.
 Ht is only the wind density changes [or dillerent orbital phases ollering different optical depth to the emitted. radiation., It is only the wind density changes for different orbital phases offering different optical depth to the emitted radiation.
 However these estimations may change i£ (7) the stellar wind is focussecl or (77) the absortion is due to svnchrotron selt-absorption in the jet., However these estimations may change if $(i)$ the stellar wind is focussed or $(ii)$ the absortion is due to synchrotron self-absorption in the jet.
 In fact recent observation of Hle 1 and 12 lines from 55039 by 2? indicates the presence of focussed wind in the binary system., In fact recent observation of He I and $\beta$ lines from 5039 by \cite{sart11} indicates the presence of focussed wind in the binary system.
 ? observed. significant changes in the 112 and He L spectral lines with the orbital phase., \cite{sart11} observed significant changes in the $\beta$ and He I spectral lines with the orbital phase.
 TPhey attributed the low equivalent. width of the μα»ectral line to the focussing of the stellar wind: towards 10 compact object due to its strong gravity., They attributed the low equivalent width of the spectral line to the focussing of the stellar wind towards the compact object due to its strong gravity.
 ? analvsed the NMM-Newton data of 55039 duringle periastron and apastron passage to study. the effect of stellarwine on the X-ray absorption properties in, \cite{br07} analysed the XMM-Newton data of 5039 duringthe periastron and apastron passage to study the effect of stellarwind on the X-ray absorption properties in
is similar to the one described in the present work. but their aim was to project the importance of the Comptonisation of infrared photons from the torus to reproduce the high energy spectrum.,"is similar to the one described in the present work, but their aim was to project the importance of the Comptonisation of infrared photons from the torus to reproduce the high energy spectrum."
 In the present work. we have used. simultaneous observation of 2279 at dillerent. energies to deduce the physical. parameters of the source.," In the present work, we have used simultaneous observation of 279 at different energies to deduce the physical parameters of the source."
 We reproduce. the observed simultaneous broadband spectrum of 2279 using a simple one zone leptonie— mocel considering svnchrotron. SSC and LEC processes.," We reproduce the observed simultaneous broadband spectrum of 279 using a simple one zone leptonic model considering synchrotron, SSC and EC processes."
 From the radio/optical svnchrotron spectrum we show that the VILE emission cannot be attributed to SSC process whereas LC scattering of It photons from the dusty torus can explain the observed: VILIS emission., From the radio/optical synchrotron spectrum we show that the VHE emission cannot be attributed to SSC process whereas EC scattering of IR photons from the dusty torus can explain the observed VHE emission.
 Interpreting the X-ray emission as continuation of EC spectrum require magnetic field much lower than its equipartition value., Interpreting the X-ray emission as continuation of EC spectrum require magnetic field much lower than its equipartition value.
 However an explanation based on SSC origin of X-ray require a magnetic field which is comparable to the equipartition value., However an explanation based on SSC origin of X-ray require a magnetic field which is comparable to the equipartition value.
 The model predicts large llux at MeV-GeV. energies., The model predicts large flux at MeV-GeV energies.
 Since the data in these energy range is not available during the considered Hare. such a prediction cannot be ruled out.," Since the data in these energy range is not available during the considered flare, such a prediction cannot be ruled out."
 The model parameters describing the source are estimated by considering a magnetic field which is in equipartition with the particle energy density., The model parameters describing the source are estimated by considering a magnetic field which is in equipartition with the particle energy density.
 A deviation from this condition will rellect. in the value of the estimated. parameters., A deviation from this condition will reflect in the value of the estimated parameters.
 Also if the jet matter contains considerable amount of energetic protons. then the contribution from these protons should be included in equipartition magnetic field.," Also if the jet matter contains considerable amount of energetic protons, then the contribution from these protons should be included in equipartition magnetic field."
 Llowever in the present work. the proton contribution to the total particle energev is considered to be negligible.," However in the present work, the proton contribution to the total particle energy is considered to be negligible."
 Also the size of the emission region estimated from equation(3)) is only an upper limit and the actual size may be smaller., Also the size of the emission region estimated from \ref{eq:size}) ) is only an upper limit and the actual size may be smaller.
 Moreover in reality the size of the emission region may be dillerent for cilferent energy bands., Moreover in reality the size of the emission region may be different for different energy bands.
 These variation in the emission region size will also be reflected in the estimated. parameters., These variation in the emission region size will also be reflected in the estimated parameters.
 SS thanks Abhas Mitra. for constant support ane encouragement., SS thanks Abhas Mitra for constant support and encouragement.
 SC acknowledge Stephan LeBohece and David Ixieda for constant support and encouragement and the financial support by the National Science. Foundation erant. PLY0856411 and PILY0555451., SG acknowledge Stephan LeBohec and David Kieda for constant support and encouragement and the financial support by the National Science Foundation grant PHY 0856411 and PHY 0555451.
 Authors also thank Werner Collmar for providing the ASCll-data forSWILT. and. observations.," Authors also thank Werner Collmar for providing the ASCII-data for, and observations."
 This research has mace use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Aeronautics and Space Administration.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration."
stars surrounding the target were used to deteruüne the coordinates of the slit in each image.,stars surrounding the target were used to determine the coordinates of the slit in each image.
 We have use standard MIDAS procedures to reduce the LSS spectra., We have use standard MIDAS procedures to reduce the LSS spectra.
 The wavelength calibration was checked again using the |O A5577 aud AG300 sky. lines., The wavelength calibration was checked again using the [O $\lambda 5577$ and $\lambda 6300$ sky lines.
 We adopted the accurate coordinates aud applied inear astrometry to the CFUT Πα. R. aud D archive nuages to determine the position of the A-rayv source in he II II region.," We adopted the accurate coordinates and applied linear astrometry to the CFHT $H\alpha$ , $R$, and $B$ archive images to determine the position of the X-ray source in the H II region."
 For an absolute photometric calibration two images of the elobulay cluster NGCILIT taken during the same üeht were utilised., For an absolute photometric calibration two images of the globular cluster NGC4147 taken during the same night were utilised.
 Six standard stars from the cluster (Odewalhn et al. 1992)), Six standard stars from the cluster (Odewahn et al. \cite{Ode92}) )
 were used to calibrate the images., were used to calibrate the images.
 The calibration was double checked by iudepeudeut uecasureienuts of the comparison stars in B-hand CCD iniages made by V. Gorauskii with the ναι SAO telescope., The calibration was double checked by independent measurements of the comparison stars in B-band CCD images made by V. Goranskii with the 1-m SAO telescope.
 To obtain a reliable astrometry of the CEITT 776.R. aud D archival images we used theUSNO-D1.0 catalogue.," To obtain a reliable astrometry of the CFHT $H\alpha, R$, and $B$ archival images we used theUSNO-B1.0 catalogue."
 The, The
We study the evolution of a distribution of relativistic electrons as it is passively advected by the Πας.,We study the evolution of a distribution of relativistic electrons as it is passively advected by the fluid.
" The relativistic clectrous are asstmed to be injected. at the initial tine #=0. with a power-law distribution N(QE.0)=NyE. defined on au initialenergy. mterval 10!«EfEy,103, where £y will be defined below."," The relativistic electrons are assumed to be injected, at the initial time $t=0$, with a power-law distribution $N(E,0)= N_0 E^{-\gamma}$, defined on an initialenergy interval $10^{-4} < E/E_0 < 10^2$, where $E_0$ will be defined below."
" As the evolution proceeds. the electrous. euerev Call Varv on a wicler interval l0ο«E/E,101,"," As the evolution proceeds, the electrons energy can vary on a wider interval $10^{-6} < E/E_0 < 10^4$."
 A would-be representative sample of w=LO of this distribution are then selected and followed. asparticles. as they travel with the fiuid. undergoing adiabatic expansioncompression effects. svuchrotrou losses aud shock acceleration.," A would-be representative sample of $n=10$ of this distribution are then selected and followed, as, as they travel with the fluid, undergoing adiabatic expansion/compression effects, synchrotron losses and shock acceleration."
 The temporalevolution equation for a distribution function N(CE.f) for the number of relativistic electrons prescut in a parcel. subject to adiabatic effects and svuchrotrou losses. can by written as (INardashey 1962): where takes iuto account adiabatic effects; aud accounts for svuchnrotrou losses.," The temporalevolution equation for a distribution function $N(E,t)$ for the number of relativistic electrons present in a parcel, subject to adiabatic effects and synchrotron losses, can by written as (Kardashev 1962): where takes into account adiabatic effects, and accounts for synchrotron losses."
 Electron ΟΠΟΙΟΥ: Is expressed in wits of he clectron cnerev lost bv svuchrotron emission in a time unit iu the initial maeguetic field. Ey=1D).," Electron energy is expressed in units of the electron energy lost by synchrotron emission in a time unit in the initial magnetic field, $E_0=1/(b B_0^2 t_{\rm c})$."
 Eq. (8)), Eq. \ref{kard}) )
" is solved uunuericallv for the selected test parecels, away from shocks and at every time step. using a Lax-Weudroff scheme. and the coupling between Eq. (8))"," is solved numerically for the selected test cels, away from shocks and at every time step, using a Lax-Wendroff scheme, and the coupling between Eq. \ref{kard}) )"
 aud the lvdrocwnamic equations (1) is eiven bv the expausion/colmpression teria V-w. while the coefücieut for svuchnrotron enussion conuies frou. the equations for the magnetic field evolutiou () aud (5).," and the hydrodynamic equations (1) is given by the expansion/compression term $\nabla \cdot \vec{v}$, while the coefficient for synchrotron emission comes from the equations for the magnetic field evolution (4) and (5)."
 The solution of the energy evolution equation is connected. to the livdvodvuaimic evolution through a time-splittiug technique. with au accurate control ou the two Courant times.," The solution of the energy evolution equation is connected to the hydrodynamic evolution through a time-splitting technique, with an accurate control on the two Courant times."
 We rote that Nardashev (1962) eives an analytical solution for Eq. (8)), We note that Kardashev (1962) gives an analytical solution for Eq. \ref{kard}) )
 under the ivpothesis that the initial distribution function is a power-law., under the hypothesis that the initial distribution function is a power-law.
 As time clapses. svuchrotron losses aud adiabatic effects iiodifv the shape of the distribution function in the hieh aud low euergv ranges of the spectrum respectively. and therefore the distribution fiction evolves in time departing from a power-law.," As time elapses, synchrotron losses and adiabatic effects modify the shape of the distribution function in the high and low energy ranges of the spectrum respectively, and therefore the distribution function evolves in time departing from a power-law."
 Tn absence of shocks. one couk adopt the Kardashey solution at any fune. but shocks introduce discontinuities in the evolution: when the parcel has crossed. a shock wave. the new initial condition for the iuteeration of Eq. (8))," In absence of shocks, one could adopt the Kardashev solution at any time, but shocks introduce discontinuities in the evolution; when the parcel has crossed a shock wave, the new initial condition for the integration of Eq. \ref {kard}) )"
 is the post-shock distribution function. which is nof a power-law auv louger aud thus does not fulfill the Nardashev (1962) prescriptions.," is the post-shock distribution function, which is not a power-law any longer and thus does not fulfill the Kardashev (1962) prescriptions."
 When the selected. test particle. represcuting a parcel of he distribution. euters a shock. Ferma acceleration takes ace.," When the selected test particle, representing a parcel of the distribution, enters a shock, Fermi acceleration takes place."
 Under the assumptions that the acceleration time scale faic(0/07. with # the spatial diffusion coefficient) is much smaller than both the svuchrotrou time faye. aud he dynamical tine for shock evolution (~ἐκ). we can apply the stationary diffusive shock acceleration (DSA) uodel (see for example Diary 1983 for a review).," Under the assumptions that the acceleration time scale $t_{\rm
acc} \ (\sim \kappa / v^2,$ with $\kappa$ the spatial diffusion coefficient) is much smaller than both the synchrotron time $t_{\rm sync}$, and the dynamical time for shock evolution $\sim t_{\rm c}$ ), we can apply the stationary diffusive shock acceleration (DSA) model (see for example Drury 1983 for a review)."
 These conditions are fully verified iu the cucrey interval over which our electron distribution is allowed to vary. as it was defined above.," These conditions are fully verified in the energy interval over which our electron distribution is allowed to vary, as it was defined above."
" According to this model. the downstream nuuber of particles distribution jV(CE.f) is related to the upstream distribution AN.(E.f) by: with where r=py,/p is the shock coipression ratio. and ZAQ is the ή. electron οποιον in the pre-shocls distribution fuuctiou."," According to this model, the downstream number of particles distribution $N_+(E,t)$ is related to the upstream distribution $N_-(E,t)$ by: with where $r=\rho_+ / \rho_-$ is the shock compression ratio, and $E_{\rm min}$ is the minimum electron energy in the pre-shock distribution function."
 This equation is derived frou the equation for the particle density distribution function FGE.f) (sce for example Kirk 1991). aud the substitution NCE.Ade=—(tdF(E.T)VE. where V(tf) is the volue occupied by the particles. viclds the compression ratio r at the denominator of Eq. (," This equation is derived from the equation for the particle density distribution function $f(E,t)$ (see for example Kirk 1994), and the substitution $N(E,t)dE = f(E,t) V(t) dE$, where $V(t)$ is the volume occupied by the particles, yields the compression ratio $r$ at the denominator of Eq. ("
11).,11).
 We note that the post-shock distribution function is not a power-law any longer., We note that the post-shock distribution function is not a power-law any longer.
 White (1985). Achterbere (1990). Schucider (1993) (see also the discussion iu Melrose Pope 1993) found that for an infinity of equally stroug shocks with ro= land decompressions. the final distribution approaches N(ELE)xEt.," White (1985), Achterberg (1990), Schneider (1993) (see also the discussion in Melrose Pope 1993) found that for an infinity of equally strong shocks with $r=4$ and decompressions, the final distribution approaches $N_+(E) \propto E^{-1}$."
" We have carried. out a simulation with a fid jet defined by the following parameters: Mach umber (= 4. density. ratio MLPrρω).= 5, "," We have carried out a simulation with a fluid jet defined by the following parameters: Mach number ${\cal M} (\equiv v_z / c_{\rm si} \sqrt{\Gamma}) = 5$ , density ratio $\nu (\equiv \rho_{\infty} / \rho_{\rm jet}) =5$ ."
We studied. the evolution of the distribution functions associated with 10 Lagraugian test particles. whose initial positions are given iu Table 1: the initial spectral iudex," We studied the evolution of the distribution functions associated with 10 Lagrangian test particles, whose initial positions are given in Table 1; the initial spectral index"
 SMBH binaries are expected to form naturally in the hierarchy of mergers that lead to massive ellipticals and they provide several mechanisms that can produce cores., SMBH binaries are expected to form naturally in the hierarchy of mergers that lead to massive ellipticals and they provide several mechanisms that can produce cores.
 The most favoured model isscouring (?).., The most favoured model is \citep{2003ApJ...596..860M}.
" At the galaxy centres the black holes form binary pairs that decay as they transfer energy to stars via three body encounters, thus they are able to eject stellar material from the central regions and form a core."," At the galaxy centres the black holes form binary pairs that decay as they transfer energy to stars via three body encounters, thus they are able to eject stellar material from the central regions and form a core."
 Numerical experiments suggest that the cumulative effect of multiple SMBH dry mergers is able to remove a stellar mass that is ~2—4 times the final SMBH mass (?).., Numerical experiments suggest that the cumulative effect of multiple SMBH dry mergers is able to remove a stellar mass that is $\sim 2-4$ times the final SMBH mass \citep{2007ApJ...671...53M}.
" This process is important from about 100 to 1 parsecs, so it is unresolved in our simulations which have 1 kpc force softening."," This process is important from about 100 to 1 parsecs, so it is unresolved in our simulations which have 1 kpc force softening."
" At the softening length, the enclosed stellar mass is larger than the BH masses therefore a binary BH system can’t form."," At the softening length, the enclosed stellar mass is larger than the BH masses therefore a binary BH system can't form."
 However there is an addition process that we do resolve: During the mergers the black holes would sink to the very central region due to dynamical friction., However there is an addition process that we do resolve: During the mergers the black holes would sink to the very central region due to dynamical friction.
 The numerical experiments presented in ? show that the energy transferred from the sinking SMBHs to stars contributes to the formation of cored profiles; the typical mass deficits are found to have a similar magnitude as the SMBH mass., The numerical experiments presented in \cite{2010ApJ...725.1707G} show that the energy transferred from the sinking SMBHs to stars contributes to the formation of cored profiles; the typical mass deficits are found to have a similar magnitude as the SMBH mass.
whose characteristic polynomial is given by Eq. (,whose characteristic polynomial is given by Eq. (
38) (see Press et al.,38) (see Press et al.
 1992 for details)., 1992 for details).
 In Fig., In Fig.
 3. we plot the dependence of the growth rate on x for the Keplerian disk with g=3/2 and &=| and for several values of the parameterB.," 3, we plot the dependence of the growth rate on $x$ for the Keplerian disk with $q=3/2$ and $\varepsilon =1$ and for several values of the parameter $\beta$."
 In all cases. the growth rate decreases monotonically with decreasing wavelength .t=2z/K because ohmic dissipation is more efficient for perturbations with a shorter wavelength.," In all cases, the growth rate decreases monotonically with decreasing wavelength $\lambda = 2 \pi/k$ because ohmic dissipation is more efficient for perturbations with a shorter wavelength."
 For any ratio of the magnetic and gas pressures. the instability does not occur if AH>12.," For any ratio of the magnetic and gas pressures, the instability does not occur if $kH > 12$."
 If the magnetic pressure is greater than the gas pressure (B< 1). the growth rate can reach relatively large values D«0.04—0.06. This corresponds to the growth time only 3-4 times longer than the rotation period.," If the magnetic pressure is greater than the gas pressure $\beta < 1$ ), the growth rate can reach relatively large values $\Gamma \approx 0.04-0.06$ This corresponds to the growth time only $3-4$ times longer than the rotation period."
 The magnetorotational instability cannot arise in such a strong magnetic field no matter how large is the electrical conductivity of gas., The magnetorotational instability cannot arise in such a strong magnetic field no matter how large is the electrical conductivity of gas.
 Even if K is not perpendicular to B.the MRE can occur only if the magnetic field and wavevector satisfy the condition kes<25Q0’.," Even if $\vec{k}$ is not perpendicular to $\vec{B}$, the MRI can occur only if the magnetic field and wavevector satisfy the condition $k^2 c_A^2 < 2 s \Omega \Omega'$."
 Assuming that s~ο. we can transform this inequality approximately into Q>c4K~λοςH NB.," Assuming that $s \Omega' \sim \Omega$, we can transform this inequality approximately into $\Omega > c_A k \sim x c_s/H \sqrt{\beta}$ ."
" Since c,/H~© in the Keplerian disk. we find that MRL arises if x/VB<I."," Since $c_s/H \sim \Omega$ in the Keplerian disk, we find that MRI arises if $x /\sqrt{\beta} <1$."
 In the caseB<I. this condition never applies and the MRI is suppressed.," In the case $\beta < 1$, this condition never applies and the MRI is suppressed."
 On the contrary. the driven instability turns out to be rather efficient in such à strong field.," On the contrary, the shear-driven instability turns out to be rather efficient in such a strong field."
 In Fig., In Fig.
 4. we plot the same dependence. but for the nonKeplerian disk with g=| and &=3.," 4, we plot the same dependence, but for the nonKeplerian disk with $q=1$ and $\varepsilon =3$."
 The other parameters are same., The other parameters are same.
 Qualitatively. the dependences are very similar to those shown in Fig.," Qualitatively, the dependences are very similar to those shown in Fig."
 3., 3.
 The instability grows faster in the disk with largerB. which seems to be a general feature of the shear- instability.," The instability grows faster in the disk with larger $\beta$, which seems to be a general feature of the shear-driven instability."
 However. the growth rate is typically smaller for a non-Keplerian disk.," However, the growth rate is typically smaller for a non-Keplerian disk."
 The range of unstable wavevectors is limitedapproximately by KE.<10., The range of unstable wavevectors is limitedapproximately by $kH < 10$.
 Note that the half-thickness H is essentially larger in a non-Keplerian disk than in the Keplerian one., Note that the half-thickness $H$ is essentially larger in a non-Keplerian disk than in the Keplerian one.
 The dependence of the growth rate on 8!=eie Is shown in Fig., The dependence of the growth rate on $\beta^{-1}= c_{A}^2 / c_{s}^2$ is shown in Fig.
 5 for the disk with g=3/2 and &=|., 5 for the disk with $q=3/2$ and $\varepsilon = 1$.
 At a given wavelength. the growth rate increases with 1/8 slowly approaching a saturation value that depends on g.The saturation growth rate is ~0.06Q and 0.025O for g=5 and 10. respectively.," At a given wavelength, the growth rate increases with $1/\beta$ slowly approaching a saturation value that depends on $q$ .The saturation growth rate is $\sim 0.06 \Omega$ and $0.025 \Omega$ for $q=5$ and $10$ , respectively."
 This correspond to the growth time of about ~3 and ~6 rotation periods., This correspond to the growth time of about $\sim3$ and $\sim6$ rotation periods.
 The dependence of the, The dependence of the
of objects of that type due to sample/cosmic variance.,of objects of that type due to sample/cosmic variance.
 We describe and test methods for recovering the underlying universal distribution in $4.2., We describe and test methods for recovering the underlying universal distribution in $\S\ref{sec:errorest}$.
 We also looked at how well redshift distributions may be recovered in a single. | square degree field.," We also looked at how well redshift distributions may be recovered in a single, 1 square degree field."
 For each field. the correlation functions were calculated using only the information from that field.," For each field, the correlation functions were calculated using only the information from that field."
 To weight each bin when fitting for correlation-function parameters. the fit was calculated using errors given by the standard deviation of the correlation function in each 0 bin over the 24 fields.," To weight each bin when fitting for correlation-function parameters, the fit was calculated using errors given by the standard deviation of the correlation function in each $\theta$ bin over the 24 fields."
 This mimics the common situation where we have few fields with data and errors are determined. from simulations., This mimics the common situation where we have few fields with data and errors are determined from simulations.
 For a single field. a linear fit for the evolution of the spectroscopic-sample correlation function parameters was not a good model. so we used the calculated parameters in each z-bin.," For a single field, a linear fit for the evolution of the spectroscopic-sample correlation function parameters was not a good model, so we used the calculated parameters in each z-bin."
 Fig., Fig.
" 8. shows the recovered distribution. o,(z). in each of the 24 fields. compared to the true redshift distribution of the photometric sample in that field."," \ref{fig:phising} shows the recovered distribution, $\phi_p(z)$, in each of the 24 fields, compared to the true redshift distribution of the photometric sample in that field."
 In the course of our calculation of the redshift distribution. we found that the error ωρίς) for each redshift bin was larger than expected from the error model used in ?.. which uses the standard. classical weak-clustering formalism.," In the course of our calculation of the redshift distribution, we found that the error in $\phi_p(z)$ for each redshift bin was larger than expected from the error model used in \cite{2008ApJ...684...88N}, which uses the standard, classical weak-clustering formalism."
" This formalism predicts that Poisson uncertainties should dominate when theclustering strength (e.g. the value of w,,) is small compared to unity (2)..", This formalism predicts that Poisson uncertainties should dominate when theclustering strength (e.g. the value of $w_{sp}$ ) is small compared to unity \citep{1980lssu.book.....P}. .
 Upon further investigation, Upon further investigation
"the greatest expected vield would come from the model proportional to the SET,4). a null vield could still be expected in the tested redshift range with probabilities of22.556..64.44... in the respective passbands.","the greatest expected yield would come from the model proportional to the $_{IR}$ $z$ ), a null yield could still be expected in the tested redshift range with probabilities of, in the respective passbands."
 lt is interesting to consider what the relative agreement with the tested models would have been had a single SN Ia at 2>1.4 been discovered in eachsearch., It is interesting to consider what the relative agreement with the tested models would have been had a single SN Ia at $z > 1.4$ been discovered in eachsearch.
 If one high-z SN Ia had been found in each the £110. and ΕΟΤ-bands. then it would have been very unlikely that $04 best-lit ως) represents the (ue SN Ia rate history. as such an outcome would be expected less than of the time.," If one $z$ SN Ia had been found in each the $F110W$ and $F160W$ -bands, then it would have been very unlikely that S04 best-fit $\mathcal R_{Ia}(z)$ represents the true SN Ia rate history, as such an outcome would be expected less than of the time."
" The S04 best-fit ;,(:) could therefore be rejected to >984. confidence.", The S04 best-fit $\mathcal R_{Ia}(z)$ could therefore be rejected to $>98\%$ confidence.
 However. one SN may have been expected in each IRUDE passbands for either (he ΕΠΗ (2) or SEB;4C) models. although with Poisson expectation probabilities of 12=284. it would appear to be a low likelihood.," However, one SN may have been expected in each IRUDF passbands for either the $_U$ $z$ ) or $_{IR}$ $z$ ) models, although with Poisson expectation probabilities of $12-28\%$, it would appear to be a low likelihood."
" Similarly. had one SN la at 2>1.4 been discovered in the Γ55012 surveys. then S04 best-lit Ry,(2) could be rejected at >945."," Similarly, had one SN Ia at $z>1.4$ been discovered in the $F850LP$ surveys, then S04 best-fit $\mathcal R_{Ia}(z)$ could be rejected at $>94\%$."
 But again the vield would be only mareinally expected from either of the other (wo models. with a Poisson probability of ~35%.," But again the yield would be only marginally expected from either of the other two models, with a Poisson probability of $\sim 35\%$."
 Although it appears as there was a statistical preference by the cata lor the best-fit RasG) model. it is clear that our null result cannot reject anv of the tested models to a significant (greater than 99%)) confidence.," Although it appears as there was a statistical preference by the data for the best-fit $\mathcal R_{Ia}(z)$ model, it is clear that our null result cannot reject any of the tested models to a significant (greater than ) confidence."
 In fact. a model would need to predict five or more SNe Ian at L4<2« 2.410 be rejected to greater than confidence by the zero vield of this survey.," In fact, a model would need to predict five or more SNe Ia at $1.4<z<2.4$ to be rejected to greater than confidence by the zero yield of this survey."
 Such a hypothetical model suggests that (he average SN Ia rate in Chis high-z range would be approximately 150 times larger than (he SN Ia rate measured in the local (2«€ 0.1) universe., Such a hypothetical model suggests that the average SN Ia rate in this $z$ range would be approximately 150 times larger than the SN Ia rate measured in the local $z\le0.1$ ) universe.
 This is verv inconsistent with trends inferred from measured SN Ia rates over anv redshift interval. and is likelv to be rejected based on theoretical considerations of the low [O/Fe] ratios it would. predict for stars and the ISM of local galaxies.," This is very inconsistent with trends inferred from measured SN Ia rates over any redshift interval, and is likely to be rejected based on theoretical considerations of the low [O/Fe] ratios it would predict for stars and the ISM of local galaxies."
 such an increase in (he SN la rate is plausible in (he SN Ia rate models considered by Maoz&Gal-Yam(2004) in clusters of galaxies., Such an increase in the SN Ia rate is plausible in the SN Ia rate models considered by \citet{2004MNRAS.347..951M} in clusters of galaxies.
 Using e—f[olding delay time functions. described in detail in Madanetal.(1998) and Dahlen&Fransson(1999).. with e—[Iold times of less (han 1 Gyr. one could expect à SN Ia rate as high as 45 SNu in galaxy clusters al 1.5. folowing a burst of star formation in these clusters at z=2.," Using $e-$ folding delay time functions, described in detail in \citet{1998MNRAS.297L..17M} and \citet{1999AA...350..349D}, with $e-$ fold times of less than 1 Gyr, one could expect a SN Ia rate as high as 45 SNu in galaxy clusters at $z\approx1.5$ , following a burst of star formation in these clusters at $z=2$."
 Ilowever. to be consistent with the observed iron masses of galaxy clusters (assuming most of this mass is attributed to SNe Ia). the SN la rate history would likely need to drop to zero at z«0.7—1.0.," However, to be consistent with the observed iron masses of galaxy clusters (assuming most of this mass is attributed to SNe Ia), the SN Ia rate history would likely need to drop to zero at $z < 0.7- 1.0$."
 This would be inconsistent with the non-negligible SN Ia rate measurements in galaxy clusters al 0.04<2<0.08 (Reiss2000)., This would be inconsistent with the non-negligible SN Ia rate measurements in galaxy clusters at $0.04 < z < 0.08$ \citep{reiss2000}.
. There is significant evidence for uncertainty in the estimates of galaxy volume densities for specific populations in the GOODS fields (Somervilleοἱal. 2004).. ancl (he survey presented in (his paper covers a smaller area of (he GOODS South field.," There is significant evidence for uncertainty in the estimates of galaxy volume densities for specific populations in the GOODS fields \citep{2004ApJ...600L.171S}, , and the survey presented in this paper covers a smaller area of the GOODS South field."
 However. the SFRe(2) model (in the z>1 regime) used in this analvsis was also determined. from," However, the $_U$ $z$ ) model (in the $z>1$ regime) used in this analysis was also determined from"
going to be preferable to just phase-rotate the array to that sky location.,going to be preferable to just phase-rotate the array to that sky location.
 A source which shows significant time variation within the course of a day must have a spatial dimension less than about a light-day across., A source which shows significant time variation within the course of a day must have a spatial dimension less than about a light-day across.
 When observed with. for example. the MERLIN array at 21 em. any such source more distant than about a kiloparsee will be unresolved.," When observed with, for example, the MERLIN array at 21 cm, any such source more distant than about a kiloparsec will be unresolved."
 Except in the case of masers. it is also unusual to find two such variable sources in close proximity.," Except in the case of masers, it is also unusual to find two such variable sources in close proximity."
 For many observations of time-variable radio sources. therefore. we may expect the source to be point-like (unresolved) and the only source in the field which shows a significant time variation.," For many observations of time-variable radio sources, therefore, we may expect the source to be point-like (unresolved) and the only source in the field which shows a significant time variation."
 In this case the light curve for the whole observed field. ο. 1$ Just a simple sum of the source light curve ομως plus a time-invariant background flux density.," In this case the light curve for the whole observed field, $s_\mathrm{total}$, is just a simple sum of the source light curve $s_\mathrm{source}$ plus a time-invariant background flux density."
 Any point in the image can therefore be expressed as a sum of just two basis functions: Here the mean notation () is used to indicate that beam | is constructed as follows., Any point in the image can therefore be expressed as a sum of just two basis functions: Here the mean notation $\langle \rangle$ is used to indicate that beam 1 is constructed as follows.
 A raw beam 1 is first formed by eridding. weighting and transforming the visibilities from a source at the phase centre which has a light curve given by Sil.," A raw beam 1 is first formed by gridding, weighting and transforming the visibilities from a source at the phase centre which has a light curve given by $s_\mathrm{total}$."
 AN amount of beam 0 is then subtracted from it such that the central value of the result is zero., An amount of beam 0 is then subtracted from it such that the central value of the result is zero.
" Beam B, is adjusted in this way so that the average flux-density information over the field is contained entirely in the distribution of component 0.", Beam $B_1$ is adjusted in this way so that the average flux-density information over the field is contained entirely in the distribution of component 0.
 A further simulation was constructed to test this technique., A further simulation was constructed to test this technique.
 This simulation contained a time-variable point source located1 at the phase centre together with much fainter. extendec1 emission (actually made up of 24 closely-spaced point sources) extending over about 0.2 arcsee (equal to 20 image pixels) either side of the central source.," This simulation contained a time-variable point source located at the phase centre together with much fainter, extended emission (actually made up of 24 closely-spaced point sources) extending over about 0.2 arcsec (equal to 20 image pixels) either side of the central source."
 The average flux density of the central source was 1 Jy/beam whereas the extended emission ranged in brightness from about 3.5x10 to 1.5x1072 Jy/beam., The average flux density of the central source was 1 Jy/beam whereas the extended emission ranged in brightness from about $3.5\times 10^{-3}$ to $1.5\times 10^{-3}$ Jy/beam.
 The light curve of the central source was the same as diagrammed in figure .. but without the data gap.," The light curve of the central source was the same as diagrammed in figure \ref{fig_a}, but without the data gap."
 It brightens by 3.7 magnitudes in the course of the observation., It brightens by 3.7 magnitudes in the course of the observation.
 A quartet of images (similar to figure 6)) to exhibit the performance of this technique is shown in figure 7.., A quartet of images (similar to figure \ref{fig_d}) ) to exhibit the performance of this technique is shown in figure \ref{fig_e}.
 For constructing the visibilities. MERLIN specifications were again used.," For constructing the visibilities, MERLIN specifications were again used."
 The integration. time was 5 seconds. and 32 channels of width 1 MHz. starting at 6 GHz. were specified.," The integration time was 5 seconds, and 32 channels of width 1 MHz, starting at 6 GHz, were specified."
 It is easily seen that the Sault-Wieringa deconvolution recovers almost all the faint emission., It is easily seen that the Sault-Wieringa deconvolution recovers almost all the faint emission.
 The Hóggbom clean is unable to remove sidelobes at a level 10 times the flux density of the extended emission and thus is incapable of revealing it., The Höggbom clean is unable to remove sidelobes at a level 10 times the flux density of the extended emission and thus is incapable of revealing it.
 Several values of the Hóggbom gain and number of iterations were tried with no improvement on what is displayed here., Several values of the Höggbom gain and number of iterations were tried with no improvement on what is displayed here.
 In this paper. a technique developed originally by Conway et al (1990)) and Sault and Wieringa (1994)) to allow cleaning of multi-frequency-synthesis images has been generalized and shown to be applicable to earth-rotation-synthesis observations in which some of the sources vary significantly in brightness over the course of the observation.," In this paper, a technique developed originally by Conway et al \cite{conway}) ) and Sault and Wieringa \cite{sault_wieringa}) ) to allow cleaning of multi-frequency-synthesis images has been generalized and shown to be applicable to earth-rotation-synthesis observations in which some of the sources vary significantly in brightness over the course of the observation."
 Sources which vary over the course of a day are not very common. but they do occur. and are sometimes (in the case for example of novae) sources which it is of the highest interest to map accurately.," Sources which vary over the course of a day are not very common, but they do occur, and are sometimes (in the case for example of novae) sources which it is of the highest interest to map accurately."
 But in fact one does not have to look for natural variations in flux density to encounter this problem: any movement of the primary beam of the array on the sky during an observation will generate artificial fluctuations. not only in the average flux density of sources. but. due to the frequency-dependent size of the primary beam. also in their spectral indices.," But in fact one does not have to look for natural variations in flux density to encounter this problem: any movement of the primary beam of the array on the sky during an observation will generate artificial fluctuations, not only in the average flux density of sources, but, due to the frequency-dependent size of the primary beam, also in their spectral indices."
 Since some kind of pointing error in à mechanically tracking dish is probably unavoidable. this is likely to be a problematic issue when performing any kind of wide-field or mosaiced observation (see e.g. Bhatnagar et al 2008)). particularly so in view of current hopes for improvements in dynamic range from the several wide-band. dish-antenna arrays. such as eVLA. eMERLIN and MeerKAT. which are currently under construction.," Since some kind of pointing error in a mechanically tracking dish is probably unavoidable, this is likely to be a problematic issue when performing any kind of wide-field or mosaiced observation (see e.g. Bhatnagar et al \cite{bhatnagar}) ), particularly so in view of current hopes for improvements in dynamic range from the several wide-band, dish-antenna arrays, such as eVLA, eMERLIN and MeerKAT, which are currently under construction."
 Deconvolutioi of time-varying sources reveals some Issues which are not usually encountered in the frequency-synthesis case., Deconvolution of time-varying sources reveals some issues which are not usually encountered in the frequency-synthesis case.
 The principal one of these is that choice of basis function is now of some importance., The principal one of these is that choice of basis function is now of some importance.
 This issue was explored with some care. in particular the avoidance of Gibbs ringing when periodic basis functions are employed.," This issue was explored with some care, in particular the avoidance of Gibbs ringing when periodic basis functions are employed."
 It was also shown that. provided the time variation in the field 1s limited to a single. unresolved source. a particularly simple 2-beam technique can produce an almost perfect deconvolution.," It was also shown that, provided the time variation in the field is limited to a single, unresolved source, a particularly simple 2-beam technique can produce an almost perfect deconvolution."
 Whereas the original parallel decomposition treatment employed at most 34 or 4 beams. some of the situations described in the present paper required as many as 30.," Whereas the original parallel decomposition treatment employed at most 3 or 4 beams, some of the situations described in the present paper required as many as 30."
 Use, Use
shock frame. but expressed in downstream coordinates. is given by: We consider now a pencil beam of particles. all moving initially in the direction µς.,"shock frame, but expressed in downstream coordinates, is given by: We consider now a pencil beam of particles, all moving initially in the direction $\mu_\circ$."
 Thus. at the shock: with F5 an obvious normalization.," Thus, at the shock: with $F_\circ$ an obvious normalization."
 lt was shown in paper I (hat Eq., It was shown in paper I that Eq.
 7 provides a suitable boundary.condition lor Eq. 2..," \ref{fattheboundary1} provides a suitable boundarycondition for Eq. \ref{main},"
 which then returns the outgoing flux: by definition. this is precisely the requirecl 227.," which then returns the outgoing flux; by definition, this is precisely the required $P_d$."
" We thus have To begin. let us deline the inward (f=f()|, joo) and outward (f=(μμ) parts of the distribution function. and let us consider a surface al a distance z from the shock. fixed in the shock Irame."," We thus have To begin, let us define the inward $f_+ \equiv f(\mu) |_{u+\mu> 0}$ ) and outward $f_- \equiv f(\mu)|_{u+\mu<0}$ ) parts of the distribution function, and let us consider a surface at a distance $z$ from the shock, fixed in the shock frame."
 The flux of particles moving backwards toward (he shock. through this surface. is: The minus sign accounts for the fact that w+ji<0. while all terms inside (he integral are positive.," The flux of particles moving backwards toward the shock, through this surface, is: The minus sign accounts for the fact that $u+\mu < 0$, while all terms inside the integral are positive."
 Strictly speaking. in the above equation. we should have written P;(jà.pz) instead of simply Pig.ji).," Strictly speaking, in the above equation, we should have written $P_d(\mu',\mu,z)$ instead of simply $P_d(\mu',\mu)$."
 In other words. for a general situation. we cannot assume that the conditional probability £2; be independent of its location inside (he dowustveam region.," In other words, for a general situation, we cannot assume that the conditional probability $P_d$ be independent of its location inside the downstream region."
 llowever. in this case this assumption is fully. justified. because the downstream region is semiinfinite: in other words. it remains identical to itself whenever we add or subtract finite regions. and its diffusive properties also remain unaltered whenever we add or subtract finite regions.," However, in this case this assumption is fully justified, because the downstream region is semi–infinite: in other words, it remains identical to itself whenever we add or subtract finite regions, and its diffusive properties also remain unaltered whenever we add or subtract finite regions."
 lt follows that the conditional probability 2; from some finite z to downstream infinity must be exactly identical to that from 0 to downstream infinity., It follows that the conditional probability $P_d$ from some finite $z$ to downstream infinity must be exactly identical to that from $0$ to downstream infinity.
 This invariance principle. and this whole discussion. are identical to those in Chaucrasekhar (1949. Chapter 4. Sections 28-29). and provide an exact justification lor the equation above.," This invariance principle, and this whole discussion, are identical to those in Chandrasekhar (1949, Chapter 4, Sections 28-29), and provide an exact justification for the equation above."
 We now differentiate the above with respect to z:, We now differentiate the above with respect to $z$ :
Jellery&Saio(2006) cliscuss variations with Y and Zo. and Alo.,"\citet{Jef06} discuss variations with $X$ and $Z_0$, and $M_{\rm c}$ ."
 In particular. varving Alo has no elfect on the stability of e-modes.," In particular, varying $M_{\rm c}$ has no effect on the stability of g-modes."
 They also found the only significant. cllect of evolution is that g-mocles cease to be excited when the core becomes radiative at the end of core Lle-burnine., They also found the only significant effect of evolution is that g-modes cease to be excited when the core becomes radiative at the end of core He-burning.
 Of course pulsation periods P? increase with radius 2., Of course pulsation periods $P$ increase with radius $R$.
 Since PxP7 or surface gravity g5 7/7. normal horizontal-branch evolution produces a period increase of ~0.2 dex in all modes.," Since $P \propto R^{3/2}$ or surface gravity $g^{-3/4}$ , normal horizontal-branch evolution produces a period increase of $\sim 0.2$ dex in all modes."
 The high-temperature end of this ZALLB sequence corresponds with the locus of the short-period EC14026 variables., The high-temperature end of this ZAHB sequence corresponds with the locus of the short-period EC14026 variables.
 PGITIG variables are to be found. at lower empoeratures. with 210008μενz29000 (Fontaineeal.2006:Ranelallet 2006).," PG1716 variables are to be found at lower temperatures, with $21\,000 \lesssim T_{\rm eff}/{\rm K} \lesssim 29\,000$ \citep{Fon06,Ran06}."
. The lower limit probably does not represent a formal red edge: horizontal branch stars a hese temperatures are very scarce., The lower limit probably does not represent a formal red edge; horizontal branch stars at these temperatures are very scarce.
 We have tested the stability of cach of our horizontal-anch models for on-radial p- and e-mocdes with spherica degree f=1... 4.," We have tested the stability of each of our horizontal-branch models for p- and g-modes with spherical degree $l=1,\ldots,4$ ."
 The frequency range considered: is 2XiQx20. where w is the angular frequeney of pulsation normalized by CALI with € being the geavitationa constant.," The frequency range considered is $0.2 \le \omega \le 20$, where $\omega$ is the angular frequency of pulsation normalized by $\sqrt{GM/R^3}$ with $G$ being the gravitational constant."
 lig., Fig.
 3. compares the results for OP and. OPAL with normal composition., \ref{g_normal} compares the results for OP and OPAL with normal composition.
 With OP. unstable moces are obtainec even for /—1.," With OP, unstable modes are obtained even for $l=1$."
 In general. the number and the temperature range of unstable modes. is increased. with OP opacities.," In general, the number and the temperature range of unstable modes is increased with OP opacities."
 Fie., Fig.
 4 compares the results for OP and OPAL with fissi(10. 10).," \ref{g_fe10ni10} compares the results for OP and OPAL with $f_{\rm Fe,Ni}=(10,10)$ ."
 For modes with /= 3. e-modes are excited. up to TouAK28000 in OP models. but only to ων25000 in OPAL models.," For modes with $l=3$ , g-modes are excited up to $T_{\rm eff}/{\rm K}\lesssim 28\,000$ in OP models, but only to $T_{\rm eff}/{\rm K}\lesssim 25\,000$ in OPAL models."
 Although less likely to be observable. they are excited up to μήν29500 for OP mocdels with /—4.," Although less likely to be observable, they are excited up to $T_{\rm eff}/{\rm K}\lesssim 29\,500$ for OP models with $l=4$."
 In contrast. the position of the models on the LI diagram hardly changes with the choice of opacity table.," In contrast, the position of the models on the HR diagram hardly changes with the choice of opacity table."
 ‘Table 2 compares the theoretical bluc-edge of the e-mode instability strip for different enhancements of iron ancl nickel. for OP and OPAL models and. for the three most observable modes. /=1.2 and 3.," Table \ref{t_blueedge} compares the theoretical blue-edge of the g-mode instability strip for different enhancements of iron and nickel, for OP and OPAL models and for the three most observable modes, $l=1,2$ and 3."
 ]t ds clear that the use of OP opacities combined with the inclusion of excess nickel can shift the theoretical blue-edge of the e-mode instability strip significantly closer to the observed. blue. edge., It is clear that the use of OP opacities combined with the inclusion of excess nickel can shift the theoretical blue-edge of the g-mode instability strip significantly closer to the observed blue edge.
 This prompts us to believe that Fontaineetal.(2003) correctly identified the oscillations in DGITIG variables as opacity-driven g-miocles. and that the discrepancy in the predicted. ancl observed. blue edges can be solved. by invoking more accurate atomic physics in the calculation of stellar opacity. as well as considering atomic μα»ecies other than iron.," This prompts us to believe that \citet{Fon03} correctly identified the oscillations in PG1716 variables as opacity-driven g-modes, and that the discrepancy in the predicted and observed blue edges can be solved by invoking more accurate atomic physics in the calculation of stellar opacity, as well as considering atomic species other than iron."
 The basic elements. of this solution are that (i) the opacity peaks due to ion ancl nickel occur at a higher temperature in OP than in OPAL. (ii) the OP nickel peak occurs at a higher temperature than the OP iron peak. (iii) at these temperatures nickel is a more efficient absorber than iron (per ion). and (iv) radiative accelerationwill force it to accumulatein the Ni-bump regioninexactly the same way as Won.," The basic elements of this solution are that (i) the opacity peaks due to iron and nickel occur at a higher temperature in OP than in OPAL, (ii) the OP nickel peak occurs at a higher temperature than the OP iron peak, (iii) at these temperatures nickel is a more efficient absorber than iron (per ion), and (iv) radiative accelerationwill force it to accumulatein the Ni-bump regioninexactly the same way as iron."
lt should. perhaps. have been no surprise that the introduction. of OP opacities would shift. the instability,"It should, perhaps, have been no surprise that the introduction of OP opacities would shift the instability"
Huge cosmological surveys are currently ongoing or planned for the near future.,Huge cosmological surveys are currently ongoing or planned for the near future.
 The large statistical power of these surveys allows us to study the statistical properties of the cosmological fields well beyond the lowest. second-order statistical level.," The large statistical power of these surveys allows us to study the statistical properties of the cosmological fields well beyond the lowest, second-order statistical level."
 In order to employ these higher-order statistics in obtaining information about the underlying cosmology. one needs to be able to accurately predict these statistics as a function of the model parameters.," In order to employ these higher-order statistics in obtaining information about the underlying cosmology, one needs to be able to accurately predict these statistics as a function of the model parameters."
 Moreover. one also needs to predict the expected errors on these higher-order measures. 1.e.. the covariance of higher-order statistics.," Moreover, one also needs to predict the expected errors on these higher-order measures, i.e., the covariance of higher-order statistics."
 Whereas there exist rather accurate fitting formulae for the power spectrum of the cosmic density field (e.g..Peacock&Dodds1996;Smithetal. 2003).. this is no longer the case for higher-order statistical properties.," Whereas there exist rather accurate fitting formulae for the power spectrum of the cosmic density field \citep[e.g.,][]{1996MNRAS.280L..19P, 2003MNRAS.341.1311S}, this is no longer the case for higher-order statistical properties."
 For example. the semi-empirical fitting formula for the bispectrum of the cosmic density field (Scoceimarro&Couchman2001) Is estimated to be accurate only at the level of several tens of percent.," For example, the semi-empirical fitting formula for the bispectrum of the cosmic density field \citep{2001MNRAS.325.1312S} is estimated to be accurate only at the level of several tens of percent."
 In order to obtain the covariance of the power spectrum and the bispectrum. even higher-order statistical properties of the field need to be known.," In order to obtain the covariance of the power spectrum and the bispectrum, even higher-order statistical properties of the field need to be known."
 The power spectrum covariance depends on fourth-order statistical properties. 1.e.. the trispectrum. which is even harder to predict.," The power spectrum covariance depends on fourth-order statistical properties, i.e., the trispectrum, which is even harder to predict."
 In principle. one needs to understand the sixth-order properties of the field in order to determine the covariance of the bispectrum.," In principle, one needs to understand the sixth-order properties of the field in order to determine the covariance of the bispectrum."
 However. depending on the statistical field under consideration. certain simplifications may apply.," However, depending on the statistical field under consideration, certain simplifications may apply."
 In particular. if the density field 15 sufficiently close to a Gaussian field. the higher-order terms in the covariance of the power spectrum and the bispectrum may become subdominant. in. which case they can be obtained solely from the power spectrum itself.," In particular, if the density field is sufficiently close to a Gaussian field, the higher-order terms in the covariance of the power spectrum and the bispectrum may become subdominant, in which case they can be obtained solely from the power spectrum itself."
 In this paper we study the covariance of the bispectrum for two-dimensional random fields., In this paper we study the covariance of the bispectrum for two-dimensional random fields.
 Whereas our prime interest is focused on the convergence field of cosmic shear (as a prime example of a two-dimensional cosmological field) (forareviewofgravitationallensing.seeSchneider 2006).. our results are not restricted to this particular application.," Whereas our prime interest is focused on the convergence field of cosmic shear (as a prime example of a two-dimensional cosmological field) \citep[for a review of gravitational lensing, see][]{2006glsw.conf....1S}, our results are not restricted to this particular application."
 Third-order cosmic shear statistics is known to provide very valuable information. complementary to that from the cosmic shear power spectrum (e.g..Takada&Jain2004:Kil-binger&Schneider2005:Hutereretal. 2006).. which is confirmed by the first measurements of third-order cosmic shear in previous surveys (Bernardeauetal.2002:Pen2003:Jarvisetal.2004:Semboloni 2011)..," Third-order cosmic shear statistics is known to provide very valuable information, complementary to that from the cosmic shear power spectrum \citep[e.g.,][]{2004MNRAS.348..897T, 2005A&A...442...69K, 2006MNRAS.366..101H}, which is confirmed by the first measurements of third-order cosmic shear in previous surveys \citep{2002A&A...389L..28B, 2003ApJ...592..664P, 2004MNRAS.352..338J, 2011MNRAS.410..143S}."
 Ongoing and future surveys. such as the Canada-France-Hawat-Telescope Legacy Survey (CFHTLS). the Kllo-Degree Survey (KIDS). the Dark Energy Survey (DES) and EUCLID. will measure the third-order cosmie shear signal with very high accuracy.," Ongoing and future surveys, such as the Canada-France-Hawaii-Telescope Legacy Survey (CFHTLS), the KIlo-Degree Survey (KIDS), the Dark Energy Survey (DES) and EUCLID, will measure the third-order cosmic shear signal with very high accuracy."
 However. estimating the statistical power of these surveys. and obtaining realistic confidence estimates for model parameters. remains a challenge that hinges on our ability to estimate the bispectrum covariance.," However, estimating the statistical power of these surveys, and obtaining realistic confidence estimates for model parameters, remains a challenge that hinges on our ability to estimate the bispectrum covariance."
 Hu(2000) estimated this covariance by analogy to the bispectrum covariance of the cosmic microwave background., \citet{2000PhRvD..62d3007H} estimated this covariance by analogy to the bispectrum covariance of the cosmic microwave background.
" As discussed in Joachimietal.(2009,hereafterJSS).. this approach has a number of drawbacks that result from the use of spherical harmonies in the analysis."," As discussed in \citet[][hereafter JSS]{2009A&A...508.1193J}, this approach has a number of drawbacks that result from the use of spherical harmonics in the analysis."
 Instead. JSS derived a general expression for the bispectrum covariance on a finite region in the flat-sky limit. which can be separated into four terms.," Instead, JSS derived a general expression for the bispectrum covariance on a finite region in the flat-sky limit, which can be separated into four terms."
 The first term contains the contribution of the power spectrum to the bispectrum covariance. and is the only term relevant for Gaussian random fields.," The first term contains the contribution of the power spectrum to the bispectrum covariance, and is the only term relevant for Gaussian random fields."
 The other three terms contain the contributions of the bispectrum. the trispectrum and the pentaspectrum.," The other three terms contain the contributions of the bispectrum, the trispectrum and the pentaspectrum."
 Dropping these higher-order terms in the expression is usually termed the Gaussian approximation of the bispectrum covariance., Dropping these higher-order terms in the expression is usually termed the Gaussian approximation of the bispectrum covariance.
 If the other terms were small for realistic cosmic fields. this would tremendously simplify the estimation of confidence regions from third-order statistics.," If the other terms were small for realistic cosmic fields, this would tremendously simplify the estimation of confidence regions from third-order statistics."
 At first glance this seems to be invalid as the present density field appears to be highly non-Gaussian. especially on small scales.," At first glance this seems to be invalid as the present density field appears to be highly non-Gaussian, especially on small scales."
 Nevertheless. this Gaussian approximation has been employed in nearly all studies of parameter forecasts from third-order cosmic shear (e.g..Takada&Jai2004:HutereretShietal. 2010)..," Nevertheless, this Gaussian approximation has been employed in nearly all studies of parameter forecasts from third-order cosmic shear \citep[e.g.,][]{2004MNRAS.348..897T, 2006MNRAS.366..101H, 2010A&A...523A..60S}."
 In this paper. we investigate the validity of the Gaussian approximation. using simulated random fields with different degrees of non-Gaussianity.," In this paper, we investigate the validity of the Gaussian approximation, using simulated random fields with different degrees of non-Gaussianity."
 Specifically. we employ random fields which we characterise by the non-Gaussianity parameter a.," Specifically, we employ log-normal random fields which we characterise by the non-Gaussianity parameter $\alpha$."
 As argued in the seminal paper by Coles&Jones (1991)... matter density fields are well described by log-normal statistics. making these statistics," As argued in the seminal paper by \citet{1991MNRAS.248....1C}, , matter density fields are well described by log-normal statistics, making these statistics"
very late phases of their lives. namely when the star formation is over.,"very late phases of their lives, namely when the star formation is over."
 In this paper we aim at studying in detail the dust evolution in elliptical galaxies by starting from the model by Caluraetal.(2008).., In this paper we aim at studying in detail the dust evolution in elliptical galaxies by starting from the model by \cite{calura08dust}.
 We update the dust production by changing the dust condensation efficiency in supernova Ia and II Gn order to take into account the above mentioned new observational constraints) and adding the possibility of QSO dust., We update the dust production by changing the dust condensation efficiency in supernova Ia and II (in order to take into account the above mentioned new observational constraints) and adding the possibility of QSO dust.
 We also revise the accretion process timescale., We also revise the accretion process timescale.
 We present models of ellipticals of different baryonic masses m the range 10°?—107M... and compare them with LBGs and with QSO hosts.," We present models of ellipticals of different baryonic masses in the range $10^{9} - 10^{12}M_{\odot}$, and compare them with LBGs and with QSO hosts."
 [In particular. after some general predictions. we focus on the particular cases: LBG 1512-cB58(as a proxy for a relatively low mass elliptical) and the host galaxy of QSO J114845251(as a proxy for the most massive spheroids).," In particular, after some general predictions, we focus on the particular cases: LBG (as a proxy for a relatively low mass elliptical) and the  host galaxy of QSO (as a proxy for the most massive spheroids)."
 The paper is organized as follows., The paper is organized as follows.
 The chemical evolution model and the dust model are described in $2 and 83. respectively.," The chemical evolution model and the dust model  are described in 2 and 3, respectively."
 Observational data are briefly summarized in $4., Observational data are briefly summarized in 4.
 We predict the chemical and dust evolution of elliptical galaxies in different conditions and apply them to interpret the observational data in 85-7., We predict the chemical and  dust evolution of elliptical galaxies in different conditions and apply them to interpret the observational data in 5-7.
 Our conclusions are summarized in 88., Our conclusions are summarized in 8.
 The model adopted here ts basically the multi-zone model. of Pipino Matteucci (2004)., The model adopted here is basically the multi-zone model  of Pipino Matteucci (2004).
 The model galaxy is divided into spherical shells 0.1. Κε; thick., The model galaxy is divided into spherical shells 0.1 $R_{eff}$ thick.
 Most of the results presented below refer to global galactic properties and are calculated by considering all the shells., Most of the results presented below refer to global galactic properties and are calculated by considering all the shells.
 The galaxy evolves as an open box in which the mitial gas mass. with primordial chemical composition. rapidly collapses. on a time scale r. into the potential well of a dark matter halo.," The galaxy evolves as  an open box in which the initial gas mass, with primordial chemical composition, rapidly  collapses, on a time scale $\tau$, into the potential well of a dark matter halo."
 The rapid collapse triggers an intense and rapid —star formation process. which can be considered as a starburst and lasts until a galactic wind. powered by the thermal energy injected by stellar winds and SN (Ia. IL) explosions. occurs.," The rapid collapse triggers an intense and rapid  star formation process, which can be considered as a starburst and lasts until a galactic  wind, powered by the  thermal energy injected by stellar winds and SN (Ia, II) explosions, occurs."
 At that time. the gas thermal energy equates the gas binding energy of and all the residual interstellar medium is assumed to be lost.," At that time, the gas thermal energy  equates the gas binding energy of and  all the residual interstellar medium is assumed to be lost."
 After that time. the galaxies evolve passively.," After that time, the galaxies evolve passively."
 The equation of chemical evolution for the element i in each galactic shell takes the following form: where Gat)=ΜιX(t) is the. fractional mass. of the element at the time in the ISM.," The equation of chemical evolution for the element $i$ in each galactic shell takes the following form: where $G_i (t)= M_{gas}(t) \,X_i (t) $ is the  fractional mass  of the element at the time in the ISM."
 The quantity X;(7) is defined as the abundance by mass of the element/., The quantity $X_i (t)$ is defined as the abundance by mass of the element.
. By definition ΣΧ)=1., By definition $\sum_i X_i=1$.
 The first term. on the right side of eq., The first term  on the right side of eq.
 1. gives the rate at which the element / is subtracted from ISM by the SF process., \ref{main} gives the rate at which the element $i$ is  subtracted from ISM by the SF process.
 The variable v is the star formation rate calculated according to the following law: namely it is assumed to be proportional to the gas mass via à constant v which represents the star formation efficiency.,  The variable $\psi$ is the star formation rate calculated according to the following law: namely it is assumed to be proportional to the gas mass via a constant $\nu$ which represents the star formation efficiency.
" In order to reproduce the ""inverse wind model of (Matteucet.1994).. an earlier version of the now popular ""downsizing"". we assume v as an increasing function of the galactic mass. (see Table 1)) The second term is the rate at which each element is restored into the ISM by single stars with masses in the range Mj - Mp... where M, is the minimum mass contributing. at a given time f. to chemical enrichment and Mp, is the minimum binary mass allowed for binary systems giving rise to SNla (3M... Greggio Renzini. 1983)."," In order to reproduce the 'inverse wind model' of \citep{m94_inv_wind}, an earlier version of the now popular ""downsizing"", we assume $\nu$ as an increasing function of the galactic mass, (see Table \ref{t1}) ) The second term is the rate at which each element is restored into the ISM by single stars with masses in the range $M_{L}$ - $M_{B_m}$, where $M_{L}$ is the minimum mass contributing, at a given time $t$, to chemical enrichment  and $M_{B_m}$ is the minimum binary mass allowed for binary systems giving rise to SNIa $3 M_{\odot}$, Greggio Renzini, 1983)."
 The initial mass function (MF) is dan)xacl! (Salpeter 1955). and it is normalized to unity in the mass interval 0.1—100M...," The initial mass function (IMF) is $\phi (m)\propto m^{-(1+1.35)}$, (Salpeter 1955), and it is normalized to unity in the mass interval $0.1 -100 M_{\odot}$."
" In particular. Ont—7,4). is à matrix which calculates for any star of a given mass 1 the amount of the newly processed and already present element /. which 15 returned to the ISM."," In particular, $Q_{mi}(t-\tau_m)$, is a matrix which calculates for any star of a given mass $m$ the amount of the newly processed and already present element $i$, which is returned to the ISM."
" The quantity 7,, 1s the lifetime of a star of mass zr (Padovani Matteucci. 1993)."," The quantity $\tau_m$ is the lifetime of a star of mass $m$ (Padovani Matteucci, 1993)."
 The third term represents the enrichment by SN Ia for which we assume the single degenerate scenario: a C-O white dwarf plus a red giant (Whelan Iben 1973)., The third term represents the enrichment by SN Ia for which we assume the single degenerate scenario: a C-O white dwarf plus a red giant (Whelan Iben 1973).
 We refer to Greegio & Renzini (1983). Matteucci & Greggio (1986) and Matteucci Recchi (2001) for further details.,"   We refer to Greggio $\&$ Renzini (1983), Matteucci $\&$ Greggio (1986) and Matteucci Recchi (2001) for further details."
 The predicted SNla explosion rate is constrained to reproduce the present day observed value (Mannucci et al..," The predicted SNIa explosion rate is constrained to reproduce the present day observed value (Mannucci et al.,"
 2008). by fixing the parameter A=0.09 in eq. (1)).," 2008), by fixing the parameter $A=0.09$ in eq.\ref{main}) )."
 The fourth and fifth terms represent the enrichment by single massive stars., The fourth and fifth terms represent the enrichment by single massive stars.
 The initial galactic infall phase enters the equation via the sixth term. for which we adopt the formula: where τμ describes the chemical composition of the accreted gas. assumed to be primordial.," The initial galactic infall phase enters the equation via the sixth term, for which we adopt the formula: where $X_{i,\rm infall}$ describes the chemical composition of the accreted gas, assumed to be primordial."
 C is the normalization constant obtained by integrating the infall law over a Hubble time., $C$ is the normalization constant obtained by integrating the infall law over a Hubble time.
 Finally. in order to calculate the potential," Finally, in order to calculate the potential"
Wilometre (SISA). and even then it will be dificult to make resolved polarization maps of these lugh-redshift galaxies.,"Kilometre (SKA), and even then it will be difficult to make resolved polarization maps of these high-redshift galaxies."
 The origin aud evolution of cosmic niaenetiuu is one of five kev science drivers for the SIKA (Cacusleretal.2001)., The origin and evolution of cosmic magnetism is one of five key science drivers for the SKA \citep{gaensler2004}.
 For the evolution of maenetic fields in spiral galaxies as a function of redshift. polarization of the integrated enüssion is most readilv observable. aud a comparison with uuresolved. galaxies at low redshift is relatively straightforward.," For the evolution of magnetic fields in spiral galaxies as a function of redshift, polarization of the integrated emission is most readily observable, and a comparison with unresolved galaxies at low redshift is relatively straightforward."
 The uuuber deusitv of faint polarized radio sources in the sky determines the unknown confusion Πιτ in polarization. aud is an important parameter for rotation iueasure studies.," The number density of faint polarized radio sources in the sky determines the unknown confusion limit in polarization, and is an important parameter for rotation measure studies."
 Below 1 wJy total flux density. star forming galaxics become an increasingly iuportant fraction of all radio sources.," Below 1 mJy total flux density, star forming galaxies become an increasingly important fraction of all radio sources."
 Knowledge of the polarization properties of these galaxies is required to make realistic predietious of the number of polarized sources at pJy levels in polarized flux density., Knowledge of the polarization properties of these galaxies is required to make realistic predictions of the number of polarized sources at $\rm \mu Jy$ levels in polarized flux density.
 Spiral ealaxics παν become an inportant fraction of the polarized 1.1 CIIz radio source population at μὴν flux densities (Stiletal.2007).., Spiral galaxies may become an important fraction of the polarized 1.4 GHz radio source population at $\mu$ Jy flux densities \citep{stil2007a}.
 This paper preseuts observations and models that show that unresolved spiral galaxies lave detectable polarized eumission. somoetinies more than polarized at Ls GIIz. aud that statistical information on magnetic fields aud internal Faraday rotation cau be derived from integrated polarization measurements of spiral galaxies.," This paper presents observations and models that show that unresolved spiral galaxies have detectable polarized emission, sometimes more than polarized at 4.8 GHz, and that statistical information on magnetic fields and internal Faraday rotation can be derived from integrated polarization measurements of spiral galaxies."
 We use a compilation of archival data for nearby ealaxies imaged in polarized radio cussion., We use a compilation of archival data for nearby galaxies imaged in polarized radio emission.
 Observations at Ls Guz are most widely available. so this paper focuses at this frequency to maximize the sample size for a sinele frequency.," Observations at 4.8 GHz are most widely available, so this paper focuses at this frequency to maximize the sample size for a single frequency."
 Additional observatious at 8.1 GIIz are available for five galaxies., Additional observations at 8.4 GHz are available for five galaxies.
 These are listed alongside the Ls CIIz data., These are listed alongside the 4.8 GHz data.
 Three sub samples are cistineuished iu this paper., Three sub samples are distinguished in this paper.
" The first sub sample is a set of 11 nearby ""held galaxies listed in Table 1..", The first sub sample is a set of 14 nearby “field” galaxies listed in Table \ref{nearby-tab}.
 The second sub suuple is a set of 9 spiral galaxies iu the Vireo cluster from Wezeowiecetal.(2007).. Wezeeowiec et al. (," The second sub sample is a set of 9 spiral galaxies in the Virgo cluster from \citet{wezgowiec2007}, Weżggowiec et al. ("
in. prep.).,"in prep.),"
 aud Chnvzyvetal.(2007) listed in Table 2.., and \citet{chyzy2007} listed in Table \ref{virgo-tab}.
 These ealaxies exist in a cluster euvironment. with a higher probability ofinteraction with other cluster ueibers aud the intracluster eas.," These galaxies exist in a cluster environment, with a higher probability of interaction with other cluster members and the intracluster gas."
 The third sub sample of 20 barred spiral ealaxies listed in Table 30 allows us to explore the iuteerated polarization of barred galaxies., The third sub sample of 20 barred spiral galaxies listed in Table \ref{barred-tab} allows us to explore the integrated polarization of barred galaxies.
 One nearby ealaxv (NCC L631. classified as SD) was included iu Table 3..," One nearby galaxy (NGC 4631, classified as SB) was included in Table \ref{barred-tab}."
 The nearest galaxies in the sample and the galaxies in the Virgo cluster were observed with the 1001:Effelshere telescope. sometimes in combination with the VLA.," The nearest galaxies in the sample and the galaxies in the Virgo cluster were observed with the 100m-Effelsberg telescope, sometimes in combination with the VLA."
 These galaxies are not affected bw missing short spacings in the interferometer., These galaxies are not affected by missing short spacings in the interferometer.
 The barred galaxics were not observed with the Effelsbere telescope. aud the damages could iu principle lack large scale structure resolved by the shortest baselines of the iterterometer.," The barred galaxies were not observed with the Effelsberg telescope, and the images could in principle lack large scale structure resolved by the shortest baselines of the interferometer."
 A comparison of 6 cmi flux densities derived by Becketal.(2002) with published integrated flux deusities showed that NOC 1313 aud NGC 3992 in Table 3 may be affected by nüssimg short spacings. because published flux densities listed iu the NASA Extragalactic Database (NED) are substantially ligher than the flux deusitv in Decketal.(2002).," A comparison of 6 cm flux densities derived by \citet{beck2002} with published integrated flux densities showed that NGC 1313 and NGC 3992 in Table \ref{barred-tab} may be affected by missing short spacings, because published flux densities listed in the NASA Extragalactic Database (NED) are substantially higher than the flux density in \citet{beck2002}."
. If uo 6 ciu flux density was published. we compared the 21 cn fux density corrected for a spectral index 0.7 - 1 with the flix density in Becketal.(2002).," If no 6 cm flux density was published, we compared the 21 cm flux density corrected for a spectral index 0.7 - 1 with the flux density in \citet{beck2002}."
. Of the two barred galaxies with suspected missing fiux in the interferometer image. NGC 1313 showed no significant integrated polarization. while NGC 3992 has a lieh degree of polarization of LLO+AL84. ," Of the two barred galaxies with suspected missing flux in the interferometer image, NGC 1313 showed no significant integrated polarization, while NGC 3992 has a high degree of polarization of $14.9 \pm 4.8\ \%$."
Most of the eiuission of NGC 3992 detected in the interferometer nuage originates outside the bar reeion (Becketal.2002)., Most of the emission of NGC 3992 detected in the interferometer image originates outside the bar region \citep{beck2002}.
. Tn order to simulate unresolved observations frou our maps of nearby galaxies we inteerated the Stokes I. Q. and U images of these galaxies separately in ellipses.," In order to simulate unresolved observations from our maps of nearby galaxies we integrated the Stokes I, Q, and U images of these galaxies separately in ellipses."
 Their axial ratio was defined by the outer isophotes in the Stokes { image aud the ellipses include the cutive galaxy up to the noise level of the Stokes Timap., Their axial ratio was defined by the outer isophotes in the Stokes $I$ image and the ellipses include the entire galaxy up to the noise level of the Stokes I map.
" The integrated Q aud CU flux densities were used to calculate the integrated polarized fix density 5,=ο|C2). that was corrected for polarization bias following Siunous&Stewart(1985). to obtain the iutriusic polarized fiux eustv 5,0."," The integrated $Q$ and $U$ flux densities were used to calculate the integrated polarized flux density $S_p=\sqrt{(Q^2+U^2)}$, that was corrected for polarization bias following \citet{simmons1985} to obtain the intrinsic polarized flux density $S_{p,0}$."
 The correction for polarization bias did uot have a measurable effect for most galaxies because of the high signal to noise ratio of the integrated fiux enusities., The correction for polarization bias did not have a measurable effect for most galaxies because of the high signal to noise ratio of the integrated flux densities.
 The inteerated fractional polarization of cach galaxy was calculated as Ty=ους where 5 is the otal dux density. including thermal anc non-theruial cussion.," The integrated fractional polarization of each galaxy was calculated as $\Pi_0 = S_{p,0}/S$, where $S$ is the total flux density, including thermal and non-thermal emission."
" The polarization augle =4arctanU/Q) of he inteerated emission is expected0,4 to be aligned with the apparent minor axis of the optical galaxy.", The polarization angle $\theta_{\rm pol} = \onehalf \arctan(U/Q)$ of the integrated emission is expected to be aligned with the apparent minor axis of the optical galaxy.
 The seusitivitv of the observatious is included iu the errors for Ty hrough the noise in the maps., The sensitivity of the observations is included in the errors for $\Pi_0$ through the noise in the maps.
 The error estimates also iuclude the wncertaity in the zero level. that dominates he uncertainty for galaxies with a large augular size such as M 31.," The error estimates also include the uncertainty in the zero level, that dominates the uncertainty for galaxies with a large angular size such as M 31."
 It is customary to list the position angle of the optical major axis. and also to rotate the observed E- by 90° to obtain D-vectors in the plane of the sky.," It is customary to list the position angle of the optical major axis, and also to rotate the observed E-vectors by $90\degr$ to obtain B-vectors in the plane of the sky."
 We therefore define 0p=Aci|90° for comparison with published position augles of the optical major axis.," We therefore define $\thetaB = \theta_{\rm pol}+90\degr$ for comparison with published position angles of the optical major axis, $\thetaopt$."
 The results are listed in Tables 1.. 2.. aud 3.. θωμι.," The results are listed in Tables \ref{nearby-tab}, \ref{virgo-tab}, and \ref{barred-tab}."
Bandwidth depolarization is negligible iu these data., Bandwidth depolarization is negligible in these data.
 For a rotation measure as hieh as 300 rad in7. the poluized intensity is decreased by less than," For a rotation measure as high as 300 rad $^{-2}$, the polarized intensity is decreased by less than."
 The inteerated polarized fux densities are not affected by siguificaut residual instrumental polarization., The integrated polarized flux densities are not affected by significant residual instrumental polarization.
 Small values for the iutegrated fractional polarization are the result of πορτα siguificant flux in Stokes Q and U. with nearly αςequal positive aud negative contributions.," Small values for the integrated fractional polarization are the result of integrating significant flux in Stokes Q and U, with nearly equal positive and negative contributions."
 The uncertainty in the polarization angle of the inteerated emission is typically less than 5 degrees., The uncertainty in the polarization angle of the integrated emission is typically less than 5 degrees.
" Some galaxies (ALD 31. AD 81. NCC 1565 in Table 1.. NGC 1192. NGC 1302, NGC 1535 in Table 2.. NGC 1300. NGC 1193.. NGC 3953, NCC 3992 in Table 3)) have integrated fractional polarization Ij>."," Some galaxies (M 31, M 81, NGC 4565 in Table \ref{nearby-tab}, NGC 4192, NGC 4302, NGC 4535 in Table \ref{virgo-tab}, NGC 1300, NGC 1493, NGC 3953, NGC 3992 in Table \ref{barred-tab}) ) have integrated fractional polarization $\Pi_0 > 7\%$."
 Five of these ealaxies (M 31. NGC 1565. NOC 1192. NGC 1193. aud NGC 3992) are more than 1054 polarized after integration over solid angle.," Five of these galaxies (M 31, NGC 4565, NGC 4192, NGC 1493, and NGC 3992) are more than $10\%$ polarized after integration over solid angle."
 Five of the Virgo galaxies have additional observations at ὃν CGIIz., Five of the Virgo galaxies have additional observations at 8.4 GHz.
 The fractional polarization at both frequencies agrees to within a few percent for these ealaxies., The fractional polarization at both frequencies agrees to within a few percent for these galaxies.
 Sinall differences can be attributed to statistical errors. madnlv at S.1 GIIz where the signal to noise ratio of the emission is lower.," Small differences can be attributed to statistical errors, mainly at 8.4 GHz where the signal to noise ratio of the emission is lower."
 The differences in Wy at Ls GIIz and at 8.1 GIIz per galaxy. are Ίο. smaller, The differences in $\Pi_0$ at 4.8 GHz and at 8.4 GHz per galaxy are much smaller
galaxies.,galaxies.
" This is also consistent with the well-known fact that low mass galaxies are in general more active and blue in colour, while high mass galaxies are red and passively evolved."," This is also consistent with the well-known fact that low mass galaxies are in general more active and blue in colour, while high mass galaxies are red and passively evolved."
" In ?, they use the HOD method to model the luminosity-dependent projected correlation function of DEEP2 and SDSS surveys, and study the stellar mass growth of galaxies, by estimating the stellar mass from galaxy luminosity and colour based on the mean relation between these properties."," In \citet{zheng2007}, they use the HOD method to model the luminosity-dependent projected correlation function of DEEP2 and SDSS surveys, and study the stellar mass growth of galaxies, by estimating the stellar mass from galaxy luminosity and colour based on the mean relation between these properties."
" Compared with their result shown in their Fig.9, the contribution of high redshift galaxies to galaxy mass of the present day has a similar trend with halo mass, but the absolute values of our model are in general higher than their result."," Compared with their result shown in their Fig.9, the contribution of high redshift galaxies to galaxy mass of the present day has a similar trend with halo mass, but the absolute values of our model are in general higher than their result."
" Besides, the increase at halo mass of around 10!2h~'Mo is more steeper in our model."," Besides, the increase at halo mass of around $10^{12}h^{-1}M_{\odot}$ is more steeper in our model."
" Notice that they are modelling observation of DEEP2, whose redshift range is around 1, while our model is to fit the VVDS, with redshift of around 0.8, this discrepancy is in the right direction to be explained by the increase of galaxy mass through time."," Notice that they are modelling observation of DEEP2, whose redshift range is around 1, while our model is to fit the VVDS, with redshift of around $0.8$, this discrepancy is in the right direction to be explained by the increase of galaxy mass through time."
" As pointed out by ?,, around 25 percent more of the stellar mass could have been in place in the z~1 progenitors due to the fact that the DEEP2 sample they used are not entirely volume limited for red galaxies."," As pointed out by \citet{zheng2007}, around $25$ percent more of the stellar mass could have been in place in the $z\sim1$ progenitors due to the fact that the DEEP2 sample they used are not entirely volume limited for red galaxies."
 This would decrease the discrepancy between these two model results., This would decrease the discrepancy between these two model results.
" However, for massive haloes, galaxies inside them are still more massive at higher redshift in our model than in their model result."," However, for massive haloes, galaxies inside them are still more massive at higher redshift in our model than in their model result."
 This may be caused by the fact that the DEEP2 sample could have missed a quite fraction of red massive galaxies because of their colour selection of target galaxies., This may be caused by the fact that the DEEP2 sample could have missed a quite fraction of red massive galaxies because of their colour selection of target galaxies.
" When a central galaxy falls into a larger group and becomes a satellite, the gas around the galaxy is shock-heated."," When a central galaxy falls into a larger group and becomes a satellite, the gas around the galaxy is shock-heated."
 The gas stops cooling and the star formation ceases in a short time scale., The gas stops cooling and the star formation ceases in a short time scale.
 The stellar mass of the galaxy can increase by only a small amount through star formation., The stellar mass of the galaxy can increase by only a small amount through star formation.
" On the other hand, the galaxy stellar mass may decrease a bit due to the tidal stripping effect."," On the other hand, the galaxy stellar mass may decrease a bit due to the tidal stripping effect."
" We now assume that in total, the stellar components of satellite galaxies do not change compared with the mass at the time when they are central objects."," We now assume that in total, the stellar components of satellite galaxies do not change compared with the mass at the time when they are central objects."
" In this case, Mitars- Mi,ai relation for a satellite galaxy is the same as the Mstars-Minfat relation for centrals at an earlier epoch, when the satellite galaxy falls into a larger group."," In this case, $M_{stars}$ $M_{infall}$ relation for a satellite galaxy is the same as the $M_{stars}$ $M_{infall}$ relation for centrals at an earlier epoch, when the satellite galaxy falls into a larger group."
" We now try to build a unified model to describe the evolution of Mstars-Minfau relation with redshift, for both central and satellite galaxies."," We now try to build a unified model to describe the evolution of $M_{stars}$ $M_{infall}$ relation with redshift, for both central and satellite galaxies."
" We assume that at all redshifts, the median of the Mstars-Min fai relation can be described by a double power law form."," We assume that at all redshifts, the median of the $M_{stars}$ $M_{infall}$ relation can be described by a double power law form."
" We assume that the power law indexes and the scatter around the median relation are fixed with time, while the critical mass and the corresponding normalization parameter evolve with time linearly."," We assume that the power law indexes and the scatter around the median relation are fixed with time, while the critical mass and the corresponding normalization parameter evolve with time linearly."
" At any given redshift, the stellar mass of central galaxy is connected to its host halo mass according to the relation."," At any given redshift, the stellar mass of central galaxy is connected to its host halo mass according to the relation."
" For satellite galaxy, its stellar mass is connected to its halo mass at infall time, according to the Mstars-Minfalt relation at the time when the galaxy falls into a larger group and becomes a satellite."," For satellite galaxy, its stellar mass is connected to its halo mass at infall time, according to the $M_{stars}$ $M_{infall}$ relation at the time when the galaxy falls into a larger group and becomes a satellite."
" Based on this picture, we can get the stellar masses for all galaxies at any given redshift, and calculate their"," Based on this picture, we can get the stellar masses for all galaxies at any given redshift, and calculate their"
suge@ests (here is a common origin.,suggests there is a common origin.
 We propose that this is an artifact of the absorbed blackbody fit: if the true spectrum of iis more slronely peaked (han a blackbody. blackbody fits will forced to a high Ny value and inflate the inferred. Li.," We propose that this is an artifact of the absorbed blackbody fit: if the true spectrum of is more strongly peaked than a blackbody, blackbody fits will forced to a high $_H$ value and inflate the inferred $_{\rm bol}$."
 Το test this hypothesis. we have fitted these 6 spectra with a second model.," To test this hypothesis, we have fitted these 6 spectra with a second model."
 After some experimentation. we have fixed Nj to 4x10? 7. a reasonable value for an object in the disk of MIOl.," After some experimentation, we have fixed $_H$ to $\times 10^{20}$ $^{-2}$, a reasonable value for an object in the disk of M101."
" The underlving model is a variable blackbody plus a relativistie line from an accretion disk (7diskline as implemented inxspec)"".", The underlying model is a variable blackbody plus a relativistic line from an accretion disk (“diskline” as implemented in.
. This model is often invoked for the Fe Ix lines in active galactic nuclei (AGN)., This model is often invoked for the Fe K lines in active galactic nuclei (AGN).
 More recently. Branchiardi-Ravimontοἱal.(2001) have fitted (he RRGS spectra of two AGN using relativistic lines from OVIII. NVI. and CV. and the same physical interpretation can in principle apply toULA-L.," More recently, \cite{Bea2001} have fitted the RGS spectra of two AGN using relativistic lines from OVIII, NVI, and CV, and the same physical interpretation can in principle apply to."
". The parameters for the diskline were fixed at the following values. after experimentation: the central energy. 0.5 keV: 5? (power law index for the radial dependence of emissivitv). —2: range of accretion disk radius. 61000 M,: and disk inclination. 75°."," The parameters for the diskline were fixed at the following values, after experimentation: the central energy, 0.5 keV; $\beta$ (power law index for the radial dependence of emissivity), $-$ 2; range of accretion disk radius, 6–1000 $_g$; and disk inclination, $^\circ$."
 We show the July 2004 data as fitted with this model in relabsori., We show the July 2004 data as fitted with this model in \\ref{absori}.
 The line enerey (0.5 keV) suggests NVI. while for this spectrum alone (in fact. onlv the July 6 spectrum). an addiüonal line al 0.3 keV would further improve the fit.," The line energy (0.5 keV) suggests NVI, while for this spectrum alone (in fact, only the July 6 spectrum), an additional line at 0.8 keV would further improve the fit."
 Alternatively. this feature could be due to a transient edge αἱ 0.9 keV (IXongetal.2004).," Alternatively, this feature could be due to a transient edge at 0.9 keV \citep{KDY2004}."
. As [or the 0.6 keV. edge also noted by IXongetal.(2004)... this is not required for a good fit once the 0.5 keV emission line is included in the moclel.," As for the 0.6 keV edge also noted by \cite{KDY2004}, this is not required for a good fit once the 0.5 keV emission line is included in the model."
 We stunmarize the results lor all hieh state spectra in reftrendiab ancl in the right column of reltrend.., We summarize the results for all high state spectra in \\ref{trendtab} and in the right column of \\ref{trend}.
" Ii contrast to the absorbed blackbocly fits. the inferred Li, values are positively correlated with the count rates using this model."," In contrast to the absorbed blackbody fits, the inferred $_{\rm bol}$ values are positively correlated with the count rates using this model."
" The inferred bolometric huninositv and the unabsorbed 0.3LO keV. Iuminositv for the 2004 July data are ~1.xLO"" aand ~6xLOLF.. in contrast to the much higher value obtained with the absorbed blackbody fit."," The inferred bolometric luminosity and the unabsorbed 0.3–10 keV luminosity for the 2004 July data are $\sim 1 \times 10^{39}$ and $\sim 6 \times 10^{38}$, in contrast to the much higher value obtained with the absorbed blackbody fit."
 The 2005 January ddata ean also be fitted with either model reltrendtab))., The 2005 January data can also be fitted with either model \\ref{trendtab}) ).
 In these fits. the model parameters are statistically well-constrained. (e.g... the blackbody temperature has (vpical errors of 5 to 20 eV). but it is clear that the true uncertainties are dominated by the svstematies due (o our choice of models.," In these fits, the model parameters are statistically well-constrained (e.g., the blackbody temperature has typical errors of 5 to 20 eV), but it is clear that the true uncertainties are dominated by the systematics due to our choice of models."
"of the dark matter halo, implying that the light profile is not necessarily expected to follow the same model that describes the inner stellar body.","of the dark matter halo, implying that the light profile is not necessarily expected to follow the same model that describes the inner stellar body."
" Alternatively, this excess light may simply be the residual background in the images, reflecting unresolved light from the group environment in which LRGs typically reside."," Alternatively, this excess light may simply be the residual background in the images, reflecting unresolved light from the group environment in which LRGs typically reside."
" Excess light was also observed by Z05, who studied the ICL around brightest cluster galaxies from a stack of 683 SDSS images."," Excess light was also observed by Z05, who studied the ICL around brightest cluster galaxies from a stack of 683 SDSS images."
 Such galaxies typically live in dense halos with total mass of 1014 to 10!? and are inherently different from LRGs whose group Mchalos are a few times 101? in mass., Such galaxies typically live in dense halos with total mass of $10^{14}$ to $10^{15} M\solar$ and are inherently different from LRGs whose group halos are a few times $10^{13} M\solar$ in mass.
" Z05 found that in clusters, this “extra light"" Mcconstitutes only a small fraction of the total cluster profile, accounting for less than of the light inside of 500 kpc."," Z05 found that in clusters, this “extra light” constitutes only a small fraction of the total cluster profile, accounting for less than of the light inside of 500 kpc."
" Nevertheless, the ICL profile departs from a single parameter Sérrsic model already at r~50kpc, compared to the departure radius of 100 kpc that is observed in our LRG stacks (figure 9))."," Nevertheless, the ICL profile departs from a single parameter Sérrsic model already at $r\sim50 kpc$, compared to the departure radius of 100 kpc that is observed in our LRG stacks (figure \ref{fig:zibetti}) )."
 This suggests that the massive clusters studied by Z05 may more readily support a population of intergalactic stars than the groups in which LRGs reside., This suggests that the massive clusters studied by Z05 may more readily support a population of intergalactic stars than the groups in which LRGs reside.
 In their paper Z05 correct their light profiles for unresolved cluster sources using the luminosity function given by ?.., In their paper Z05 correct their light profiles for unresolved cluster sources using the luminosity function given by \cite{mobasher_photometric_2003}.
" We note that the PSF, which is not deconvolved from the ICL+BCG profiles presented in Z05 may scatter light at all radii and increase the errors of the Sérrsic model fit."," We note that the PSF, which is not deconvolved from the ICL+BCG profiles presented in Z05 may scatter light at all radii and increase the errors of the Sérrsic model fit."
" Unlike the outer parts of LRGs, the centers of these galaxies are not well resolved in our stacks."," Unlike the outer parts of LRGs, the centers of these galaxies are not well resolved in our stacks."
 Studies utilizing high resolution HST images showed that the profile at the inner parts of nearby ellipticals often departs from the Sérrsic model that traces their outskirts., Studies utilizing high resolution HST images showed that the profile at the inner parts of nearby ellipticals often departs from the Sérrsic model that traces their outskirts.
" More specifically, the most massive ellipticals exhibit flattened central light profiles (e.g.,????).."," More specifically, the most massive ellipticals exhibit flattened central light profiles \citep[e.g.,][]{lauer_cores_1985,
 kormendy_hst_1994, lauer_centers_1995, faber_centers_1997}."
" Recently, used a compilation of HST and ground based data to show that although well fitted by a Sérrsic model out to large radii, the most massive Virgo ellipticals exhibit 1 kpc scale cores."," Recently, used a compilation of HST and ground based data to show that although well fitted by a Sérrsic model out to large radii, the most massive Virgo ellipticals exhibit 1 kpc scale cores."
 In our stacks we cannot resolve such physical scales as 1 pixel in the SDSS data is equivalent to 1.9 kpc at the stack mean redshift of 0.34., In our stacks we cannot resolve such physical scales as 1 pixel in the SDSS data is equivalent to 1.9 kpc at the stack mean redshift of 0.34.
" We are nevertheless able to confirm the excellent fit of massive elliptical galaxy profiles to a single Sérrsic profile out to a few effective radii that ? found for individual Virgo galaxies (reaching Ay,> 0.2 mag arcsec? at ry>100 kpc).", We are nevertheless able to confirm the excellent fit of massive elliptical galaxy profiles to a single Sérrsic profile out to a few effective radii that \cite{kormendy_structure_2009} found for individual Virgo galaxies (reaching $\Delta\mu_\lambda\geq$ 0.2 mag $^2$ at $r_\lambda\geq 100$ kpc).
 The deep stacks allow us to test how much light is missed in typical studies of the profiles of individual LRGs and derive a correction factor that can be applied in such cases., The deep stacks allow us to test how much light is missed in typical studies of the profiles of individual LRGs and derive a correction factor that can be applied in such cases.
" To do so we first selected all the LRGs in a single magnitude bin, 18.0<m,<18.2, and used GALFIT to produce a Sérrsic model to each object individually."," To do so we first selected all the LRGs in a single magnitude bin, $\leq$$m_r$$<$ 18.2, and used GALFIT to produce a Sérrsic model to each object individually."
" We then excluded all fits with errors of more than in either the n parameter or the effective radius, resulting in a mean effective radius value of 11.7 kpc."," We then excluded all fits with errors of more than in either the n parameter or the effective radius, resulting in a mean effective radius value of 11.7 kpc."
 The difference between this value and the one derived by GALFIT for the stacked image (re =13.1 kpc) is then ~10%.., The difference between this value and the one derived by GALFIT for the stacked image $r_e=$ 13.1 kpc) is then $\sim$.
 'This implies that surveys may underestimate the size of massive red galaxies by this amount., This implies that surveys may underestimate the size of massive red galaxies by this amount.
" The total flux in the stack, however, accounts for — more than the mean value for the individually derived profiles, suggesting that a non-negligible amount of light is typically missed and that the total stellar mass is underestimated."," The total flux in the stack, however, accounts for $\sim$ more than the mean value for the individually derived profiles, suggesting that a non-negligible amount of light is typically missed and that the total stellar mass is underestimated."
 It has long been known that the color profiles of nearby massive ellipticals exhibit a relatively smooth gradient toward bluer colors from the galaxy centers outward., It has long been known that the color profiles of nearby massive ellipticals exhibit a relatively smooth gradient toward bluer colors from the galaxy centers outward.
features in Figure 36 (right) are HI absorption near —80 lo Land —135 |.,"features in Figure 36 (right) are HI absorption near $-$ 80 $-$ , and $-$ 135."
 The lack of absorption due to either the —100 inolecular cloud or the —65 molecular could iudicate that FIR { could be located in [ront of these clouds but beyoid the 3-kpe arm at 5 kpe. since the —Slkins absorption componen is present.," The lack of absorption due to either the $-$ 100 molecular cloud or the $-$ 65 molecular could indicate that FIR 4 could be located in front of these clouds but beyond the 3-kpc arm at 5 kpc, since the $-$ 54 absorption component is present."
 Source C has an absoriO spectrum which appears very simular to the otler sources in the Ser C complex. with absorption near —60 L. —100 ald —126 4.," Source C has an absorption spectrum which appears very similar to the other sources in the Sgr C complex, with absorption near $-$ 60, $-$ 100 and $-$ 126."
 By couUrast. Source D only has HI absorpion features i he range of —30 to 30.. suggesting tha may be nearer to he Sun along tie line of sight.," By contrast, Source D only has HI absorption features in the range of $-$ 30 to 30, suggesting that it may be nearer to the Sun along the line of sight."
 Usiug the comparison of atomic absorption and molecular aud ionizecl gas velocllies. we Cal nake a schematic of tle line-of-sight arrangejent of the sources aid ISM sturrousding Ser C. A yossible arrangement from the restits. presented in this paper is 5lowh ln Figure 160. (as viewec rom above. looking down ou the regio1. with the observer to the left in the drawing).," Using the comparison of atomic absorption and molecular and ionized gas velocities, we can make a schematic of the line-of-sight arrangement of the sources and ISM surrounding Sgr C. A possible arrangement from the results presented in this paper is shown in Figure 40 (as viewed from above, looking down on the region, with the observer to the left in the drawing)."
 We make the ollowiug assumptions: Source D is a foreground source located soijewhere between the Sul alle he 3 kpe arm. not associated with ile rest of the Ser C region.," We make the following assumptions: Source D is a foreground source located somewhere between the Sun and the 3 kpc arm, not associated with the rest of the Sgr C region."
 Tle atomic gas associate witl he —65 uolecular cloud is Lisely to be locaecd in [οί of the Ser C HIE Regiou. Source C aud likely to be physically associated with he Ser C NTF.," The atomic gas associated with the $-$ 65 molecular cloud is likely to be located in front of the Sgr C HII Region, Source C and likely to be physically associated with the Sgr C NTF."
 The atomic gas associated wih the —100 LOecular cloud is also ikely to be located ou the near skle of the Ser C NTF (aud possibly pliysicalls! related) aud of Source C. The results presented bere (inclucling the liue-oES arrangement of couponents associated with Ser C) agree very well with those derived iu Boy (2003) using the GNART., The atomic gas associated with the $-$ 100 molecular cloud is also likely to be located on the near side of the Sgr C NTF (and possibly physically related) and of Source C. The results presented here (including the line-of-sight arrangement of components associated with Sgr C) agree very well with those derived in Roy (2003) using the GMRT.
 The spatial aud. velocity resolutious are very comparable: our survey clilers in that it covers a la‘ee region whereas the Roy (2003) observations were targeted at several ΧΤΕΣ., The spatial and velocity resolutions are very comparable; our survey differs in that it covers a large region whereas the Roy (2003) observations were targeted at several NTFs.
 Complementary HI observations of the Ser A field were carried ouw by Dwarakauath. Goss. Zhao aud Lang (2001) using the VLA in the A. B. C aud D arrays in January ane October of 2002.," Complementary HI observations of the Sgr A field were carried out by Dwarakanath, Goss, Zhao and Lang (2004) using the VLA in the A, B, C and D arrays in January and October of 2002."
 The purpose of these observatious was to elucidate the nature of the wide line (AV yapyay ov about LOO 1)) toward Ser A. These complementary observaious have a much la‘eer velocity coverage of —600 aud a velocity resolution of 1.3|., The purpose of these observations was to elucidate the nature of the wide line $\Delta$ $_{FWHM}$ $\sim$ about 100 ) toward Sgr A. These complementary observations have a much larger velocity coverage of $\sim$ 600 and a velocity resolution of 1.3.
.. The wide velocity range was required to cover the large number of velocity couponeuts at the GC. while the |igh velocity resolution was required to identify aud remove the narrow HI absorption lines.," The wide velocity range was required to cover the large number of velocity components at the GC, while the high velocity resolution was required to identify and remove the narrow HI absorption lines."
 Figre {1 shows the HI spectra obtained with au augular resolution of ~8” at four positions in SerA West: The spectrum ‘a’ is toward SerA* while b is displacec by to the SW., Figure 41 shows the HI spectra obtained with an angular resolution of $\sim$ at four positions in SgrA West: The spectrum 'a' is toward SgrA* while 'b' is displaced by to the SW.
 Positions ο and qr are located E aud NE of SgrA* and within the SNR SerA East., Positions 'c' and 'd' are located E and NE of SgrA* and within the SNR SgrA East.
 A number of nar“OW lines (10 4)) are obvious., A number of narrow lines $\sim$ 10 ) are obvious.
 In the b direction a broad shoilder is observed. Πρίνας : Vwide Component with a AV pipgra; of ~120.," In the 'b' direction a broad shoulder is observed, implying a wide component with a $\Delta$ $_{FWHM}$ of $\sim$ 120."
 Al positions ο €aud ος the wide line is not «elected.," At positions 'c' and 'd', the wide line is not detected."
 The wide line is iuterpreted to originate in va‘ious HI coimporents of the cireumnuclear disk οΝΟ with a radius of centered on SgrA*., The wide line is interpreted to originate in various HI components of the circumnuclear disk ('CND') with a radius of centered on SgrA*.
 Tlese components have central velocities of JLOO to the N of Ser À* and ~—100 Hothe S. The observed wide line in the direction ofserAd does uot represeut a component of low opaciy. turblent shocked HI clouds: this feature is the result of the," These components have central velocities of $\sim$ 100 to the N of Sgr A* and $\sim$$-$ 100 to the S. The observed wide line in the direction ofSgrA does not represent a component of low opacity, turblent shocked HI clouds; this feature is the result of the"
Rich get richer aud ]xnor get poorer.,Rich get richer and poor get poorer.
 Worse. rich people do not seem to be sjeuificautlv cleverer or more hardworking than the poorer lot.," Worse, rich people do not seem to be significantly cleverer or more hardworking than the poorer lot."
 This has puzzled philosophers aud econowists alike all the way from Buddha to Miux., This has puzzled philosophers and economists alike all the way from Buddha to Marx.
 A century ago. an Ttaliau economist Pareto gave a celebrated empirical law suggesting that it is just a law of nature that of the wealth is in hands.," A century ago, an Italian economist Pareto gave a celebrated empirical law suggesting that it is just a law of nature that of the wealth is in hands."
 In fact. on surveving various coulvies and economics in Europe. he eave a famous lav. now known as Pareto kuv.," In fact, on surveying various countries and economies in Europe, he gave a famous law, now known as Pareto law."
 It said that the probability PCr) that an individual has wealth w follows a power law for huge c. Por)~orU.," It said that the probability $P(x)$ that an individual has wealth $x$ follows a power law for large $x$, $ P(x)\sim x^{-\nu}$."
 Distribution of personal wealth aix income in countries as diverse as USA. UK. Japan and Iudia secu to haxὉ a power law tail |l.2.3.αν5].," Distribution of personal wealth and income in countries as diverse as USA, UK, Japan and India seem to have a power law tail \cite{Dragulescu,Fujiwara,Dimatto,Sitabhra,chatyard}."
 Since it secs to be indepeudent of the volitical svstems of those countries. which were widely differeut. if ean be conjectured that this distribution is the inherent outcome of economic activities.," Since it seems to be independent of the political systems of those countries, which were widely different, it can be conjectured that this distribution is the inherent outcome of economic activities."
 lu fact. it was recently observed that even dm aucieut Eevptian society. wealt1 distribution could be following the power law|6|..," In fact, it was recently observed that even in ancient Egyptian society, wealth distribution could be following the power \cite{pre}."
" Iu this society, obviously nivriad of factors plaviug role iu moderu economics do"," In this society, obviously myriad of factors playing role in modern economies do"
"with ay is the fine structure constant. and r,=eim,>c the electron radius (Svensson 1984).","with $\alpha_f$ is the fine structure constant, and $r_e = e^2/m_ec^2$ the electron radius (Svensson 1984)."
" ↴⋅expression is ⋅⋅valid [or ⋅⋉⋅↽↓⊇7 «6,and we used (2/2) οpo+(8/2)au|.to approximate exp(1/0,.)Ix2(1/0,.).This"," This expression is valid for $x\ll\theta_e$ and we used $(\pi/2)^{1/2}\theta_e^{1/2}[1 +
(8/\pi)^{1/2}\theta_e^{3/2}]$ to approximate $\exp(1/\theta_e)\hbox{K}_2(1/\theta_e)$."
 Flow al a given position is heated (or cooled) by the inverse Comptonization olf electrons., Flow at a given position is heated (or cooled) by the inverse Comptonization off electrons.
" We use the heating rate (Levich Sunvaev 1971) where Ey(ή) is the radiation energv densitv [rom equation (8)) and 04=kTy/m,c the radiation temperature from equation (9)).", We use the heating rate (Levich Sunyaev 1971) where $E_X(r)$ is the radiation energy density from equation \ref{eq:EXr}) ) and $\theta_X \equiv kT_X/m_e c^2$ the radiation temperature from equation \ref{eq:TXr}) ).
 In original CDAF. the temperature of the gas is determined by the balance between the viscous heating plus the convective energy transport versus the radiative cooling.," In original CDAF, the temperature of the gas is determined by the balance between the viscous heating plus the convective energy transport versus the radiative cooling."
 However. if the radiative heating is dominant in some region of the flow (the condition under which (his assumption is valid is cliscussed in §33.4.).," However, if the radiative heating is dominant in some region of the flow (the condition under which this assumption is valid is discussed in 3.4.),"
 (he temperature in (hat region will change to reach a new equilibrium., the temperature in that region will change to reach a new equilibrium.
 The new equilibrium temperature of the flow will be determined by the balance between radiative heating and radiative cooling., The new equilibrium temperature of the flow will be determined by the balance between radiative heating and radiative cooling.
 In CDAF considered in this work. Compton heating versus Comptonized bremsstrahlung cooling are the main radiative processes.," In CDAF considered in this work, Compton heating versus Comptonized bremsstrahlung cooling are the main radiative processes."
" The thermal equilibrium temperature T;,.then. satisfies al given position (r.0)."," The thermal equilibrium temperature $T_{eq}$,then, satisfies at given position $(r,\vartheta)$."
" From equations (20)) and (27)). 64=KT,muc is determined by since the number densitv ο.2) decrease as v—0 (toward (he pole). the derived electron temperature increases toward (he pole as long as 84> 0."," From equations \ref{eq:LambCbr}) ) and \ref{eq:GammaC}) ), $\theta_{eq} \equiv kT_{eq}/m_e c^2$ is determined by Since the number density $n_e(r,\vartheta)$ decrease as $\vartheta
\rightarrow 0$ (toward the pole), the derived electron temperature increases toward the pole as long as $\theta_X > \theta_e$ ."
1.5. (,. (
"Certainly u,Qu,/Or«0 throughout this range. whereas for5>1.5. u,Qu,/Qr>0).","Certainly $u_r\partial u_r/\partial r < 0$ throughout this range, whereas for$\gamma > 1.5$, $u_r\partial u_r/\partial r > 0$ )."
 This helps ensure that for all cases where the postshock gas decelerates. the radial /=0 mode will be stable. in agreement with the conclusions of Nakavama(1992).. ancl Burrows(1993) ancl Yamasaki&Yaimacla(2005).. where we are assuming a neutrine huninositv below the critical value in these last two references.," This helps ensure that for all cases where the postshock gas decelerates, the radial $l=0$ mode will be stable, in agreement with the conclusions of \citet{nakayama92}, and \citet{burrows93} and \citet{yamasaki05}, where we are assuming a neutrino luminosity below the critical value in these last two references."
 Taking A/?=P9 (ie. an approximately isothermal perturbation: this gives a considerable simplification. see Appendix D) the equation to first order in small quantities becomes We note that For a global mode we expect A to be of order 1/r. (in Lact lor 4=4/3. Ac2/r: see equations 16 below).," Taking $\Delta P=P\delta$ (i.e. an approximately isothermal perturbation; this gives a considerable simplification, see Appendix B) the equation to first order in small quantities becomes We note that For a global mode we expect $\lambda$ to be of order $1/r$ , (in fact for $\gamma =4/3$ , $\lambda\simeq 2/r$; see equations 16 below)."
" If w represents laterally propagating sound waves. w is in (he range efr—cf|L|. whereas wee22(r/u,Mrfc) for racially propagating vorticity perturbations."," If $\omega$ represents laterally propagating sound waves, $\omega$ is in the range $c_s/r - c_s/\left|L\right|$, whereas $\omega\sim
2\pi\left(r/u_r+r/c_s\right)$ for radially propagating vorticity perturbations."
" In either case. with Qu,/Or=(u,/r)(3—23)/(51) from Appendix A. 1 and we max pul In equation MEM7 we neglect terms in 20003409ος. u7/c; 542275776(ol order (5—1) GEM/25) and integrate using equation 9. further assuming |i""/u,+A l/r|. to get With 4,=0 and Qu,./O08= 0. equation 7 gives where we have substitutedfromequation 10 for e, to simplily the rieht hand side."," In either case, with $\partial u_r/\partial r=\left(u_r/r\right)\left(3-2\gamma\right)/\left(
\gamma -1\right)$ from Appendix A, ${-d\lambda /dr+i\left(\omega /u_rr\right)\left(3-2\gamma\right)/\left(
\gamma -1\right)\over\left(i\omega
^{\prime}/u_r+\lambda\right)^2} <<1$ and we may put In equation 7 we neglect terms in $u_r^2/c_s^2$, $u_{\phi}^2/c_s^2$ (of order $\left(\gamma -1\right)/2\gamma$ ) and integrate using equation 9, further assuming $\left|i\omega ^{\prime}/u_r+\lambda\right| >>\left|1/r\right|$ , to get With $u_{\phi}=0$ and $\partial u_r/\partial\theta =0$ , equation 7 gives where we have substitutedfromequation 10 for $v_r$ to simplify the right hand side."
 TakingXIποο1 from. Appendix A. we derive," Taking$u_r\propto r^{\left(3-2\gamma\right)/\left(\gamma -1\right)}$ from Appendix A, we derive"
" shows the cumulative percentage of the 933 quasars that have a GCL above a certain value. GCL,. shown by the bold solid curve.","\\ref{allperc} shows the cumulative percentage of the 933 quasars that have a GCL above a certain value, $GCL_o$, shown by the bold solid curve."
" Roughly 2656 (243) of the known quasars were seen as variable in the QUEST variability scans with GCL,=99.", Roughly $26\%$ (243) of the known quasars were seen as variable in the QUEST variability scans with $GCL_o = 99$.
 Almost 39'% (361) are variable with GCL>93., Almost $39\%$ (361) are variable with $GCL \geq 93$.
" After an initial rise due to strongly variable quasars. decreasing GCL, only gradually increases the percentage of known quasars reliably considered to vary."," After an initial rise due to strongly variable quasars, decreasing $GCL_o$ only gradually increases the percentage of known quasars reliably considered to vary."
" The break in the distribution at GCL,=93. shown by the solid. vertical line. suggests an empirical criterion for considering a QVS object as significantly variable."," The break in the distribution at $GCL_o = 93$, shown by the solid vertical line, suggests an empirical criterion for considering a QVS object as significantly variable."
 However. is somewhat misleading as it fails to take into account (he relativistic time dilation.," However, \\ref{allperc} is somewhat misleading as it fails to take into account the relativistic time dilation."
 To correct [for (his. it is necessary to shift to the quasars’ rest frames. and (o study. the variability completeness as a ΠΙΟΠο of redshilt.," To correct for this, it is necessary to shift to the quasars' rest frames and to study the variability completeness as a function of redshift."
 The nominal time baseline between first ancl last observations for the QVS is 26 months., The nominal time baseline between first and last observations for the QVS is 26 months.
 Data were taken between February 1999 and. April 2001: however. considering the patchy RA coverage over the course of the scans. anv given light curve may. have a time baseline noliceably shorter than the full 26 months.," Data were taken between February 1999 and April 2001; however, considering the patchy RA coverage over the course of the scans, any given light curve may have a time baseline noticeably shorter than the full 26 months."
 The left-hand panel in reftimelrames. shows a histogram of the observer-frame time baselines for the 933 known quasars., The left-hand panel in \\ref{timeframes} shows a histogram of the observer-frame time baselines for the 933 known quasars.
 The right-hand panel of reftimeframes shows a histogram of the rest-frame time baselines. deredshifted using published redshifts.," The right-hand panel of \\ref{timeframes} shows a histogram of the rest-frame time baselines, deredshifted using published redshifts."
 The mean quasar rest-frame time baseline for the 933 known quasars is 335x124 davs., The mean quasar rest-frame time baseline for the 933 known quasars is $335 \pm 124$ days.
 While deredshifting works to reduce the amount of time which we are investigating. it also results in better light curve coverage as a function of time in the quasars’ rest Irames.," While deredshifting works to reduce the amount of time which we are investigating, it also results in better light curve coverage as a function of time in the quasars' rest frames."
 also shows the cumulative distributions for quasars in various rest-lrame time bins., \\ref{allperc} also shows the cumulative distributions for quasars in various rest-frame time bins.
 With tlie range of rest-Irame time baselines shown in reftimeframes.. there is not an exact correspondence between lime frame and redshift bins.," With the range of rest-frame time baselines shown in \\ref{timeframes}, there is not an exact correspondence between time frame and redshift bins."
 shows the redshift distributions for each of the time bins in relallperc.., \\ref{zhistos} shows the redshift distributions for each of the time bins in \\ref{allperc}.
 With the exception of the longest time baseline bin. all histograms have a low redshift tail. corresponding to the few short observer-[rame lime baselines shown in the plot of rellimelranies..," With the exception of the longest time baseline bin, all histograms have a low redshift tail, corresponding to the few short observer-frame time baselines shown in the left-hand plot of \\ref{timeframes}. ."
 As expected. there is a strong correlation between rest-frame time baseline and variability detection," As expected, there is a strong correlation between rest-frame time baseline and variability detection"
"gas patch is 0.24—0.47R,.",gas patch is 0.24–0.47.
. This means that the upwelling gas patch at 1.45 in 2008 can reach 1.7-1.9 in 2009., This means that the upwelling gas patch at 1.45 in 2008 can reach 1.7–1.9 in 2009.
 Likewise. if we assume that the fast downdrafting patch with 20-30 detected in 2009 accelerated inward linearly with time starting from 0s7!.. it must have traveled 0.71—1.07 im | year.," Likewise, if we assume that the fast downdrafting patch with 20–30 detected in 2009 accelerated inward linearly with time starting from 0, it must have traveled 0.71–1.07 in 1 year."
 This suggests that the fast downdrafting gas patch could have been located as far as at 2.2-2.5 iin 2008 and could have fallen to 1.45 iin one year., This suggests that the fast downdrafting gas patch could have been located as far as at 2.2–2.5 in 2008 and could have fallen to 1.45 in one year.
" Therefore. the vigorous gas motions can be present up to ~2&,.."," Therefore, the vigorous gas motions can be present up to $\sim$ 2."
 These inhomogeneous gas motions in the extended atmosphere of Betelgeuse have also been detected by other observations., These inhomogeneous gas motions in the extended atmosphere of Betelgeuse have also been detected by other observations.
 Recently Harper et al. (2009a)), Recently Harper et al. \cite{harper09a}) )
 have studied the dynamies of the cool extended outer atmosphere of Betelgeuse based on high-spectral resolution mid-IR observations of the [Fe II] lines at 17.94 and 24.53µηι., have studied the dynamics of the cool extended outer atmosphere of Betelgeuse based on high-spectral resolution mid-IR observations of the [Fe II] lines at 17.94 and 24.53.
. These [Fe Il] lines form at  1.6 (converted with the angular diameter of Betelgeuse derived here) in the cool extended outer atmosphere (see Fig., These [Fe II] lines form at $\sim$ 1.6 (converted with the angular diameter of Betelgeuse derived here) in the cool extended outer atmosphere (see Fig.
 8 of Harper et al. 2009a)), 8 of Harper et al. \cite{harper09a}) )
 with estimated excitation temperatures of 1520-1950 K. Therefore. the [Fe II] lines originate in the region similar to the MOLsphere where the CO first overtone lines form.," with estimated excitation temperatures of 1520–1950 K. Therefore, the [Fe II] lines originate in the region similar to the MOLsphere where the CO first overtone lines form."
 The profiles of the [Fe II] lines indicate turbulent gas motions without signatures of significant outflows of 210kms7!., The profiles of the [Fe II] lines indicate turbulent gas motions without signatures of significant outflows of $\ga$ 10.
. This is consistent with the velocity fields derived from our two-epoch AMBER observations., This is consistent with the velocity fields derived from our two-epoch AMBER observations.
 Harper et al. (2009a)), Harper et al. \cite{harper09a}) )
 detected no significant changes in the [Fe II] line profiles at three epochs over 14 months., detected no significant changes in the [Fe II] line profiles at three epochs over 14 months.
 However. this may be because the changes in the velocity field are smeared out in their spatially unresolved observations.," However, this may be because the changes in the velocity field are smeared out in their spatially unresolved observations."
 As can be seen in Fig., As can be seen in Fig.
 jaa. the CO line profiles observed with AMBER only show a low redshift. despite the remarkable change in the velocity field.," \ref{obsresCO}a a, the CO line profiles observed with AMBER only show a low redshift, despite the remarkable change in the velocity field."
 Complex gas motions have been detected in the extended chromosphere of Betelgeuse as well., Complex gas motions have been detected in the extended chromosphere of Betelgeuse as well.
" Lobel Dupree (2001)) present the modeling of the chromospheric velocity field up to ~3R,.", Lobel Dupree \cite{lobel01}) ) present the modeling of the chromospheric velocity field up to $\sim$ 3.
 Moreover. the velocity field changed from overall inward motions to outward motions within 0.5-1 year.," Moreover, the velocity field changed from overall inward motions to outward motions within 0.5–1 year."
 Therefore. both the cool and hot components in the extended outer atmosphere are characterized by strongly temporally variable inhomogeneous gas motions.," Therefore, both the cool and hot components in the extended outer atmosphere are characterized by strongly temporally variable inhomogeneous gas motions."
 The physical mechanism responsible for these vigorous motions and their drastic change within one year is not yet clear. although it is likely related to the unknown wind-driving mechanism.," The physical mechanism responsible for these vigorous motions and their drastic change within one year is not yet clear, although it is likely related to the unknown wind-driving mechanism."
" The convective energy flux is expected to be low in the MOLsphere. which extends to ~1.3-1.4R,."," The convective energy flux is expected to be low in the MOLsphere, which extends to $\sim$ 1.3–1.4."
. This poses a problem for the interpretation of the detected gas motions in terms of convection., This poses a problem for the interpretation of the detected gas motions in terms of convection.
 Other possible mechanisms include Alfvénn waves and pulsation., Other possible mechanisms include Alfvénn waves and pulsation.
 The recent detection of magnetic fields in Betelgeuse. albeit weak (~1 G). indicates that the prerequisite for Alfvénn-driven-winds ts available (Auriérre et al. 2010)).," The recent detection of magnetic fields in Betelgeuse, albeit weak $\sim$ 1 G), indicates that the prerequisite for Alfvénn-driven-winds is available (Aurièrre et al. \cite{auriere10}) )."
 Airapetian et al. (2000)), Airapetian et al. \cite{airapetian00}) )
 show that Alfvénn waves can drive mass outflows from the chromosphere with the velocity and mass-loss rate in agreement with those observed for Betelgeuse., show that Alfvénn waves can drive mass outflows from the chromosphere with the velocity and mass-loss rate in agreement with those observed for Betelgeuse.
 However. the effects of the Alfvénn-waves on the more dominant. cool outer atmosphere including the CO MOLsphere are not addressed.," However, the effects of the Alfvénn-waves on the more dominant, cool outer atmosphere including the CO MOLsphere are not addressed."
" The MHD simulations of Suzuki (2007)) for red giants show that the stellar winds are highly temporally variable and ""structured"". in which hot (2107 K) gas bubbles are embedded in cool («2000 K) gas (see. however. Alrapetian et al."," The MHD simulations of Suzuki \cite{suzuki07}) ) for red giants show that the stellar winds are highly temporally variable and “structured”, in which hot $\ga \! 10^4$ K) gas bubbles are embedded in cool $\sim$ 2000 K) gas (see, however, Airapetian et al."
 2010. for critical discussion)., \cite{airapetian10} for critical discussion).
 The radial velocity within ~10 aalso shows significant time variations from ~+40 ((outward motions) to —40 (inward motions)., The radial velocity within $\sim$ 10 also shows significant time variations from $\sim \! +40$ (outward motions) to $\sim \! -40$ (inward motions).
 This is compatible to the change in the velocity field detected by our AMBER observations., This is compatible to the change in the velocity field detected by our AMBER observations.
 However. the simulations of Suzuki (2007)) were carried out for red giant stars. which are much less luminous (€10° Lo)) compared to Betelgeuse (1.3x10°Lo.. Harper et al. 2008)).," However, the simulations of Suzuki \cite{suzuki07}) ) were carried out for red giant stars, which are much less luminous $\la \! 10^3$ ) compared to Betelgeuse $1.3 \times 10^5$, Harper et al. \cite{harper08}) )."
 Extending the MHD simulations of Suzuki (2007)) for more luminous stars. as well as the inclusion of thecool molecular component in the work of Airapetian et al. (2000)).," Extending the MHD simulations of Suzuki \cite{suzuki07}) ) for more luminous stars, as well as the inclusion of thecool molecular component in the work of Airapetian et al. \cite{airapetian00}) ),"
 would be valuable for a comparison with the present and future AMBER observations., would be valuable for a comparison with the present and future AMBER observations.
 Lobel (2010)) infers that strong shock waves generated by convection in the photosphere that are propagating outward may carry the energy and momentum to accelerate the wind and heat the chromosphere., Lobel \cite{lobel10}) ) infers that strong shock waves generated by convection in the photosphere that are propagating outward may carry the energy and momentum to accelerate the wind and heat the chromosphere.
 The qualitative similarity between the inhomogeneous velocity field in the chromosphere and in the photosphere/MOLsphere may point toward this scenario., The qualitative similarity between the inhomogeneous velocity field in the chromosphere and in the photosphere/MOLsphere may point toward this scenario.
 However. obviously. it is indispensable to map the dynamical structure of the cool outer atmosphere at various radii to clarity the driving mechanism of mass outflows in RSGs.," However, obviously, it is indispensable to map the dynamical structure of the cool outer atmosphere at various radii to clarify the driving mechanism of mass outflows in RSGs."
 We have succeeded. for the first time. in. one-dimensional aperture synthesis imaging of Betelgeuse in the individual CO first overtone lines. as well as in the continuum approximately free from molecular/atomic lines. with a spatial resolution of 9.8 mas and a spectral resolution of 6000 using VLTI/AMBER.," We have succeeded, for the first time, in one-dimensional aperture synthesis imaging of Betelgeuse in the individual CO first overtone lines, as well as in the continuum approximately free from molecular/atomic lines, with a spatial resolution of 9.8 mas and a spectral resolution of 6000 using VLTI/AMBER."
 The one-dimensional projection images in the CO lines reconstructed with the self-calibration technique. which restores the complex visibility using differential phase measurements. reveal that the star appears different within the individual CO lines.," The one-dimensional projection images in the CO lines reconstructed with the self-calibration technique, which restores the complex visibility using differential phase measurements, reveal that the star appears different within the individual CO lines."
" The one-dimensional projection images in the blue wing and line center show a pronounced exteded component up to 1.3R,.. while the images in the red wing follow that in the continuum without an extended component."," The one-dimensional projection images in the blue wing and line center show a pronounced extended component up to 1.3, while the images in the red wing follow that in the continuum without an extended component."
 Our image reconstruction represents the first study to image the so-called MOLsphere of an RSG in the individual CO first overtone lines., Our image reconstruction represents the first study to image the so-called MOLsphere of an RSG in the individual CO first overtone lines.
 Our modeling suggests that the dynamics in the photosphere and MOLsphere in 2009 ts characterized by strong downdrafts with 20-30 aand slight outward motions with 0—5s7!., Our modeling suggests that the dynamics in the photosphere and MOLsphere in 2009 is characterized by strong downdrafts with 20–30 and slight outward motions with 0–5.
. This indicates a drastic change in the velocity field within one year from 2008. when the dynamics was characterized by both upwelling and downdrafting components with 10-15 s'..," This indicates a drastic change in the velocity field within one year from 2008, when the dynamics was characterized by both upwelling and downdrafting components with 10–15 ."
Table 4 also compares these limits on the ccolumn density with values for the column densities of a variety of molecules previously observed toward the various features in our earlier work.,Table \ref{tab:coldens} also compares these limits on the column density with values for the column densities of a variety of molecules previously observed toward the various features in our earlier work.
 To compare with dark cloud values. the right-most column ofTable 4+ gives the abundances of the various species seen in TMC-I1.," To compare with dark cloud values, the right-most column ofTable \ref{tab:coldens} gives the abundances of the various species seen in TMC-1."
 Our upper limits on the ccolumn density are in all cases quite low compared to those of the other species shown in Table 4.. and are generally at or modestly below the abundance ratios seen in TMC-1. especially toward 3C111.," Our upper limits on the column density are in all cases quite low compared to those of the other species shown in Table \ref{tab:coldens}, and are generally at or modestly below the abundance ratios seen in TMC-1, especially toward 3C111."
 For instance N(CCH;OH)J/CS « 0.2. 0.1. and 0.13 forLac.. NRAO150. and 3C111. respectively. compared with a value 0.2 toward TMC-I.," For instance )/CS $<$ 0.2, 0.1, and 0.13 for, NRAO150, and 3C111, respectively, compared with a value 0.2 toward TMC-1."
 As noted in Section 3. the upper limits on the line profile integral of HC3N absorption in. Table 3 were converted to column density for inclusion in Table 4 using N(HC5N) =104em [τάν. following the excitation calculations shown in Fig.," As noted in Section 3, the upper limits on the line profile integral of $_5$ N absorption in Table 3 were converted to column density for inclusion in Table 4 using $_5$ N) $= 10^{14} \pcc \int \tau dv$ , following the excitation calculations shown in Fig."
 I., 1.
 The HCN/HCSN ratio. approximately 7 in TMC-I. is at least 3-10 times higher than this toward B2200 and B04154379.," The $_5$ N ratio, approximately 7 in TMC-1, is at least 3-10 times higher than this toward B2200 and B0415+379."
 Table 4 serves as a summary of our absorption line chemistry work to date. for sightlines and clouds with somewhat higher column density N(HCO7)) >1015em which have the richest chemistry.," Table \ref{tab:coldens} serves as a summary of our absorption line chemistry work to date, for sightlines and clouds with somewhat higher column density ) $> 10^{12}\pcc$ which have the richest chemistry."
 These patterns are not universal: the abundances of CO and all other detected species listed beneath tin the table increase dramatically with respect to ffor NCHCO7)) 210)”. as shown for instance in Fig.," These patterns are not universal: the abundances of CO and all other detected species listed beneath in the table increase dramatically with respect to for ) $ \ga 10^{12}$, as shown for instance in Fig."
 3 of Liszt (2001)., 3 of \cite{LisLuc01}.
". CO. which is found in nearly all features identified inHCO.. even at N(HCO)) «10"". is a special case. varying widely due to the influence of photodissocation and self-shielding (Liszt.2007)."," CO, which is found in nearly all features identified in, even at ) $ < 10^{12}$, is a special case, varying widely due to the influence of photodissocation and self-shielding \citep{Lis07CO} ."
 It cài however be understood as the electron recombination product of wwhen N(HCO7))/N(H2)) =2x107°. as observed (ibid).," It can however be understood as the electron recombination product of when ) $= 2\times 10^{-9}$, as observed )."
 Despite the overall similarity in relative abundances of many species with the TMC-1 patterns. some differences with TMC-1 are also apparent. even beyond the absence of aand HCsN. In particular. the low HNC/HCN ratio in diffuse clouds is characteristic of warmer gas. consistent with the observed rratio (Liszt&Lucas.2001:Lisztetal..2004).," Despite the overall similarity in relative abundances of many species with the TMC-1 patterns, some differences with TMC-1 are also apparent, even beyond the absence of and $_5$ N. In particular, the low HNC/HCN ratio in diffuse clouds is characteristic of warmer gas, consistent with the observed ratio \citep{LisLuc01,LisBla+04}."
. The HCN/HNC and rratios are important clues to the diffuse nature of the host gas., The HCN/HNC and ratios are important clues to the diffuse nature of the host gas.
 Previous indications that diffuse gas was being observed were the low reddening (0.32 mag) known to exist toward B2200—-420 (BL Lac). the weakness of mm-wave emission from species other than CO — only us detected (Liszt&Lucas.1994:LucasLiszt.1996) — and finding that N(OH) and N(CO) were comparable to the column densities observed in uv absorption toward aand some other bright stars.," Previous indications that diffuse gas was being observed were the low reddening (0.32 mag) known to exist toward B2200+420 (BL Lac), the weakness of mm-wave emission from species other than CO – only is detected \citep{LisLuc94,LucLis96} – and finding that N(OH) and N(CO) were comparable to the column densities observed in $uv$ absorption toward and some other bright stars."
 The general properties of diffuse gas are summarized by Snow&McCall(2006)., The general properties of diffuse gas are summarized by \cite{SnoMcC06}.
. In the context of our work. the kinetic temperature and the density and thermal partial pressure of aare indicated in various ways by the chemistry. fractionation and rotational excitation of CO (Liszt&Lucas.1998:2007).. and are typical of the diffuse ISM.," In the context of our work, the kinetic temperature and the density and thermal partial pressure of are indicated in various ways by the chemistry, fractionation and rotational excitation of CO \citep{LisLuc98,Lis07CO}, and are typical of the diffuse ISM."
 The partial thermal pressures Tk»|-5x107em K are comparable to those derived for the bulk of the gas from C I fine-structure excitation seen in wy absorption (Jenkins&Tripp.2001). NCOCO), The partial thermal pressures $\approx 1-5\times10^3 \pccc$ K are comparable to those derived for the bulk of the gas from C I fine-structure excitation seen in $uv$ absorption \citep{JenTri01}. )
»y/N(C?CO)) ratios may be as low as 15-20 in clouds with N(CO) €1016πι”. from which it may be inferred that the kinetic temperature of lines of sight like those summarized in Table 4 is 25 - 50 K. somewhat below the mean kinetic temperature inferred from obsevation of litself (70-80 K. see Rachfordetal.(2002))) but consistent with formation and rotational excitation of CO. at n(H2) =100cm™.," ratios may be as low as 15-20 in clouds with N(CO) $\la 10^{16}\pcc$, from which it may be inferred that the kinetic temperature of lines of sight like those summarized in Table 4 is 25 - 50 K, somewhat below the mean kinetic temperature inferred from obsevation of itself (70-80 K, see \cite{RacSno+02}) ) but consistent with formation and rotational excitation of CO at ) $\approx 100 \pccc$."
 The very weak mm-wave emission of optically-thick is consistent with such Π(Η1) if n(e/n(H»)) =4x104 as expectedfor diffuse gas in which only a small fraction |— 5%)) of the free gas-phase carbon resides in CO and the rest is in the form ofC., The very weak mm-wave emission of optically-thick is consistent with such ) if ) $\approx 4\times10^{-4}$ as expectedfor diffuse gas in which only a small fraction $\la 1-5$ ) of the free gas-phase carbon resides in CO and the rest is in the form of.
 Despite the consistency of these arguments. it is the case that no quiescent ion-molecule chemistry will reproduce the observed abundances at such low Π(Η2)).," Despite the consistency of these arguments, it is the case that no quiescent ion-molecule chemistry will reproduce the observed abundances at such low )."
 Some recent models of the diffuse cloud chemistry regard these conditions as a general background against which transient processes may operate (Falgaroneetal..2006:Smith 2004).. affecting the observed chemical abundance patterns without necessarily imprinting themselves observably on the internal degrees of freedom in the molecules themselves.," Some recent models of the diffuse cloud chemistry regard these conditions as a general background against which transient processes may operate \citep{FalPin+06,SmiPav+04}, , affecting the observed chemical abundance patterns without necessarily imprinting themselves observably on the internal degrees of freedom in the molecules themselves."
number of quasars contributing at each redshift interval is given in Col.,number of quasars contributing at each redshift interval is given in Col.
 4 of Table 1.., 4 of Table \ref{tab:cc_construct}.
" As evident from Fig. 12,,"," As evident from Fig. \ref{fig:rqrl_ciii},"
 the form of the emission line complex differs between the master- and FD-quasar-templates., the form of the emission line complex differs between the master- and FD-quasar-templates.
" The size of the empirical transformations necessary to bring the FD-quasar redshift estimates onto the reference system, in which the emission line centroid does not vary, with either redshift or absolute magnitude, are significantly reduced compared to the quasar population as a whole."," The size of the empirical transformations necessary to bring the FD-quasar redshift estimates onto the reference system, in which the emission line centroid does not vary, with either redshift or absolute magnitude, are significantly reduced compared to the quasar population as a whole."
" For redshifts 11l<z<2.1 a reduction of Az/(1+ z)=1.42x10~* in the redshifts, independent of redshift and absolute magnitude, is necessary."," For redshifts $\le$$z$$<$ 2.1 a reduction of $\Delta
z/(1+z)$ $\times$ $^{-4}$ in the redshifts, independent of redshift and absolute magnitude, is necessary."
" For redshifts an absolute magnitude dependent correction of 4.19x ?, in the opposite sense to that for the master template, is required, i.e. for bright quasars the redshifts arereduced."," For redshifts an absolute magnitude dependent correction of $\times$ $^{-5}$, in the opposite sense to that for the master template, is required, i.e. for bright quasars the redshifts are."
" However, given the 4 mmag dynamicεο range of the quasar sample, the maximum correction for any quasar is Az/(1+ z)S10~*."," However, given the $\simeq$ mag dynamic range of the quasar sample, the maximum correction for any quasar is $\Delta z/(1+z)$$\la$ $^{-4}$."
" For the small number of quasars where it is necessary to employ the emission line, the redshifts require a correction with slope 3.44x 10, in the IV.same sense as the larger correction necessary for the master template, i.e. for bright quasars the redshifts areincreased (Fig. 9))."," For the small number of quasars where it is necessary to employ the emission line, the redshifts require a correction with slope $\times$ $^{-4}$, in the same sense as the larger correction necessary for the master template, i.e. for bright quasars the redshifts are (Fig. \ref{ciii_civ_raw}) )."
 Table 4 includes redshifts and error estimates for 6665 quasars., Table \ref{tab:cat} includes redshifts and error estimates for 665 quasars.
 Col., Col.
" 1: is the SDSS coordinate object name, taken from the SDSS DR7 Legacy Release whenever available."," 1: is the SDSS coordinate object name, taken from the SDSS DR7 Legacy Release whenever available."
 Cols., Cols.
 2 and 3 give the object J2000 right ascension and declination in decimal degrees., 2 and 3 give the object J2000 right ascension and declination in decimal degrees.
 The redshift and redshift error are given in Cols., The redshift and redshift error are given in Cols.
 4 and 5 respectively., 4 and 5 respectively.
 Col., Col.
" 6 provides a code specifying the FIRST-detection (FD) status of the quasar (-1: not detected, 0: outside FIRST footprint, 1: detected)."," 6 provides a code specifying the FIRST-detection (FD) status of the quasar (–1: not detected, 0: outside FIRST footprint, 1: detected)."
 Col., Col.
" 7, alternate redshift for quasars with Col."," 7, alternate redshift for quasars with Col."
 6 detection code =0 (derived using the FD-quasar template) and =1 (derived using the master quasar template)., 6 detection code =0 (derived using the FD-quasar template) and =1 (derived using the master quasar template).
 The alternate redshift is assigned a value of '-999.0' for quasars with Col., The alternate redshift is assigned a value of `–999.0' for quasars with Col.
 6 detection code —-1., 6 detection code =–1.
 Col., Col.
" 8 specifies the origin of the redshift estimate via a numerical code (1:,, 2:,, 3:,, 4:,, 5:,, 6: 7: SDSS)."," 8 specifies the origin of the redshift estimate via a numerical code (1:, 2:, 3:, 4:, 5:, 6: cc, 7: SDSS)."
" The SDSS spectrumcc from which the Iv.redshiftcc estimate ccc,is derived is specified via the spectroscopic plate number.", The SDSS spectrum from which the redshift estimate is derived is specified via the spectroscopic plate number.
 modified Julian date of observation and fibre number in Cols., modified Julian date of observation and fibre number in Cols.
" 9, 10 and 11 respectively."," 9, 10 and 11 respectively."
" The redshifts are given to six decimal places but, as evident from the size of the associated errors, the accuracy for individual objects is two orders of magnitude larger."," The redshifts are given to six decimal places but, as evident from the size of the associated errors, the accuracy for individual objects is two orders of magnitude larger."
 The high level of precision is retained to avoid quantisation when comparing different redshift estimates specified to only four decimal places., The high level of precision is retained to avoid quantisation when comparing different redshift estimates specified to only four decimal places.
" The provision of alternate redshifts for FD-quasars and quasars whose FIRST detection status is unclear, allows the use of an appropriate redshift by researchers with particular definitions of ‘radio’-quasar subsamples and/or additional radio-observations for quasars outside the current FIRST footprint."," The provision of alternate redshifts for FD-quasars and quasars whose FIRST detection status is unclear, allows the use of an appropriate redshift by researchers with particular definitions of `radio'-quasar subsamples and/or additional radio-observations for quasars outside the current FIRST footprint."
 The primary (Col., The primary (Col.
 4) and alternate (Col., 4) and alternate (Col.
 7) redshifts differ only when the primary redshift is derived from cross-correlation (with one of the two quasar templates) and has a value z>1.1., 7) redshifts differ only when the primary redshift is derived from cross-correlation (with one of the two quasar templates) and has a value $z$$>$ 1.1.
" Two quasars, JJ134415.75+331719.1 and JJ142507.32+323137.4, exhibit distinctive double-peaked narrow emission."," Two quasars, J134415.75+331719.1 and J142507.32+323137.4, exhibit distinctive double-peaked narrow emission."
" In both cases, the redshift corresponding to the higher velocity system is included in the table."," In both cases, the redshift corresponding to the higher velocity system is included in the table."
 The majority of researchers will be interested in the combined redshift error (Col., The majority of researchers will be interested in the combined redshift error (Col.
 5) arising from the limited SNR of the SDSS spectra and intrinsic variation from quasar-to-quasar., 5) arising from the limited SNR of the SDSS spectra and intrinsic variation from quasar-to-quasar.
" However, the internal contribution can be recovered straightforwardly via use of the amplitude of the quasar-to-quasar errors listed in Table 3.."," However, the internal contribution can be recovered straightforwardly via use of the amplitude of the quasar-to-quasar errors listed in Table \ref{tab:z_error}."
 Table 5 presents the master quasar templates used to estimate the cross-correlation redshifts., Table \ref{tab:spec} presents the master quasar templates used to estimate the cross-correlation redshifts.
 Col., Col.
 1 lists the rest-frame wavelength (A))., 1 lists the rest-frame wavelength ).
 Cols., Cols.
" 2, and 3 include the relative flux (per unit wavelength) and the number of spectra contributing for the master template, while Cols."," 2, and 3 include the relative flux (per unit wavelength) and the number of spectra contributing for the master template, while Cols."
 4 and 5 provide the same information for the FD-quasar template., 4 and 5 provide the same information for the FD-quasar template.
 The FD-quasar template does not extend quite as far to the blue and the flux column contains entries of ‘999.0’ for wavelengths A<ΑΑ.., The FD-quasar template does not extend quite as far to the blue and the flux column contains entries of `–999.0' for wavelengths $\lambda$$<$.
" While the spectra should prove of use in the context of redshift estimation, the templates arenot suitable for studies of quasar spectral energy distributions, where care must be taken in defining the large-scale shape of such composite spectra."," While the spectra should prove of use in the context of redshift estimation, the templates are suitable for studies of quasar spectral energy distributions, where care must be taken in defining the large-scale shape of such composite spectra."
" The approach adopted in this paper to the question of deriving redshifts with a common zero-point over an extended dynamic range in redshift, and hence involving disjoint spectral wavelength coverage, differs from that normally employed."," The approach adopted in this paper to the question of deriving redshifts with a common zero-point over an extended dynamic range in redshift, and hence involving disjoint spectral wavelength coverage, differs from that normally employed."
 The majority of studies to date have focussed on the parameterisation of the rest-frame centroid differences between the strongest emission lines present in the quasar spectraexample)., The majority of studies to date have focussed on the parameterisation of the rest-frame centroid differences between the strongest emission lines present in the quasar spectra.
". Use of the cross-correlation redshifts directly, bypasses many of the difficulties associated in providing reliable, reproducible, parameterisations of low SNR, asymmetric, often blended, emission lines present on ‘continua’ that also show significant variation from quasar to quasar."," Use of the cross-correlation redshifts directly, bypasses many of the difficulties associated in providing reliable, reproducible, parameterisations of low SNR, asymmetric, often blended, emission lines present on `continua' that also show significant variation from quasar to quasar."
 The resultant quasar-to-quasar dispersion and the internal reproducibility of the new HW-redshifts represent significant improvements over even the most careful studies utilising individual emission features., The resultant quasar-to-quasar dispersion and the internal reproducibility of the new HW-redshifts represent significant improvements over even the most careful studies utilising individual emission features.
" Systematic, luminosity-dependent relative emission line shifts have not featured in many previous studies of the quasar population."," Systematic, luminosity-dependent relative emission line shifts have not featured in many previous studies of the quasar population."
" In part, the lack of such work may reflect the difficulty of performing such studies prior to the availability of the more recent SDSS Data Releases."," In part, the lack of such work may reflect the difficulty of performing such studies prior to the availability of the more recent SDSS Data Releases."
 An exception is the work of who find a clear relationship between emission line, An exception is the work of who find a clear relationship between emission line
simulations.,simulations.
 Fig., Fig.
" 8 demonstrates the simulated SNR evolution in a uniform ambient medium of temperature Το=10"" KK and electron density ne=0.01.cm?, appropriate for a region near the center of the spheroid."," \ref{F:SNejecta} demonstrates the simulated SNR evolution in a uniform ambient medium of temperature $T_0 = 10^7$ K and electron density $n_e = 0.01\, {\rm~cm^{-3}}$, appropriate for a region near the center of the spheroid."
 The core that encloses Mo reaches a size of ppc at the age of 104 years and increases only slightly after that., The core that encloses $\rm M_\odot$ reaches a size of pc at the age of $10^4$ years and increases only slightly after that.
 This is also roughly the time scale for the ejecta to be fully thermalized by the converging reverse shock., This is also roughly the time scale for the ejecta to be fully thermalized by the converging reverse shock.
" Then the core turns into a tenuous hot bubble, with a very low density and high temperature."," Then the core turns into a tenuous hot bubble, with a very low density and high temperature."
 Outside the iron core is an envelope of the rest of the SN ejecta (assumed to be 0.7M)., Outside the iron core is an envelope of the rest of the SN ejecta (assumed to be $_\odot$ ).
 The swept-up material can also be heated to more than 10° KK only initially by the strong forward blastwave; the averaged temperature of the swept-up material is considerably lower because of the quick weakening of the expanding blastwave and the adiabatic cooling of the SNR., The swept-up material can also be heated to more than $10^{8}$ K only initially by the strong forward blastwave; the averaged temperature of the swept-up material is considerably lower because of the quick weakening of the expanding blastwave and the adiabatic cooling of the SNR.
 The radiative cooling time scale (Fig. 9)), The radiative cooling time scale (Fig. \ref{F:snr_cooltime}) )
" for such an SNR is much too long to be important, compared to the outflow time of the hot gas from a spheroid (<107 yrs)."," for such an SNR is much too long to be important, compared to the outflow time of the hot gas from a spheroid $\lesssim 10^7$ yrs)."
" In particular, the X-ray emission from the ejecta is largely undetectable."," In particular, the X-ray emission from the ejecta is largely undetectable."
 We now consider additional processes that an SNR should experience in a spheroid., We now consider additional processes that an SNR should experience in a spheroid.
 One is the dilution due to mass injection from evolved stars (or evaporation of cloud-lets)., One is the dilution due to mass injection from evolved stars (or evaporation of cloud-lets).
" As the dilution takes place, ne increases while A,(T) drops."," As the dilution takes place, $n_e$ increases while $\Lambda_{_{\rm Fe}}(T)$ drops."
 The net result is that the cooling rate peaks when the iron abundance drops to ~100 solar (Brighenti&Mathews2005)., The net result is that the cooling rate peaks when the iron abundance drops to $\sim 100$ solar \citep{Brighenti2005}.
. Further dilution tends to decrease the cooling rate., Further dilution tends to decrease the cooling rate.
 Take the above 1-D SNR as an example., Take the above 1-D SNR as an example.
" It takes about MMyr for the SNR core to accumulate an additional 5.4 Mo, which dilutes the ejecta to an iron abundance of 100 solar, the value to avoid rapid radiative cooling (Brighenti&Mathews2005)."," It takes about Myr for the SNR core to accumulate an additional 5.4 $M_\odot$, which dilutes the ejecta to an iron abundance of 100 solar, the value to avoid rapid radiative cooling \citep{Brighenti2005}."
". In comparison, the time for the SNR to flow this radius to kkpc is about MMyr."," In comparison, the time for the SNR to flow this radius to kpc is about Myr."
" Thus the dilution is important, although the core should still have a high iron abundance when being transported out of the spheroid."," Thus the dilution is important, although the core should still have a high iron abundance when being transported out of the spheroid."
 Another process is the mixing of the iron ejecta with the ambient medium., Another process is the mixing of the iron ejecta with the ambient medium.
 The density, The density
"mass accretion history of our haloes, so our sample can be considered a reasonably unbiased representation of 10?M. haloes in the MS-II.","mass accretion history of our haloes, so our sample can be considered a reasonably unbiased representation of $10^{10}\Ms$ haloes in the MS-II."
" The high-resolution simulations presented here have been performed using the Tree-PM code (??), which includes gravity and smoothed particle hydrodynamics."," The high-resolution simulations presented here have been performed using the Tree-PM code \citep{Springel-2005,
 Springel-2008}, which includes gravity and smoothed particle hydrodynamics."
" As an extension, metal-dependent cooling, star formation, chemical enrichment and energy injection from type II and type Ia supernovae have been implemented in the multiphase gas model of ??.."," As an extension, metal-dependent cooling, star formation, chemical enrichment and energy injection from type II and type Ia supernovae have been implemented in the multiphase gas model of \cite{Scannapieco-2005, Scannapieco-2006}."
" This model has previously been used to study the formation both of large disk galaxies (??),, and of dwarf spheroidal galaxies (?).."," This model has previously been used to study the formation both of large disk galaxies \citep{Scannapieco-2008, Scannapieco-2009}, and of dwarf spheroidal galaxies \citep{Sawala-2010}."
" In Sections ?? to 4.5,, we briefly explain the most important characteristics of this code, and refer the interested reader to the above references for a more detailed description."," In Sections \ref{sec:methods:softening} to \ref{sec:ism}, we briefly explain the most important characteristics of this code, and refer the interested reader to the above references for a more detailed description."
" In order to reduce two-body interactions arising from the particle representation of the matter distribution, the gravitational potential is modified by replacing the divergent 1/r? dependence with 1/(r?+e?), where c is the gravitational softening scale (?).."," In order to reduce two-body interactions arising from the particle representation of the matter distribution, the gravitational potential is modified by replacing the divergent $1/r^{2}$ dependence with $1/(r^2 +\epsilon^2)$, where $\epsilon$ is the gravitational softening scale \citep{Aarseth-1963}."
" The choice of e represents a compromise between the errors due to residual two-body effects, and the loss of spatial resolution below several softening scales."," The choice of $\epsilon$ represents a compromise between the errors due to residual two-body effects, and the loss of spatial resolution below several softening scales."
" We begin our simulations with a softening length fixed in comoving coordinates to 1/10th of the mean interparticle spacing for each particle type, corresponding to ~111 kpc in the high resolution region."," We begin our simulations with a softening length fixed in comoving coordinates to $1/10$ th of the mean interparticle spacing for each particle type, corresponding to $\sim1$ $^{-1}$ kpc in the high resolution region."
" After the collapse of the halo, we keep the softening scale in this region constant in physical coordinates from z—7, at a value of 155 pc."," After the collapse of the halo, we keep the softening scale in this region constant in physical coordinates from $z=7$, at a value of 155 pc."
" ? give a lower limit €ace=r200//Na2oo to prevent strong discreteness effects in haloes, which corresponds to 140 pc for a 10'°Mo object resolved with Nooo~10° particles."," \cite{Power-2003} give a lower limit $\epsilon_{acc} = r_{200}/\sqrt{N_{200}}$ to prevent strong discreteness effects in haloes, which corresponds to $\sim140$ pc for a $10^{10}\Ms$ object resolved with $N_{200}\sim 10^5$ particles."
" We also resimulated one of our haloes, Halo 4, with a physicalsoftening scale of 77.5 pc, and checked that this did not alter the results significantly."," We also resimulated one of our haloes, Halo 4, with a physicalsoftening scale of 77.5 pc, and checked that this did not alter the results significantly."
" Above the hydrogen ionisation temperature of 104 K, our gas cooling model is based on metal-dependent cooling functions of ?.."," Above the hydrogen ionisation temperature of $10^4$ K, our gas cooling model is based on metal-dependent cooling functions of \cite{Sutherland-1993}."
" The model assumes collisional excitation equilibrium, and does not include metal or molecular cooling below 10*K. In addition, we include Compton cooling, which is the main coolant at high redshift."," The model assumes collisional excitation equilibrium, and does not include metal or molecular cooling below $10^4$ K. In addition, we include Compton cooling, which is the main coolant at high redshift."
" It depends on the free electron density, as well as on the temperature difference between the gas and the evolving CMB."," It depends on the free electron density, as well as on the temperature difference between the gas and the evolving CMB."
" For this purpose, the ionisation states of H, He, and the free electron number density are computed analytically, following the model of ?.."," For this purpose, the ionisation states of H, He, and the free electron number density are computed analytically, following the model of \cite{Katz-1996}."
" We have included UV background radiation in our model, which adds a heating term to the net cooling function of the partially ionised gas."," We have included UV background radiation in our model, which adds a heating term to the net cooling function of the partially ionised gas."
" In all simulations, the UV background is present from z=6, and its spectral energy distribution and the time evolution of its intensity follow the model of ?.."," In all simulations, the UV background is present from $z=6$, and its spectral energy distribution and the time evolution of its intensity follow the model of \cite{Haardt-1996}."
" A test simulation of Halo 4 without the UV background produced over twice as many stars by z=1, compared to the simulation which includes UV radiation."," A test simulation of Halo 4 without the UV background produced over twice as many stars by $z=1$, compared to the simulation which includes UV radiation."
" Cold gas particles can spawn, or be converted into, star particles, subject to certain conditions."," Cold gas particles can spawn, or be converted into, star particles, subject to certain conditions."
 We require the gas particle to be in a region of convergent flow., We require the gas particle to be in a region of convergent flow.
" In addition, we impose a physical density threshold ρε on the local gas density."," In addition, we impose a physical density threshold $\rho_c$ on the local gas density."
 The existence of a threshold for star formation is motivated by observations (e.g.??)..," The existence of a threshold for star formation is motivated by observations \citep[e.g.][]{Kennicutt-1989, Kennicutt-1998}."
" Calculations by ? as well as numerical simulations, e.g. by ??? and others have shown that the observed Kennicutt-Schmidt relation can be reproduced in disk galaxies by imposing a volume density threshold, even though different values are assumed."," Calculations by \cite{Quirk-1972} as well as numerical simulations, e.g. by \cite{Katz-1996, Springel-2003, Bush-2008} and others have shown that the observed Kennicutt-Schmidt relation can be reproduced in disk galaxies by imposing a volume density threshold, even though different values are assumed."
" ? demonstrated with high-resolution simulations of the turbulent interstellar medium that the star formation rate depends only weakly on the choice of ρε, and values in the range 0.1 cm? (?) to 100 cm? (?) can be found in the recent literature."," \cite{Koyama-2009} demonstrated with high-resolution simulations of the turbulent interstellar medium that the star formation rate depends only weakly on the choice of $\rho_c$ , and values in the range 0.1 $^{-3}$ \citep{Stinson-2009} to 100 $^{-3}$ \citep{Governato-2010} can be found in the recent literature."
 7 reported better convergence in their, \citeauthor{Governato-2010} reported better convergence in their
redshifts.,redshifts.
" To illustrate this, and to facilitate future comparisons, we summarize our best estimation of the minor merger fraction for r?*=30h7!,50h7', and 100h7! kpc in Table 4,, and show the minor, major and total (major + minor) merger fractions for ry""=100! kpc in Fig. 5.."," To illustrate this, and to facilitate future comparisons, we summarize our best estimation of the minor merger fraction for $r_{\rm p}^{\rm max} = 30h^{-1}, 50h^{-1}$, and $100h^{-1}$ kpc in Table \ref{ffmmtab}, and show the minor, major and total (major + minor) merger fractions for $r_{\rm p}^{\rm max} = 100h^{-1}$ kpc in Fig. \ref{ffmmfig}."
 The typical error in the minor merger fraction is ~30—40%., The typical error in the minor merger fraction is $\sim30-40$.
. Our measurements seem to indicate that the minor merger fraction increases with cosmic time., Our measurements seem to indicate that the minor merger fraction increases with cosmic time.
" This trend becomes more robust when we further compare our results to a local (z~ 0.1) estimation of the minor merger fraction, Sect. ??.."," This trend becomes more robust when we further compare our results to a local $z \sim 0.1$ ) estimation of the minor merger fraction, Sect. \ref{ffmmevol}."
 In this section we study the merger fraction as a function of the blue or red colour of the principal galaxy in the pair., In this section we study the merger fraction as a function of the blue or red colour of the principal galaxy in the pair.
" To split our ΜΕx—20 galaxies into red and blue, we study their distribution in the Mwuv—M, versus M,—M; plane."," To split our $M_B^{\rm e} \leq -20$ galaxies into red and blue, we study their distribution in the $M_{NUV} - M_{r}$ versus $M_{r} - M_{J}$ plane."
" The UV — optical colours is a better tracer of recent star formation than typical optical — optical colours(????),, while the addition of an optical — infrared colour to the UV — optical helps to break the degeneracy between old and dusty star-forming (SF) red galaxies(??)."," The UV – optical colours is a better tracer of recent star formation than typical optical – optical colours, while the addition of an optical – infrared colour to the UV – optical helps to break the degeneracy between old and dusty star-forming (SF) red galaxies."
. Another possibility to separate old and dusty red galaxies is to perform a dust reddening correction., Another possibility to separate old and dusty red galaxies is to perform a dust reddening correction.
" This also makes possible a clean separation between the red quiescent sequence and the blue star-forming cloud, since the ""green valley"" region between both sequences is mainly populated by "," This also makes possible a clean separation between the red quiescent sequence and the blue star-forming cloud, since the ""green valley"" region between both sequences is mainly populated by dusty SF galaxies ."
"In Fig. 6,,"," In Fig. \ref{nuvrjtotfig}, ,"
" we show the number density contours of M5xgalaxies in the Μνυν—M, versus M,—M; plane for the two redshifts ranges under study, ζει=[0.2,0.65) and Z2=[0.65,0.95)."," we show the number density contours of $M_B^{\rm e} \leq -20$galaxies in the $M_{NUV} - M_{r}$ versus $M_{r} - M_{J}$ plane for the two redshifts ranges under study, $z_{\rm r,1} = [0.2,0.65)$ and $z_{\rm r,2} = [0.65,0.95)$."
 We only show those galaxies detected in the K band to avoid that M; was an extrapolation from the fit to the optical photometry., We only show those galaxies detected in the $K$ band to avoid that $M_{J}$ was an extrapolation from the fit to the optical photometry.
" We find a red sequence and a blue cloud in both redshift ranges, as expected from previousworks ??).."," We find a red sequence and a blue cloud in both redshift ranges, as expected from previousworks ."
 Both populations are well separated using aconstant, Both populations are well separated using aconstant
Total yields of copper from massive stars by Matteucci et al. (,Total yields of copper from massive stars by Matteucci et al. (
1993. squares) and Nomoto et al. (,"1993, squares) and Nomoto et al. ("
2007. dots). comprising both the weak component and the explosive one. are shown and compared one another in Fig. 3..,"2007, dots), comprising both the weak component and the explosive one, are shown and compared one another in Fig. \ref{fig:yields},"
 for solar metallicity stars (upper panel) and zero metallicity objects (lower panel)., for solar metallicity stars (upper panel) and zero metallicity objects (lower panel).
 At Z = 0. the yields reflect the pure explosive contribution.," At $Z$ = 0, the yields reflect the pure explosive contribution."
 It is seen that. while the explosive yields adopted by Matteucci et al. (," It is seen that, while the explosive yields adopted by Matteucci et al. ("
1993) do not vary with the initial mass of the star. those computed by Nomoto et al. (,"1993) do not vary with the initial mass of the star, those computed by Nomoto et al. ("
2007) vary steeply as a function of mass. especially for Mi;7 20M...,"2007) vary steeply as a function of mass, especially for $M_{\mathrm{ini}} >$ 20 $_\odot$."
 Models where most of solar Cu comes from SNIa explosions ollowing the prescriptions of Matteucci et al. (, Models where most of solar Cu comes from SNIa explosions following the prescriptions of Matteucci et al. (
1993) match very well the observational data for solar neighbourhood stars (see Fig. l..,"1993) match very well the observational data for solar neighbourhood stars (see Fig. \ref{fig:cop1},"
 left panel. thick long-dashed line). but leave the lower Cw/Fe] ratios in wCCen totally unexplained (see Fig. |..," left panel, thick long-dashed line), but leave the lower [Cu/Fe] ratios in $\omega$ Cen totally unexplained (see Fig. \ref{fig:cop1},"
 right xinel. thin long-dashed line).," right panel, thin long-dashed line)."
 When reducing the contribution from SNela according to the results of Iwamoto et al. (, When reducing the contribution from SNeIa according to the results of Iwamoto et al. (
1999). a better agreement with the relation observed for a CCen. members is ound (except. perhaps. for the two objects lying at the highest metallicities — Fig. |.,"1999), a better agreement with the relation observed for $\omega$ Cen members is found (except, perhaps, for the two objects lying at the highest metallicities – Fig. \ref{fig:cop1},"
 right panel. thin short-dashed line). but the agreement with the solar neighbourhood data at [Fe/H] > 10 is completely destroyed (Fig. |..," right panel, thin short-dashed line), but the agreement with the solar neighbourhood data at [Fe/H] $> -$ 1.0 is completely destroyed (Fig. \ref{fig:cop1},"
 left panel. thick short-dashed line).," left panel, thick short-dashed line)."
 If. instead. most of solar Cu is produced through the weak s-pprocess in massive stars. both the solar neighbourhood and," If, instead, most of solar Cu is produced through the weak process in massive stars, both the solar neighbourhood and"
of the Coma cluster of salaxies lnuainDodyCitationEndA.,of the Coma cluster of galaxies .
..252..528C.. There. the probable source of the radio plasma is visible: it is the ealaxy NCC 1789. which is located upstream of the relie. aud which secs to be onu au ascending orbit after a cluster core passage (?).," There, the probable source of the radio plasma is visible: it is the galaxy NGC 4789, which is located upstream of the relic, and which seems to be on an ascending orbit after a cluster core passage ."
. Its narrow angle tailed radio outflow 4789 seclus to be bent aud drageedao by the iufalliug matter (falling iuto Comas gravitational potential) to the location of the relic., Its narrow angle tailed radio outflow – – seems to be bent and dragged by the infalling matter (falling into Coma's gravitational potential) to the location of the relic.
 There. it brightens up aud exhibits a steep but straight spectrun with a slope of 1.18.," There, it brightens up and exhibits a steep but straight spectrum with a slope of $1.18$."
 For details of the spectrtim aud the geometry. see Cüovaunuini et al.," For details of the spectrum and the geometry, see Giovannini et al."
 aud Euflin et al., and lin et al.
(2).. We follow a blob of the radio plasima. which welt have been injected with au overpressure of a factor 10 into the infalling gas stream with possibly s;=0.3410Fem5m and AT=0.6keV.," We follow a blob of the radio plasma, which might have been injected with an overpressure of a factor 10 into the infalling gas stream with possibly $n_{\rm e} = 0.3\cdot 10^{-5}\,{\rm cm^{-3}}$ and $kT = 0.6\, {\rm
keV}$."
 The inflow of the plasina and the compression at the cluster accretion shock wave might have taken a few hundreds of Myr., The inflow of the plasma and the compression at the cluster accretion shock wave might have taken a few hundreds of Myr.
" We απο a pressure juup of only P,/P»=10 at the shock wave. not higher. in order to allow the temperature of the post-slock gas to stay below the average cluster temperature of 8.2 keV(?).. As can be seen in Fie. L."," We assume a pressure jump of only $P_3/P_2 = 40$ at the shock wave, not higher, in order to allow the temperature of the post-shock gas to stay below the average cluster temperature of 8.2 keV. As can be seen in Fig. \ref{fig:syncC},"
 the radio spectrum below 1 CGIIz stavs practically iubent for a couple of tens of Myr after the shock passage., the radio spectrum below 1 GHz stays practically unbent for a couple of tens of Myr after the shock passage.
 We have argued here that adiabatic compression 1u cluster shocks can revive fossil radio plasma to radio detection. even up to 2 Cir after its release from the parent radio galaxy.," We have argued here that adiabatic compression in cluster shocks can revive fossil radio plasma to radio detection, even up to 2 Gyr after its release from the parent radio galaxy."
 The computed radio spectra provide a good match to the observed spectra of cluster radio relics., The computed radio spectra provide a good match to the observed spectra of cluster radio relics.
 Hence. this is a promising model for the regions of diffuse radio enission found in clusters of galaxies.," Hence, this is a promising model for the regions of diffuse radio emission found in clusters of galaxies."
 Below. We παΊο sone merits aud potential shortcoming of this," Below, we summarize some merits and potential shortcoming of this"
to determine the fraction of CW events within 200 Mpc that would be detected by an optical survey with a eiven liuiting magnitude aud cadeuce.,to determine the fraction of GW events within 200 Mpc that would be detected by an optical survey with a given limiting magnitude and cadence.
 For targeted follow-up searches we use a I-dav cadeuce with laniting magnitudes of 22 (PTF). 23.5 (Pan-STARRS). aud 26.5 (LSSTY: we also include a Ἱ-ααν aud [day cadeuce with the standard LSST depth of 21.7 mae.," For targeted follow-up searches we use a 1-day cadence with limiting magnitudes of 22 (PTF), 23.5 (Pan-STARRS), and 26.5 (LSST); we also include a 1-day and 4-day cadence with the standard LSST depth of 24.7 mag."
 The results. sunuuarized iu Table 2.. show that if the jet eunergv aud cicunburst deusity are similar to those required to explain the axis SCRB data (Figure 3)). then eveuts with Ooi. are sufficiently bright to bo detected i at least 3 20;epochs. given a survey with a depth similar to the standard LSST suvwev (217 imag) but with a faster cadence of  d. Shallower searches are also capable of detecting energetic1 afterelows in a few epochs. but this nav not be sufficient for a clear identification.," The results, summarized in Table \ref{tab:afterglow}, show that if the jet energy and circumburst density are similar to those required to explain the on-axis SGRB data (Figure \ref{fig:onaxis}) ), then events with $\theta_{\rm obs}\lesssim 2\theta_j$ are sufficiently bright to be detected in at least 3--5 epochs, given a survey with a depth similar to the standard LSST survey $24.7$ mag), but with a faster cadence of $\sim 1$ d. Shallower searches are also capable of detecting energetic afterglows in a few epochs, but this may not be sufficient for a clear identification."
 By contrast. m most cases events viewed at larecr angles (uusm 20i) are not detectable. even near peak emission with LSST.," By contrast, in most cases events viewed at larger angles $\theta_{\rm obs}\gtrsim 2\theta_{\rm
j}$ ) are not detectable, even near peak emission with LSST."
 The same information is presented. eraphically in Figure 7 where we plot contours of detection fraction iu 3? and 5 epochs as a function of depth and caclence., The same information is presented graphically in Figure \ref{fig:agfrac} where we plot contours of detection fraction in 3 and 5 epochs as a function of depth and cadence.
 We find that in the czise of Ej~10? ere. the standard LSST cadence aud deph are sufficient for multiple detections.," We find that in the case of $E_{j}\sim 10^{50}$ erg, the standard LSST cadence and depth are sufficient for multiple detections."
 However. for lower energies (which may be typical of most SCIBDs). a aster cadence and ereater depth (~26.5 mae} are required for multiple detections.," However, for lower energies (which may be typical of most SGRBs), a faster cadence and greater depth $\sim 26.5$ mag) are required for multiple detections."
 To achieve a detection fractio iof 50% in 3(5) epochs for the case of Oo.=20; requires a depth of at least 23.5(26) mae for a l-dav cadence., To achieve a detection fraction of $50\%$ in 3(5) epochs for the case of $\theta_{\rm obs}=2\theta_j$ requires a depth of at least $23.5$ $26$ ) mag for a 1-day cadence.
 Since detectahe optical e1uission is Limited to off-axis angles of & we estimate the corresponding fraction of CAV events 20.wih potential optical afterglow detectious as where 6)< Lis the average opening angle. aud is the detection probability of eveuts with iuclinatiou angles between 0 aud 0|dO (ee... Schutz 2011: their," Since detectable optical emission is limited to off-axis angles of $\lesssim 2\theta_j$, we estimate the corresponding fraction of GW events with potential optical afterglow detections as: where $\bar{\theta}_{\rm j}\ll 1$ is the average opening angle, and is the detection probability of events with inclination angles between $\theta$ and $\theta+d\theta$ (e.g., Schutz 2011; their"
observations are comparable to the ones obtained with the Thomson limit assumption (ie. from the determination of the column density and the assumption that the material is not Thomson thick).,observations are comparable to the ones obtained with the Thomson limit assumption (i.e. from the determination of the column density and the assumption that the material is not Thomson thick).
 Those derived with the microcalorimeter are better only if the number of counts is high enough (i.e. for GRB050904)., Those derived with the microcalorimeter are better only if the number of counts is high enough (i.e. for GRB050904).
" As a best case we considered one of the brightest GRB observed by Swift, i.e. the naked-eye GRB080319B (Racusin et al."," As a best case we considered one of the brightest GRB observed by Swift, i.e. the naked-eye GRB080319B (Racusin et al."
 2008)., 2008).
" This burst is not unique rivaling the recent bright bursts discovered by Fermi in brightness (e.g. GRB080916C or GRB090323, Abdo et al."," This burst is not unique rivaling the recent bright bursts discovered by Fermi in brightness (e.g. GRB080916C or GRB090323, Abdo et al."
 2009)., 2009).
 GRB 080319B was observed by the Swift narrow field instruments 64 s after its discovery and its brightness made it possible to follow it continuously with the BAT and XRT instruments., GRB 080319B was observed by the Swift narrow field instruments 64 s after its discovery and its brightness made it possible to follow it continuously with the BAT and XRT instruments.
 This burst was relatively close (redshift z—0.94) and low absorbed (Ng=1.2x10?cm?)., This burst was relatively close (redshift $z=0.94$ ) and low absorbed $N_H=1.2\times 10^{21}\cmdue$ ).
 We consider a test-case with GRB080319B exploding at z=7 either with its observed column density or with an intrinsic column density of 1033cm~?., We consider a test-case with GRB080319B exploding at $z=7$ either with its observed column density or with an intrinsic column density of $10^{22}\cmdue$.
" Concerning the redshift determination, the low column density case is not favorable whereas the high column density case results in a very precise redshift location of the GRB (see Table 2)."," Concerning the redshift determination, the low column density case is not favorable whereas the high column density case results in a very precise redshift location of the GRB (see Table 2)."
" In fact, despite the large number of counts, if the column density is relatively low (NuS10?!cm?) it cannot imprint measurable signatures on the spectrum."," In fact, despite the large number of counts, if the column density is relatively low $N_H\lsim 10^{21}\cmdue$ ) it cannot imprint measurable signatures on the spectrum."
 The same occurs for the study of the metallicity., The same occurs for the study of the metallicity.
" We are able to set only loose limits on the metallicity in the low column density case, but still at least one order of magnitude better than the Thomson limit, and we are able to set tight limits on the metallicity (within a factor of 3 of the input value) in the case of high column density."," We are able to set only loose limits on the metallicity in the low column density case, but still at least one order of magnitude better than the Thomson limit, and we are able to set tight limits on the metallicity (within a factor of 3 of the input value) in the case of high column density."
" As a further note we point out that for very distant objects there is the possibility that a fraction or even all of the observed column density is not due to material within the GRB host galaxy, but comes from intervening system(s) (Campana et al."," As a further note we point out that for very distant objects there is the possibility that a fraction or even all of the observed column density is not due to material within the GRB host galaxy, but comes from intervening system(s) (Campana et al."
" 2006, 2009)."," 2006, 2009)."
 Based on quasar studies (Wolfe et al., Based on quasar studies (Wolfe et al.
 2005; Pérroux et al., 2005; Pérroux et al.
" 2003) we simulated for each of our bursts a distribution of line-of-sights (10,000 trials), evaluating the corresponding X-ray absorption at the GRB redshift scaling the intervening column density as it would be observed at the GRB redshift (i.e. as (1+z)?9, using the absorption energy dependence of Morrison McCammon 1983)."," 2003) we simulated for each of our bursts a distribution of line-of-sights (10,000 trials), evaluating the corresponding X–ray absorption at the GRB redshift scaling the intervening column density as it would be observed at the GRB redshift (i.e. as $(1+z)^{2.6}$, using the absorption energy dependence of Morrison McCammon 1983)."
 'This will provide a distribution of column densities for each GRB due to intervening systems only., This will provide a distribution of column densities for each GRB due to intervening systems only.
" It can be shown that for the three bursts under consideration the mode (50%) of this distribution is below the Ng observed value, but not the 9096 value."," It can be shown that for the three bursts under consideration the mode $50\%$ ) of this distribution is below the $N_H$ observed value, but not the $90\%$ value."
" In other words, there are line of sights where the contribution from the intervening systems dominate but they are a minority."," In other words, there are line of sights where the contribution from the intervening systems dominate but they are a minority."
 Additional evidence can be gathered to circumvent this problem such as studies of column density variability (see also below) or observations in the radio band from which one can probe the local density from optically thick synchrotron emission., Additional evidence can be gathered to circumvent this problem such as studies of column density variability (see also below) or observations in the radio band from which one can probe the local density from optically thick synchrotron emission.
" In the case of GRB050904, Frail et al. ("," In the case of GRB050904, Frail et al. ("
2006) estimated a very high local density (n~84—680 cm?) whereas for GRB090423 Chandra et al. (,2006) estimated a very high local density $n\sim 84-680$ $^{-3}$ ) whereas for GRB090423 Chandra et al. (
2009) estimated n~1 cm?.,2009) estimated $n\sim 1$ $^{-3}$.
 This might indicate a sizable contamination from intervening systems in the case of GRB090423., This might indicate a sizable contamination from intervening systems in the case of GRB090423.
 Robust evidence for a decrease with time of the X— absorbing column in GRB050904 was reported by several authors (Watson et al., Robust evidence for a decrease with time of the X--ray absorbing column in GRB050904 was reported by several authors (Watson et al.
 2006; Campana et al., 2006; Campana et al.
 2007; Cusumano et al., 2007; Cusumano et al.
 2007; Gendre et al., 2007; Gendre et al.
 2007)., 2007).
 Campana et al. (, Campana et al. (
"2007) modelled the evolution of the column density due to the flash ionization of the GRB and early afterglow photons, allowing constraints on the geometry of the absorbing cloud.","2007) modelled the evolution of the column density due to the flash ionization of the GRB and early afterglow photons, allowing constraints on the geometry of the absorbing cloud."
 This was done by dividing the X-ray light curve into four time bins and evaluating the absorbed spectrum with a cut-off power law model (see Campana et al., This was done by dividing the X–ray light curve into four time bins and evaluating the absorbed spectrum with a cut-off power law model (see Campana et al.
 2007 for more details)., 2007 for more details).
 A decrease of the column density indicates the presence of a sizable amount of matter close to the GRB site., A decrease of the column density indicates the presence of a sizable amount of matter close to the GRB site.
 We simulate also this case obtaining a factor of ~6 , We simulate also this case obtaining a factor of $\sim 6$ 
"(1995), the standard Poisson staüstical formulae cannot be used because the different events contribute to 7 with different weights.",", the standard Poisson statistical formulae cannot be used because the different events contribute to $\tau$ with different weights."
 Following Bennettetal.(1995) and Alcocketal.(19972).. L account for this with a Monte Carlo method.," Following \citet{dpb-md_dm} and \citet{macho-blg45}, I account for this with a Monte Carlo method."
" The number of expected events, .Vexp. is taken to be a variable, and we construct simulated event sets with n values drawn from the observed distribution. and determine what fracuon, /, of the simulated data sets has a 7 value that exceeds the measured value."," The number of expected events, $N_{\rm exp}$, is taken to be a variable, and we construct simulated event sets with $\that_{st}$ values drawn from the observed distribution, and determine what fraction, $f$, of the simulated data sets has a $\tau$ value that exceeds the measured value."
" If f=0.81 for à particular assumed ους value, then that particular Vox), value corresponds to the [--σ upper limit on 7. which is listed as the 0.8| confidence level in Table 7.."," If $f=0.84$ for a particular assumed $N_{\rm exp}$ value, then that particular $N_{\rm exp}$ value corresponds to the $\sigma$ upper limit on $\tau$ , which is listed as the $0.84$ confidence level in Table \ref{tab-taucl}."
" Each .N., can be converted to a microlensing opücal depth by τιωι=Nepτι. where the mean values of τι is assumed."," Each $N_{\rm exp}$ can be converted to a microlensing optical depth by $\tau_{\rm tot} = N_{\rm exp} \, \tau_1$, where the mean values of $\tau_1$ is assumed."
" The procedure described in the previous paragraph was used for the optical depth esümates in and AOO, but it must be modified here to include the event identification uncertainty."," The procedure described in the previous paragraph was used for the optical depth estimates in \citet{macho-lmc2} and A00, but it must be modified here to include the event identification uncertainty."
" First, the n distribution used for the Monte Carlo weights the unconfirmed event n with of the weight of the confirmed events."," First, the $\that_{st}$ distribution used for the Monte Carlo weights the unconfirmed event $\that_{st}$ with of the weight of the confirmed events."
" Then, the comparison to the observed 7 value uses not the most likely value, τ0.99x10*, but the distribution given in Table 6.."," Then, the comparison to the observed $\tau$ value uses not the most likely value, $\tau = 0.99\times 10^{-7}$, but the distribution given in Table \ref{tab-true}."
 This method effectively combines the Poisson uncertainties with the event identification uncertainty and results in the 7 confidence levels given in Table 7.., This method effectively combines the Poisson uncertainties with the event identification uncertainty and results in the $\tau$ confidence levels given in Table \ref{tab-taucl}.
 So. the final LMC microlensing optical depth value is 7=(0.99+0.33)x10* with I—c errors and 7—(0.99i)x10.* with 2-o errors.," So, the final LMC microlensing optical depth value is $\tau = (0.99\pm 0.33)\times 10^{-7} $ with $\sigma$ errors and $\tau = (0.99 {+ 0.83\atop -0.55})\times 10^{-7}$ with $\sigma$ errors."
 The confidence level lower limitis 7>0.50x10'., The confidence level lower limit is $\tau > 0.50\times 10^{-7}$.
" For comparison, Table 7 also shows the optical depth confidence intervals for selection criteria A [rom AQO as well as the confidence intervals that would result from using only the 4 events with follow-up data to estimate the number of true microlensing events."," For comparison, Table \ref{tab-taucl} also shows the optical depth confidence intervals for selection criteria A from A00 as well as the confidence intervals that would result from using only the 4 events with follow-up data to estimate the number of true microlensing events."
 Table 8 shows the expected microlensing properties of the known stellar populations along the line of site to the LMC as discussed in AOO., Table \ref{tab-stars} shows the expected microlensing properties of the known stellar populations along the line of site to the LMC as discussed in A00.
" The first four lines give the numbers for the standard models of the Milky Way and LMC, and the fifth line gives the total microlensing optical depth, rate, and number of expected events [or these standard models."," The first four lines give the numbers for the standard models of the Milky Way and LMC, and the fifth line gives the total microlensing optical depth, rate, and number of expected events for these standard models."
" An alternative to the standard Milky Way disk model is the maximum disk model, which may be needed to explain the high microlensing optical depth seen towards the Galactic bulge (Sackett1997;Drimmel&Spergel2001:BissantzGerhard2002)."," An alternative to the standard Milky Way disk model is the maximum disk model, which may be needed to explain the high microlensing optical depth seen towards the Galactic bulge \citep{sackett-maxdisk,drim-sperg,bg-disk-mod}."
". In à maximum disk model. the rotation curve of the inner part of the galaxy is almost enurely supported by the stellar mass of the disk and bulge, so these models predict higher microlensing optical depths and rates than standard models."," In a maximum disk model, the rotation curve of the inner part of the galaxy is almost entirely supported by the stellar mass of the disk and bulge, so these models predict higher microlensing optical depths and rates than standard models."
" The sixth and seventh lines give microlensing predictions for maximum disk models lor both the Milky Way and LMC, and the last line of the table is the total assuming the maximum disk models."," The sixth and seventh lines give microlensing predictions for maximum disk models for both the Milky Way and LMC, and the last line of the table is the total assuming the maximum disk models."
" The numbers given in Table 8 are identical to those givenin A00, except lor the number of expected events, .Voxp. which has been updated to reflect the correction to the detection elficiencies that I have presented."," The numbers given in Table \ref{tab-stars} are identical to those givenin A00, except for the number of expected events, $N_{\rm exp}$, which has been updated to reflect the correction to the detection efficiencies that I have presented."
" Newer models of the LMC (Mancini,CalchiNovati,Jetzer,&Scarpetta2004;Alves2004:Gyuk, give predictions for 7and I that are almost identical to the standard model listed in Table 8.."," Newer models of the LMC \citep{man-lmc-mod,alves-lmc-mod,gyuk-lmc-mod,nikolaev-lmc-mod,vdMarel-lmc-struc}
 give predictions for $\tau$and $\Gamma$ that are almost identical to the standard model listed in Table \ref{tab-stars}. ."
 Comparison of Tables 7 and 8 reveals that the measured LMC microlensing optical depth exceeds the, Comparison of Tables \ref{tab-taucl} and \ref{tab-stars} reveals that the measured LMC microlensing optical depth exceeds the
"Fermi integrals of the order 77 with argument 8 are denoted by F5,(6).",Fermi integrals of the order $\eta$ with argument $\theta$ are denoted by $F_\eta\left(\theta\right)$ .
" The lactor D(T) ls For consistency. the same particle separation energy. $, is used as lor (he reaction rate caleulations of Rauscher&Thielemann(2000)."," The factor $D(T)$ is For consistency, the same particle separation energy $S_x$ is used as for the reaction rate calculations of \citet{RATH}."
. It is taken either [rom experiment or from a mass formula where no experimental information is available., It is taken either from experiment or from a mass formula where no experimental information is available.
" The level densitv at the zero-temperature Fermi surface is given as using the nuclear radius #2 and the nucleon mass m,.", The level density at the zero-temperature Fermi surface is given as using the nuclear radius $R$ and the nucleon mass $m_x$.
 With that definition the ground slate energy becomes Belore evaluating (he above equations. the appropriate (temperature dependent) Lagrange multiplicators with and without corrections have to be determined.," With that definition the ground state energy becomes Before evaluating the above equations, the appropriate (temperature dependent) Lagrange multiplicators with and without corrections have to be determined."
 This is done by requiring states in (he grand. canonical ensemble to have. on the average. the correct. number of nucleons. XV. and therefore bv finding the root of the following equations with respect to α and a’: The proper a or a’ found above has to be inserted also in relec:nucleonpart.. of course.," This is done by requiring states in the grand canonical ensemble to have, on the average, the correct number of nucleons, $X$, and therefore by finding the root of the following equations with respect to $\alpha$ and $\alpha'$: The proper $\alpha$ or $\alpha'$ found above has to be inserted also in \\ref{eq:nucleonpart}, of course."
 Finally. the relevant partition function GT) is Chen obtained by multüplviug (he previous function (from relsec:proc)) wilh Che correction C: Thus. the correctionfactor C found with the approach above is applied to the partition function derived in the [ull computation described in relsec:proc..," Finally, the relevant partition function $\overline{G}(T)$ is then obtained by multiplying the previous function (from \\ref{sec:proc}) ) with the correction $C$: Thus, the correctionfactor $C$ found with the approach above is applied to the partition function derived in the full computation described in \\ref{sec:proc}."
 The corrections start (o act at temperaturesZ5750—60 for light ancl intermediate nuclei and as low as Ty~14 for heavy nuclei., The corrections start to act at temperatures$T_9\simeq 50-60$ for light and intermediate nuclei and as low as $T_9\simeq 14$ for heavy nuclei.
 Corrections are negligible for 75< 10. implving," Corrections are negligible for $T_9\leq 10$ , implying"
50 for n—2.,50 for $n=-2$.
 The overall observation is that there is no much difference of halo shapes if one compare realizations of both spectra., The overall observation is that there is no much difference of halo shapes if one compare realizations of both spectra.
 In both. the halos show a wide range of riaxalitv ranging from prolate to oblate (while in the they are systematically prolate).," In both, the halos show a wide range of triaxality ranging from prolate to oblate (while in the they are systematically prolate)."
 A drawback of our method comes from the fact that the overdensity of a collapsing block. 9. is not necessarily equal o the mean overdensity of the resulting halo. ὃμ.," A drawback of our method comes from the fact that the overdensity of a collapsing block, $\deltaa$, is not necessarily equal to the mean overdensity of the resulting halo, $\deltat$."
 I is the former value which we must associate with the halo if the opologv of the merger tree is to be preserved. (or at least we must maintain the same ordering of densities for halos as their parent. blocks)., It is the former value which we must associate with the halo if the topology of the merger tree is to be preserved (or at least we must maintain the same ordering of densities for halos as their parent blocks).
 The dillerences can be quantified in erms of the ratio v=(διδι)δι which is plotted in ab a time when half the mass is in collapsed structures: we show the mean value plus one sigma error bars., The differences can be quantified in terms of the ratio $\chi=(\deltaa-\deltat)/\deltaa$ which is plotted in \ref{fig:dmas} at a time when half the mass is in collapsed structures: we show the mean value plus one sigma error bars.
 Note first that. halos of fewer than eight. cells have overdensities which are much less than the assigned. one., Note first that halos of fewer than eight cells have overdensities which are much less than the assigned one.
 ‘These structures are. however. leftovers of the merging process (the smallest blocks have a mass of S units) and so they should. not. be considered. as collapsed halos. but rather clouds of interealactic material to be accreted later by a neighbouring halo.," These structures are, however, leftovers of the merging process (the smallest blocks have a mass of 8 units) and so they should not be considered as collapsed halos, but rather clouds of intergalactic material to be accreted later by a neighbouring halo."
 For halos of mass S or larger the agreement is much better. but. nevertheless the true overdensity of a halo remains systematically lower than the assigned one.," For halos of mass 8 or larger the agreement is much better, but nevertheless the true overdensity of a halo remains systematically lower than the assigned one."
 The cllect is largest for n.=O where the mean value of X is about 0.15., The effect is largest for $n=0$ where the mean value of $\chi$ is about 0.15.
 For n=2. it varies [rom approximately zero in the largest halos to 0.1 in the low mass ones.," For $n=-2$, it varies from approximately zero in the largest halos to 0.1 in the low mass ones."
 The reason for the olfset is that high-density cells can contribute to the overdensity of more than one block., The reason for the offset is that high-density cells can contribute to the overdensity of more than one block.
 Itefering again to 2cc. if the region of overlap between the two blocks were of higher density than its surroundings then the density of the whole halo would. be lower than that of either. block from which it is constructed.," Refering again to \ref{fig:halo}c c, if the region of overlap between the two blocks were of higher density than its surroundings then the density of the whole halo would be lower than that of either block from which it is constructed."
 Lf desired the assigned. halo densities could be systematically reduced to bring them into, If desired the assigned halo densities could be systematically reduced to bring them into
or sink of energv through the boundary. we would not be able to use it after all.,"or sink of energy through the boundary, we would not be able to use it after all."
" We must therefore show that To do so. we begin bv noting that in terms of the individual components (D...Ba.2.) and (4).Ja.i). so that. using also the generally valid. result A. Next. (12) can be expressed as so applied atary. where we remember ο=D,J.0. we lind that 27.4=0 as well."," We must therefore show that To do so, we begin by noting that in terms of the individual components $(B_r,B_\theta,B_\phi)$ and $(J_r,J_\theta,J_\phi)$, so that, using also the generally valid result $J_\phi=-D^2 A$ , Next, (12) can be expressed as so applied at$r_i$, where we remember $A=B_r=J_r=0$, we find that $D^2 A=0$ as well."
 We therefore have that which establishes our required result (19)., We therefore have that which establishes our required result (19).
" 1n contrast. at 7, one finds that these surface ternis clo not vanish."," In contrast, at $r_o$ one finds that these surface terms do not vanish."
 Instead. they turn out to be precisely what is needed to take into account changes in the energy stored in the external field.," Instead, they turn out to be precisely what is needed to take into account changes in the energy stored in the external field."
 The final result is then where the integral on the left extends over rkzc75; and the one on the right over à;Xr<r.," The final result is then where the integral on the left extends over $r\ge r_i$, and the one on the right over $r_i\le r\le r_o$."
 Equation (24) is thus the desired energy balance. namely that the total magnetic energy in all of space decreases only as a result of Ohimic clecay.," Equation (24) is thus the desired energy balance, namely that the total magnetic energy in all of space decreases only as a result of Ohmic decay."
 Hall drift rearranges the field. and hence also the energy. but neither creates nor destrovs it.," Hall drift rearranges the field, and hence also the energy, but neither creates nor destroys it."
 In addition to its role in illuminating the physies of LEall drift and Ohmic decay. (24) is also à very. useful diagnostic tool in assessing the accuracy of our solutions.," In addition to its role in illuminating the physics of Hall drift and Ohmic decay, (24) is also a very useful diagnostic tool in assessing the accuracy of our solutions."
 Iteassuringlv.> we found that not only does the magnetic energy. indeed decrease monotonically in time (hardly a very stringent test). but that all of our runs satisfied (24) to within 1 per cent or better.," Reassuringly, we found that not only does the magnetic energy indeed decrease monotonically in time (hardly a very stringent test), but that all of our runs satisfied (24) to within 1 per cent or better."
" “Phat is. if we posteriori) compute the quantity then q never exceeded. 0.0. M""with typical values being much smaller. still."," That is, if we ) compute the quantity then $q$ never exceeded 0.01, with typical values being much smaller still."
 For if we consider not the maximum values. but instead the rms values over a given run. then du. never exceeded. 0.001.," For example, if we consider not the maximum values, but instead the rms values over a given run, then $q_{\rm rms}$ never exceeded 0.001."
 Following Shalvbkoy Urpin (1997). we start with the simplest. possible initial condition. namely just. the lowest poloidal decay mode D.," Following Shalybkov Urpin (1997), we start with the simplest possible initial condition, namely just the lowest poloidal decay mode ${\bf B}_{p1}$."
" Figure 2 shows how the first three harmonies 6). b4 and bs of the external field then evolve in time. where these 6; are defined by That is. (0) is nothing more than the coellicient of DB, in our initial. condition."," Figure 2 shows how the first three harmonics $b_1$, $b_3$ and $b_5$ of the external field then evolve in time, where these $b_l$ are defined by That is, $b_l(0)$ is nothing more than the coefficient of ${\bf B}_{pl}$ in our initial condition."
" Amel indeed. we note how b, starts out at 1. and then slowly decavs."," And indeed, we note how $b_1$ starts out at 1, and then slowly decays."
 I. does. not decay monotonically. but never deviates very much [rom the οχρίETD rate that Ohmic decay alone would have vielded.," It does not decay monotonically, but never deviates very much from the $\exp(-49 R_B^{-1}\,t)$ rate that Ohmic decay alone would have yielded."
 For these runs at least. the inclusion of Hall drift has not significantly changed the decay rate.," For these runs at least, the inclusion of Hall drift has not significantly changed the decay rate."
 That is not to sav that Hall απ has no inlluence on the field though: we note how 6; oscillates. on a timescale of approximately 0.05. and reaching amplitudes as large as 0.15. with both the period. and the amplitude largely independent of By.," That is not to say that Hall drift has no influence on the field though; we note how $b_3$ oscillates, on a timescale of approximately 0.05, and reaching amplitudes as large as 0.15, with both the period and the amplitude largely independent of $R_B$ ."
 Converting back to dimensional time therefore. we could expect. periods on the order of or O(107) vears for the very strongest fields.," Converting back to dimensional time therefore, we could expect periods on the order of or $O(10^5)$ years for the very strongest fields."
 These so-called helicoidal oscillations are in excellent agreement with hose previously obtained by Shakybkov Urpin. who went on to derive an associated dispersion relation. verifving that one should obtain waves that oscillate on the O(1) Πα! imescale and decay on the O(fe) Ohmic timescale. exactly as we see here.," These so-called helicoidal oscillations are in excellent agreement with those previously obtained by Shalybkov Urpin, who went on to derive an associated dispersion relation, verifying that one should obtain waves that oscillate on the $O(1)$ Hall timescale and decay on the $O(R_B)$ Ohmic timescale, exactly as we see here."
" Based on these results therefore. one would think that he solution ought to exist for arbitrarily large Be. with the only οσο of ever larger values being to postpone to ever arger times the decay of both the main field b, and these oscillations in the induced. field. 55."," Based on these results therefore, one would think that the solution ought to exist for arbitrarily large $R_B$, with the only effect of ever larger values being to postpone to ever larger times the decay of both the main field $b_1$ and these oscillations in the induced field $b_3$."
 Nell. perhaps such a solution does exist for arbitrarily largo Re. but we certainly. could not obtain it numerically.," Well, perhaps such a solution does exist for arbitrarily large $R_B$ , but we certainly could not obtain it numerically."
 Every attempt. to increase Re much bevond 200 failed. even at truncations as high as 120.30 and timesteps as smallas 10," Every attempt to increase $R_B$ much beyond 200 failed, even at truncations as high as $120\times30$ and timesteps as smallas $10^{-8}$ ."
we conclude that. if present. any. emission must be arising from some internal source.,"we conclude that, if present, any emission must be arising from some internal source."
 This would be plausible if these clusters were very young (Le.« 10 vr) and massive O/B stars were present., This would be plausible if these clusters were very young $<$ $^{7}$ yr) and massive O/B stars were present.
 However. this is not onky inconsistent with their integrated. colours. but also the spectra of these clusters do not show the characteristic blue continua of very voung objects.," However, this is not only inconsistent with their integrated colours, but also the spectra of these clusters do not show the characteristic blue continua of very young objects."
 There is some evidence that the SSP models a 10.0 voung ages may be at fault (for. 115)., There is some evidence that the SSP models at these young ages may be at fault (for $\beta$ ).
 Ehe. disagreement in the cluster ages occurs at < 3 νι. coincident with were the SSPoomocdels are most uncertain due to the necessary extrapolation required in the Lick/LDS fitting-functions.," The disagreement in the cluster ages occurs at $<$ 3 Gyr, coincident with were the SSP models are most uncertain due to the necessary extrapolation required in the Lick/IDS fitting-functions."
 Moreover. the voung. metal-poor regions of the SSP erids are precisely the areas of parameter space which are inadequately covered by the spectral libraries input into the models.," Moreover, the young, metal-poor regions of the SSP grids are precisely the areas of parameter space which are inadequately covered by the spectral libraries input into the models."
 Clearly. this issue needs to be investigated Buther with a larger sample of integrated spectra for. Magellanie Cloud. clusters in this age rango.," Clearly, this issue needs to be investigated futher with a larger sample of integrated spectra for Magellanic Cloud clusters in this age range."
1s present (0.9.. Stern ct al.,"is present (e.g., Stern et al.,"
 1995: Micela ct al..," 1995; Micela et al.,"
 1996)., 1996).
" The observed spread iu L, at fixed age is associated to the spread in rotational periods. to which the level of activity is linked. (Pizzolato et al."," The observed spread in $L_x$ at fixed age is associated to the spread in rotational periods, to which the level of activity is linked (Pizzolato et al.,"
 2003). that depends on circunstellar disk evolution iu the preiain sequence phase.," 2003), that depends on circumstellar disk evolution in the pre–main sequence phase."
 Iu light of the discussion above. it is needed to consider the evolution of the complete huuinositv distribution iu order to uuderstaud the possible effects ou planctary atinospheres.," In light of the discussion above, it is needed to consider the evolution of the complete luminosity distribution in order to understand the possible effects on planetary atmospheres."
 Iu this study we will focus oulv ou the huninositv distribution of €type stars., In this study we will focus only on the luminosity distribution of G–type stars.
 Because of interstellar absorption. it is not possible with present instrumentation to achieve information about the huuimositv of a large sample of stars in the EUV (200900 ÀJ. so in this work we are focussing on XNταν data.," Because of interstellar absorption, it is not possible with present instrumentation to achieve information about the luminosity of a large sample of stars in the EUV (200–900 $\mbox{\AA}$ ), so in this work we are focussing on X–ray data."
 Whi the eutire band should be considered. X.ravs have however au iportaut role inducing two classes of effects.," While the entire band should be considered, X–rays have however an important role inducing two classes of effects."
 First. they modify the ionization aud the chemical equilibrium of the outer planetary atmosphere. aud second. they produce a siguificaut population of secondary electrons that can penetrate down in the atmosphere contrbutius to its heating (CecchiPestelliii et al.," First, they modify the ionization and the chemical equilibrium of the outer planetary atmosphere, and second, they produce a significant population of secondary electrons that can penetrate down in the atmosphere contributing to its heating (Cecchi–Pestellini et al.,"
 To eet information about the temporal evolution of the Xrav huunmositv we constructed a scaling law using data of stellar clusters with a known age aud data fro the a sample of nearby solartype stars., To get information about the temporal evolution of the X–ray luminosity we constructed a scaling law using data of stellar clusters with a known age and data from the a sample of nearby solar–type stars.
 For a given cluster. we parameterize the logarithm of the Xrav luminosity distribution function following a loguormal distribution aud then calculate the distribution for the whole sample observed in the solar neighborhood where a mix of age is prescut (Sclunitt. 1997).," For a given cluster, we parameterize the logarithm of the X–ray luminosity distribution function following a log–normal distribution and then calculate the distribution for the whole sample observed in the solar neighborhood where a mix of age is present (Schmitt, 1997)."
 The cumulative distribution function for a lognormal distribution is given as where fp and c are the mean and standard deviation of the variable’s logarithi., The cumulative distribution function for a log–normal distribution is given as where $\mu$ and $\sigma$ are the mean and standard deviation of the variable's logarithm.
 As a representative of voung stars we used the Pleiaces cluster. which has au estimated age of LOO Myr (Stauffer et al..," As a representative of young stars we used the Pleiades cluster, which has an estimated age of 100 Myr (Stauffer et al.,"
 2005. and references therein).," 2005, and references therein)."
 The παπι likelyhood luuimositv function of € stars in the Pleiades clusters is eiven m Micela. (2002)., The maximum likelyhood luminosity function of G stars in the Pleiades clusters is given in Micela (2002).
 This can be fitted well with a lognormal distribution with po=67.58 (correspoudiug to Ly=1022 (ejοὐκ) and o=1.1 (Fig. 1))., This can be fitted well with a log–normal distribution with $\mu=67.58$ (corresponding to $L_X=10^{29.35}$ erg/s) and $\sigma=1.1$ (Fig. \ref{comp}) ).
 For intermediate age stars we use the Uvacdes cluster with au age of about 600 Myr (Stauffoer et al..," For intermediate age stars we use the Hyades cluster with an age of about 600 Myr (Stauffer et al.,"
 2005. aud references therein). with a Dunuinositv function eiveu in Stern et al. (," 2005, and references therein), with a luminosity function given in Stern et al. ("
1995).,1995).
" The loe-normal parameters for the ITvades are pp=66.8 (Ly=1075"" οοκ) aud o=0.9 (Fig. 1)).", The log-normal parameters for the Hyades are $\mu=66.8$ $L_X=10^{29.0}$ erg/s) and $\sigma=0.9$ (Fig. \ref{comp}) ).
 For L6 Gyr old stars we asstune the same standard deviation as for the Iyadoes aud a mean value of µ=63.3 consistent with present day solar cussions., For 4.6 Gyr old stars we assume the same standard deviation as for the Hyades and a mean value of $\mu=63.3$ consistent with present day solar emissions.
 Under the assumption of a constant standard, Under the assumption of a constant standard
larger and thus the enclosed mass correspondingly larger.,larger and thus the enclosed mass correspondingly larger.
 We will make a detailed comparison of NGC 839 with M 82 in Section ??.., We will make a detailed comparison of NGC 839 with M 82 in Section \ref{M82}.
 The majority of the emission line gas can be fit by two Gaussians., The majority of the emission line gas can be fit by two Gaussians.
" In the plane of the galaxy, as remarked above, the gas shows an organized rotation curve."," In the plane of the galaxy, as remarked above, the gas shows an organized rotation curve."
" This is also true of the stellar component, shown in Figure 6.."," This is also true of the stellar component, shown in Figure \ref{fig6}."
" Here, we have extracted the spectrum in the region around using several apertures along the major axis of the galaxy each 3""in diameter."," Here, we have extracted the spectrum in the region around using several apertures along the major axis of the galaxy each in diameter."
 This also shows the dominance of the A-type stellar figureabsorption clearlycomponent in the outer parts of the galaxy., This figure also clearly shows the dominance of the A-type stellar absorption component in the outer parts of the galaxy.
 The gas appears to have a maximum in its velocity coincident with the dust lanes apparent in the image (Figures 4 and 5))., The gas appears to have a maximum in its velocity coincident with the dust lanes apparent in the image (Figures \ref{fig4} and \ref{fig5}) ).
" The extended morphology revealed by the SINGG images and by maps generated from our data is typical of that seen in galaxies with biconical galactic scale superwinds (e.g., Heckmanetal.1987,1990;Veilleux1994;Lehnert&&Rupke 2002))."," The extended morphology revealed by the SINGG images and by maps generated from our data is typical of that seen in galaxies with biconical galactic scale superwinds (e.g., \citealt{Heckman87,Heckman90,Veilleux94,Lehnert96,Shopbell98,Veilleux02}) )."
" The emission extends a few kpc above and below the disk along the minor axis in a conical shape, though due to the distance of NGC 839 and the available ground-based data it is difficult to determine detailed characteristics of the bicone."," The emission extends a few kpc above and below the disk along the minor axis in a conical shape, though due to the distance of NGC 839 and the available ground-based data it is difficult to determine detailed characteristics of the bicone."
 Our spectra also reveal kinematic evidence for a large-scale outflow or superwind extending both above and below the disk., Our spectra also reveal kinematic evidence for a large-scale outflow or superwind extending both above and below the disk.
 We see extensive line splitting with typical Av~250 km s~! along the minor axis up to ~2 kpc above and below the plane., We see extensive line splitting with typical $\Delta v \sim 250$ km $^{-1}$ along the minor axis up to $\sim2$ kpc above and below the plane.
 The maximum velocity splitting seen at any point in the flow is Av~305 km s-!., The maximum velocity splitting seen at any point in the flow is $\Delta v \sim 305$ km $^{-1}$.
" As evidenced by Figure 6 there is also evidence for a blueshifted Na D component, which traces the neutral of the "," As evidenced by Figure \ref{fig6} there is also evidence for a blueshifted Na D component, which traces the neutral component of the superwind."
"The in this NGC 839 componentis inclined such superwind.that we largestobserve the separationblueshifted component below the disk, along lines of sight toward the disk itself."," The largest separation in this NGC 839 is inclined such that we observe the blueshifted component below the disk, along lines of sight toward the disk itself."
" As the stellar continuum drops rapidly below the disk, we are unable to trace the extent of the Na D much beyond the disk and so focus mainly on the emission line data."," As the stellar continuum drops rapidly below the disk, we are unable to trace the extent of the Na D much beyond the disk and so focus mainly on the emission line data."
" The dispersion of the emission line gas is generally lowest in the velocitydisk, on the order of 50 km s~?, and increases above and below the disk to 100-200 km s, consistent with the kinematic signatures of a galactic wind (e.g., Lehnert 1996)."," The velocity dispersion of the emission line gas is generally lowest in the disk, on the order of 50 km $^{-1}$, and increases above and below the disk to 100–200 km $^{-1}$, consistent with the kinematic signatures of a galactic wind (e.g., \citealt{Lehnert96}) )."
 Where two components are fit the ratio of the velocity dispersions are within a factor of . 1-2.5 of one another., Where two components are fit the ratio of the velocity dispersions are within a factor of $\sim 1$ $2.5$ of one another.
" Tracing the velocity dispersion is somewhat complicated due to the presence of multiple Gaussian components of varying relative flux and is limited by our spatial and spectral resolution, so in order to quantify these signatures, we have analyzed the data in terms of the line flux and the square of the velocity dispersion, c?, along the line of sight."," Tracing the velocity dispersion is somewhat complicated due to the presence of multiple Gaussian components of varying relative flux and is limited by our spatial and spectral resolution, so in order to quantify these signatures, we have analyzed the data in terms of the line flux and the square of the velocity dispersion, $\sigma^{2}$, along the line of sight."
" The lline flux is given by Fu4ο:apgngneAR, where o is the effective Case-B recombination coefficient, ng is the hydrogen incm?, n, is the electron density in cm?, and At is densitythe path length through the ionized medium."," The line flux is given by $F_{\rm H \alpha} \propto \alpha_{\rm B} n_{\rm H} n_{\rm e} \Delta R$, where $\alpha$ is the effective Case-B recombination coefficient, $n_{\rm H} $ is the hydrogen density in$^{-3}$, $n_{\rm e} $ is the electron density in $^{-3}$, and $\Delta R$ is the path length through the ionized medium."
" This equation can be expressed more simply as Fu« Une, where » is the ionized mass surface density."," This equation can be expressed more simply as $F_{\rm H \alpha} \propto \Sigma n_{\rm e} $ , where $\Sigma$ is the ionized mass surface density."
 Thus to the extent, Thus to the extent
"ave X.ray depressions in the innermost cluster regions which spatially correspond to significant radio emission (e.g.???)., ","are X–ray depressions in the innermost cluster regions which spatially correspond to significant radio emission \citep[e.g.][]{Owen2000, Blanton2001,
Clarke2005}."
The most plausible candidate for inducing these features is the central BLL. which is generating jet-inllated radio lobes. often simply dubbed bubbles’.," The most plausible candidate for inducing these features is the central BH, which is generating jet-inflated radio lobes, often simply dubbed `bubbles'."
 There bas been considerable. theoretical ellort to understancl the interplay of ACGN-clriven bubbles with the intracluster medium (16ΔΕΟ (ος.?iam ," There has been considerable theoretical effort to understand the interplay of AGN-driven bubbles with the intracluster medium (ICM) \citep[e.g.][]{Churazov2001, Quilis2001, Brueggen2002, Ruszkowski2002,
DallaVecchia2004, Omma2004a, Sijacki2006a, Sijacki2006b,
Sijacki2007}."
Alost of these studies have. for simplicity. considered: bubbles that are [filled with hot thermal eas. and by following their evolution with time. they tried to constrain how much heat AGN bubbles can deliver to the surrounding medium.," Most of these studies have, for simplicity, considered bubbles that are filled with hot thermal gas, and by following their evolution with time, they tried to constrain how much heat AGN bubbles can deliver to the surrounding medium."
 Llowever. the synchrotron. and. inverse Compton emission detected. from. the radio lobes suggests that they contain a significant amount of relativistic electrons and that they are permeated with magnetic fields.," However, the synchrotron and inverse Compton emission detected from the radio lobes suggests that they contain a significant amount of relativistic electrons and that they are permeated with magnetic fields."
 Besides relativistic electrons and magnetic fields. it is also very. plausible that an important part of the pressure support in the bubbles stems from relativistic protons. especially if the GN jets are heavy.," Besides relativistic electrons and magnetic fields, it is also very plausible that an important part of the pressure support in the bubbles stems from relativistic protons, especially if the AGN jets are heavy."
 To date it is however not clear. both [rom an observational ane a theoretical point of view. what the precise Composition of the bubbles. the relative mixture of hot gas. ancl non-thermal particle components really is.," To date it is however not clear, both from an observational and a theoretical point of view, what the precise composition of the bubbles, the relative mixture of hot gas, and non-thermal particle components really is."
 Also. we have no detailed knowledge about the strength and configuration of the magnetic fields within the bubbles.," Also, we have no detailed knowledge about the strength and configuration of the magnetic fields within the bubbles."
 Reearcding the contribution from hot thermal gas. the work of 2) suggested that the bubble in the MINW 3s galaxy cluster may have a predominantly thermal origin. while ?) found that in the Perseus cluster a thermal gas componen cooler than ~IlkeV filing the bubbles seems ruled. out.," Regarding the contribution from hot thermal gas, the work of \citet{Mazzotta2002} suggested that the bubble in the MKW 3s galaxy cluster may have a predominantly thermal origin, while \citet{Schmidt2002} found that in the Perseus cluster a thermal gas component cooler than $\sim 11\,{\rm keV}$ filling the bubbles seems ruled out."
 Moreover. it is not clear whether entrainment of therma gas by the radio jet is elfective and how this should depen on the BLL properties.," Moreover, it is not clear whether entrainment of thermal gas by the radio jet is effective and how this should depend on the BH properties."
 A study of a Larger sample of galaxy clusters with central X-ray cavities by 2). hints. towards a rather complex picture. leaving several possibilities stil open. both for significant pressure support by non-therma protons or bv hot thermal plasma. and for scenarios where the magnetic fields are filamentary at least in some of the Cases.," A study of a larger sample of galaxy clusters with central X-ray cavities by \citet{Dunn2005} hints towards a rather complex picture, leaving several possibilities still open, both for significant pressure support by non-thermal protons or by hot thermal plasma, and for scenarios where the magnetic fields are filamentary at least in some of the cases."
 Bearing in mind the outlined. uncertainties it is still highly interesting to investigate the possible effects of cosmic ravs (CRs) in AGN-inllatec bubbles on cool core clusters. as considered already by several authors (c.g.2?22???)..," Bearing in mind the outlined uncertainties it is still highly interesting to investigate the possible effects of cosmic rays (CRs) in AGN-inflated bubbles on cool core clusters, as considered already by several authors \citep[e.g.][]{Boehringer1988, Loewenstein1991,
Mathews2007, Guo2007, Sanders2007, Ruszkowski2007}."
 πως studies have highlighted cillerent channels of €1t interaction with the thermal intracluster gas anc have demonstrated that CRs can be dynamically important in galaxy clusters. contributing up to 50% of the central cluster pressure (but see?) for somewhat lower estimates of CL pressure support of order of 10 20%)ο," These studies have highlighted different channels of CR interaction with the thermal intracluster gas and have demonstrated that CRs can be dynamically important in galaxy clusters, contributing up to $50\%$ of the central cluster pressure (but see \citet{Churazov2007} for somewhat lower estimates of CR pressure support of order of $10-20\%$ )."
 Nevertheless. due to the complicated nature of Cl. physics. most of these works were based on analytical or LD numerical calculations. ancl neglected any cosmological evolution of the host clusters. and. hence any possible dependence on its dynamical state.," Nevertheless, due to the complicated nature of CR physics, most of these works were based on analytical or 1D numerical calculations, and neglected any cosmological evolution of the host clusters, and hence any possible dependence on its dynamical state."
 On the other hand. cosmological simulations ofCRs produced at structure formation shocks by. for example. 777?) have highlighted the importance of a realistic cosmological setting for a more atelul generation. distribution and. following evolution of CRs.," On the other hand, cosmological simulations of CRs produced at structure formation shocks by, for example, \citet{Miniati2001, Miniati2002, Ryu2003, Ryu2004} have highlighted the importance of a realistic cosmological setting for a more fateful generation, distribution and following evolution of CRs."
 Recently. 2) have proposed a simplified formalism or the treatment of CR protons that it suitable for implementation anc use in self-consistent cosmological codes. às subsequently demonstrated by 7) anc ?)..," Recently, \citet{Ensslin2007} have proposed a simplified formalism for the treatment of CR protons that it suitable for implementation and use in self-consistent cosmological codes, as subsequently demonstrated by \citet{Jubelgas2007} and \citet{Pfrommer2006}."
 In hese numerical studies. the CR source processes considered were restricted to supernovae (SNe) and structure formation shock waves.," In these numerical studies, the CR source processes considered were restricted to supernovae (SNe) and structure formation shock waves."
 While it was found that. these. sources can allect the interstellar medium. of low mass. galaxies significantly. they click not prevent the overcooling in the centres of galaxy groups and clusters.," While it was found that these CR sources can affect the interstellar medium of low mass galaxies significantly, they did not prevent the overcooling in the centres of galaxy groups and clusters."
 However. the possible impact of CR: protons generated by central AGN has not been explored in these works. and this forms the primary objective of our current study.," However, the possible impact of CR protons generated by central AGN has not been explored in these works, and this forms the primary objective of our current study."
 This paper is organized as follows., This paper is organized as follows.
 In Section 2 we outline the methodology we have adopted το simulate CR bubbles. and. to follow their. cosmological evolution., In Section \ref{Methodology} we outline the methodology we have adopted to simulate CR bubbles and to follow their cosmological evolution.
 In Section 3.. we present test runs performed. for isolated halo simulations in order to analyze our numerical moctel in detail. while the bulk of our results from. cosmological simulations of galaxy cluster formation is described in Section 4..," In Section \ref{Isolated}, we present test runs performed for isolated halo simulations in order to analyze our numerical model in detail, while the bulk of our results from cosmological simulations of galaxy cluster formation is described in Section \ref{Cosmological}."
 Finally. we discuss our findings and craw our conclusions in Section 4.2.3..," Finally, we discuss our findings and draw our conclusions in Section \ref{Discussion}."
 In this study we use an improved. version of the massively parallel νου)M-SPII. code. (77)...," In this study we use an improved version of the massively parallel TreePM-SPH code \citep{Gadget2, Springel2001}."
 The SPI formulation adopted in the code manifestly conserves both energy and entropy. even in the presence of fully adaptive smoothing lengths. as implemented by 2)..," The SPH formulation adopted in the code manifestly conserves both energy and entropy even in the presence of fully adaptive smoothing lengths, as implemented by \citet{SH2002}."
 In addition to the eravity of dark matter and barvons. and to ordinary hvdrodvnamices. the code tracks radiative cooling of an optically thin plasma of hydrogen and helium. immersed in a time-varving. spatially uniform UV background (asin?)..," In addition to the gravity of dark matter and baryons, and to ordinary hydrodynamics, the code tracks radiative cooling of an optically thin plasma of hydrogen and helium, immersed in a time-varying, spatially uniform UV background \citep[as
in][]{Katz1996}."
 A subresolution multi-phase model for the ISM is used to ollows star. formation ancl supernovae feedback. processes (?).., A subresolution multi-phase model for the ISM is used to follows star formation and supernovae feedback processes \citep{S&H2003}.
 Furthermore. we adopt the model for BLE seeding and erowth that has been suggested by ο) and. ?).. modified rowever bv the introduction of a second. mode. of AGN eedback to model radio activity. as described by ο).," Furthermore, we adopt the model for BH seeding and growth that has been suggested by \citet{DiMatteo2005} and \citet{Springel2005b}, modified however by the introduction of a second mode of AGN feedback to model radio activity, as described by \citet{Sijacki2007}."
 These wo modes are thermal heating from quasars at. high. 1911 accretion rates (BILARS). and mechanical feedback in the orm of hot. buovant bubbles occurring at low accretion rates.," These two modes are thermal heating from quasars at high BH accretion rates (BHARs), and mechanical feedback in the form of hot, buoyant bubbles occurring at low accretion rates."
 1n this study. we combine the AGN feedback oescription at low BILARs with a mocel for Cl treatmen hat has been developed. implemented. and discussed by ολο. 7).. and ?)..," In this study, we combine the AGN feedback prescription at low BHARs with a model for CR treatment that has been developed, implemented, and discussed by \citet{Ensslin2007}, \citet{Jubelgas2007}, and \citet{Pfrommer2006}."
 This extension of our model! allows us to accoun or a non-thermal component permeating the radio lobes., This extension of our model allows us to account for a non-thermal component permeating the radio lobes.
 In his section. we outline the most important. features of our combined BIE and CTI models. and. we describe in. detai he approximations we have adopted to model non-therma xwticle populations in ACGN-driven bubbles.," In this section, we outline the most important features of our combined BH and CR models, and we describe in detail the approximations we have adopted to model non-thermal particle populations in AGN-driven bubbles."
the photosphere. it is at longer wavelengths that we expect to see the largest variation in magnitude. again in agreement with the In order to investigate the implications of the optical and infrared. cata presented. here in the context of the past behaviour of the star. data were taken from. the catalogue of ESO's Long Term Photometry of Variables project. (Sterken et al.,"the photosphere, it is at longer wavelengths that we expect to see the largest variation in magnitude, again in agreement with the In order to investigate the implications of the optical and infrared data presented here in the context of the past behaviour of the star, data were taken from the catalogue of ESO's Long Term Photometry of Variables project (Sterken et al."
 1995)., 1995).
 The data (Strómmegren ΗΔΗ photometry. covering the period. 1982 to 1994) along with derived indices are shown in Figure 3. and were described in Section 2.3.," The data (Strömmgren $uvby$ photometry, covering the period 1982 to 1994) along with derived indices are shown in Figure 3, and were described in Section 2.3."
 Of note is the scale of the long term variability., Of note is the scale of the long term variability.
 The range ofV. magnitude is zN V0.6. whilst ACh 3)-—0.2.," The range of magnitude is $\Delta$ $\sim$ 0.6, whilst $\Delta$ $\sim$ 0.2."
 As y) increases with optical luminositv. again the data indicate that the variations are greater at longer wavelengths.," As ) increases with optical luminosity, again the data indicate that the variations are greater at longer wavelengths."
 Figure 5 shows explicitly. the relationship between luminosity and colour. represented by V and (by) respectively.," Figure 5 shows explicitly the relationship between luminosity and colour, represented by $V$ and $(b-y)$ respectively."
 Lt is clear that in the high state. the (by) index shows the star to be redder than in the low state.," It is clear that in the high state, the $b-y$ ) index shows the star to be redder than in the low state."
 As with the infrared photometry then. the size of the variations and their dependance upon wavelength implies that they are the result. of changes in the size of the circumstellar disc.," As with the infrared photometry then, the size of the variations and their dependance upon wavelength implies that they are the result of changes in the size of the circumstellar disc."
 Hence. with the new infrared and optical data we now have an indication of the way in which the disc has decaved. recovered anc ecaved again over the past 13 vears [rom 1982 December to 1996 The complete data set shows three disc loss episodes. corresponding to the two previously observed optical minima. and the current optical decay.," Hence, with the new infrared and optical data we now have an indication of the way in which the disc has decayed, recovered and decayed again over the past 13 years from 1982 December to 1996 The complete data set shows three disc loss episodes, corresponding to the two previously observed optical minima, and the current optical decay."
 Although the infrared and spectroscopic data in the period before our own observations is sparse. they are consistent with the timescale of disc Loss and recovery suggested by the optical lighteurve.," Although the infrared and spectroscopic data in the period before our own observations is sparse, they are consistent with the timescale of disc loss and recovery suggested by the optical lightcurve."
 Similar episodes of dise loss have been observed. in other Je/N-rav binary svstems., Similar episodes of disc loss have been observed in other Be/X-ray binary systems.
 Most. notably. observations of X Persei have shown the Ho. line changing from emission to absorption over a period of months (Norton et al.," Most notably, observations of X Persei have shown the $\alpha$ line changing from emission to absorption over a period of months (Norton et al."
 1991)., 1991).
 In the case of1119-0190. complete dise Loss is clearly not the case at present. despite the decay in strength. because both the La and Ll? lines remain in emission.," In the case of 4U1145-619, complete disc loss is clearly not the case at present, despite the decay in strength, because both the $\alpha$ and $\beta$ lines remain in emission."
 In Figure 3 the epochs of X-rav outbursts are. plotted as arrows above the VW band lightcurve., In Figure 3 the epochs of X-ray outbursts are plotted as arrows above the $V$ band lightcurve.
 Again we define an outburst as an increase in [lux by a [actor of five above the quiescent Hux of ~ 10n CODES 1 207., Again we define an outburst as an increase in flux by a factor of five above the quiescent flux of $\sim$ $^{-10}$ ergs $^{-1}$ $^{-2}$.
 Sixqn BATSE detections are plotted. these corresponding to the six penultimate arrows (Scott. M. private communication).," Six BATSE detections are plotted, these corresponding to the six penultimate arrows (Scott M. private communication)."
 There appears to be a correlation between the N-ray ancl optical behaviour. with X-ray activity increased: during periods of optical decline.," There appears to be a correlation between the X-ray and optical behaviour, with X-ray activity increased during periods of optical decline."
 Although we cannot however rule out the possibility that the apparent correlation is an artifact of the epochs of the X-ray observations. such a correlation is not unexpected. as the N-rav. emission is fueled by the material in the varving disc.," Although we cannot however rule out the possibility that the apparent correlation is an artifact of the epochs of the X-ray observations, such a correlation is not unexpected, as the X-ray emission is fueled by the material in the varying disc."
 Wf the material lost from the disc is clissipatec away from the star. rather than falling back onto the surface. then some fraction of this material shoulc accrete onto the neutron star providing acdcitional fuel for X-ray emission.," If the material lost from the disc is dissipated away from the star, rather than falling back onto the surface, then some fraction of this material should accrete onto the neutron star providing additional fuel for X-ray emission."
 This scenario was suggested by Roche e al. (, This scenario was suggested by Roche et al. (
1993) to explain similar correlations in the X-ray. anc optical/infrared behaviour of the De/N-ray binary X Persei.,1993) to explain similar correlations in the X-ray and optical/infrared behaviour of the Be/X-ray binary X Persei.
 Many De/X-ray binary systems however show correlations of the opposite nature. with increased X-ray activity coinciding with optically bright phases (4U0115|63. Neeucrucla e al.," Many Be/X-ray binary systems however show correlations of the opposite nature, with increased X-ray activity coinciding with optically bright phases (4U0115+63, Negueruela et al."
 1997: AO53s8-66. Corbet et al.," 1997; A0538-66, Corbet et al."
 1985), 1985).
 A distinguishing factor between these two groups is the significant dillerence in orbital period., A distinguishing factor between these two groups is the significant difference in orbital period.
 Both 4U1145-619 and X. Persei are long period binaries. with wide orbits. 4UO115|63 ancl AOS38-66 each have periods less than 30 days. with much smaller orbits.," Both 4U1145-619 and X Persei are long period binaries, with wide orbits, 4U0115+63 and A0538-66 each have periods less than 30 days, with much smaller orbits."
 In the case of the lone period binaries. the neutron star may not become immersed in the dise during periastron passage. but rather accrete from the material that is Lost radiallv from this disc during phases of decline in the Be stars activity.," In the case of the long period binaries, the neutron star may not become immersed in the disc during periastron passage, but rather accrete from the material that is lost radially from this disc during phases of decline in the Be star's activity."
 Such a scenario would be consistent. with spherical In such a binary. where the neutron star does not accrete directlv [rom the Be stars disc. but from material ost racially from it. we might expect any orbital modulation of X-ray. [lux to be of smaller amplitude and smoother in wolile than in svstems where the neutron star. becomes immersed in the disc at periastron.," Such a scenario would be consistent with spherical In such a binary, where the neutron star does not accrete directly from the Be star's disc, but from material lost radially from it, we might expect any orbital modulation of X-ray flux to be of smaller amplitude and smoother in profile than in systems where the neutron star becomes immersed in the disc at periastron."
 Llowever in the case of 4U1145-619 the orbital modulation in the X-ray ighteurve is significant. with outbursts lasting less than V1 phase and increases in Bux of an order of magnitude above quiescence.," However in the case of 4U1145-619 the orbital modulation in the X-ray lightcurve is significant, with outbursts lasting less than 0.1 phase and increases in flux of an order of magnitude above quiescence."
 H£ this sharp modulation were caused. by centrifugal inhibition of accretion (Stella. White Rosner 1986). then we should not detect. quiescent Εαν from. the source.," If this sharp modulation were caused by centrifugal inhibition of accretion (Stella, White Rosner 1986), then we should not detect quiescent flux from the source."
 Corbet (1996). showed. that N-ray emission. may originate from the magnetosphere of the neutron star. even when accretion onto the neutron star surface was prohibited.," Corbet (1996) showed that X-ray emission may originate from the magnetosphere of the neutron star, even when accretion onto the neutron star surface was prohibited."
 We note that Corbet finds in the case of 4U1145-619. that this emission. should. be a factor of 7375 less than the minimum emission from the neutron stars surface.," We note that Corbet finds in the case of 4U1145-619, that this emission should be a factor of 7375 less than the minimum emission from the neutron star's surface."
 The quiescent Dux observed in 4U1145-619 is only a factor of 75, The quiescent flux observed in 4U1145-619 is only a factor of $\sim$ 5
has been observed on several occasions with the RGS instrument. in part for calibration purposes.,"has been observed on several occasions with the RGS instrument, in part for calibration purposes."
 Table 1. gives an overview of the observations used in this paper., Table \ref{obs} gives an overview of the observations used in this paper.
 Due to the high X-ray flux ofX-1.. a standard spectroscopy. mode observation would lead to unacceptable pile-up on the detector and loss of large amounts of observing time due to overload of the on-board processing capabilities and limited telemetry capacity.," Due to the high X-ray flux of, a standard spectroscopy mode observation would lead to unacceptable pile-up on the detector and loss of large amounts of observing time due to overload of the on-board processing capabilities and limited telemetry capacity."
 For this reason a faster readout mode was selected by reading individual single RGS CCD's in separate exposures., For this reason a faster readout mode was selected by reading individual single RGS CCD's in separate exposures.
 The high flux of also allowed for an off-axis observation mode. effectively shifting the spectrum to a different location on the CCD's.," The high flux of also allowed for an off-axis observation mode, effectively shifting the spectrum to a different location on the CCD's."
 At large offset angles (we used 27 arc-minutes). the effective area of the instrument is reduced. decreasing potential problems with pile-up thus allowing for multiple CCD readouts.," At large offset angles (we used 27 arc-minutes), the effective area of the instrument is reduced, decreasing potential problems with pile-up thus allowing for multiple CCD readouts."
 This will increase effective exposure time., This will increase effective exposure time.
 Although large offset angles do introduce some additional uncertainty in absolute flux. the change in shape of the response curve is mild and well-modeled.," Although large offset angles do introduce some additional uncertainty in absolute flux, the change in shape of the response curve is mild and well-modeled."
 In the limited wavelength range of interest (21-24 Α)) the effect is negligible and it is almost inconceivable that the off-axis positions will introduce (or erase) a spectral modulation indicative of EXAFS., In the limited wavelength range of interest (21-24 ) the effect is negligible and it is almost inconceivable that the off-axis positions will introduce (or erase) a spectral modulation indicative of EXAFS.
 Combining observations with different offsets will decrease systematic errors in the spectra due to hot and erratic pixels on the CCD., Combining observations with different offsets will decrease systematic errors in the spectra due to hot and erratic pixels on the CCD.
 Combining observations with large offsets will also decrease small unknown fluctuations of effective area due to inhomogeneous CCD response. effectively smoothing errors in the effective area.," Combining observations with large offsets will also decrease small unknown fluctuations of effective area due to inhomogeneous CCD response, effectively smoothing errors in the effective area."
 This will increase the possibility of detecting real source broad wavelength flux fluctuations., This will increase the possibility of detecting real source broad wavelength flux fluctuations.
 The large offset has the extra advantage that the important oxygen edge Is covered by both RGS instruments., The large offset has the extra advantage that the important oxygen edge is covered by both RGS instruments.
 In default on axis pointing mode the oxygen edge is only visible by one RGS (RGSI) since the corresponding CCD on the other RGS has failed early in the mission., In default on axis pointing mode the oxygen edge is only visible by one RGS (RGS1) since the corresponding CCD on the other RGS has failed early in the mission.
 The large offset shifted the oxygen edge to a different CCD location where both instruments have operational CCD's., The large offset shifted the oxygen edge to a different CCD location where both instruments have operational CCD's.
 In all. these special calibration mode observations have made this set of observations ideally suited for the search for EXAFS.," In all, these special calibration mode observations have made this set of observations ideally suited for the search for EXAFS."
 Due to the shifted spectrum in the offset pointings. the total usable spectral range of the combined observations extends from 12 to 38Α..," Due to the shifted spectrum in the offset pointings, the total usable spectral range of the combined observations extends from 12 to 38."
 All data were reduced with the data analysis system SAS version 7., All data were reduced with the data analysis system SAS version 7.
 Since the source was slightly variable between different observations and the scale of the off-axis effective area is not accurately known. obtained fluxes from the different observations have been scaled to fit the revolution 0224.," Since the source was slightly variable between different observations and the scale of the off-axis effective area is not accurately known, obtained fluxes from the different observations have been scaled to fit the revolution 0224."
 The average of the scaled. fluxed spectra (obtained using task “resfluxer”) was taken for further analysis (Fig. 1))," The average of the scaled, fluxed spectra (obtained using task ""rgsfluxer"") was taken for further analysis (Fig. \ref{spect}) )"
 Defining the edge energy at Li we can compute the wave number /: of the escaping photo-electron as: WithhY #7 the electron mass. A the wavelength and 7; and c Planck's constant and the velocity of light respectively.," Defining the edge energy at $E_0$ we can compute the wave number $k$ of the escaping photo-electron as: With $m$ the electron mass, $\lambda$ the wavelength and $h$ and $c$ Planck's constant and the velocity of light respectively."
 \ is defined as the relativechange in the absorption coefficient µ with respect to the smooth continuum jiy (see Fig. 2..," $\chi$ is defined as the relativechange in the absorption coefficient $\mu$ with respect to the smooth continuum $\mu_0$ (see Fig. \ref{esco},"
 top) at energies above the edge: Because changes&) in the observed flux due to EXAFS are small with respect to the absolute flux. ((&) can be obtained directly from the relative changes of the flux with respect to the smooth continuum flux.," top) at energies above the edge: Because changes in the observed flux due to EXAFS are small with respect to the absolute flux, $\chi(k)$ can be obtained directly from the relative changes of the flux with respect to the smooth continuum flux."
 This continuum is computed by taking the atomic oxygen absorption cross-section as given by ? applied to a linear slope across the small wavelength region of interest (21-24 A). fixing the continuum to the flux actually observed at the edges of the wavelength region. (," This continuum is computed by taking the atomic oxygen absorption cross-section as given by \cite{mclaughlin} applied to a linear slope across the small wavelength region of interest (21-24 ), fixing the continuum to the flux actually observed at the edges of the wavelength region. ("
see Fig. 2..,"see Fig. \ref{esco},"
 top plot) Plotting « as function of & (see Fig. 2..," top plot) Plotting $\chi$ as function of $k$ (see Fig. \ref{esco},"
 middle plot). will reveal EXAFS as a sinusoidal structure.," middle plot), will reveal EXAFS as a sinusoidal structure."
 Analyzing the spatial frequencies m this plot. by taking the absolute value (ΝΕΤCET)? of the Fourier transform (FT). which scales linearly with EXAFS amplitudes. will show peaks representing the distances of the scattering atoms in the absorbing solid. (," Analyzing the spatial frequencies in this plot, by taking the absolute value $\sqrt{ {\rm (FT)} \cdot {\rm (FT)^*}}$ ) of the Fourier transform (FT), which scales linearly with EXAFS amplitudes, will show peaks representing the distances of the scattering atoms in the absorbing solid. ("
The surface area under the peak corresponds to the total amplitude of the EXAFS. since zeroes added to extend the & range prior to the transform (see e.g. ?)) cause a smoothing (convolution) of the FT-magnitude graph).,"The surface area under the peak corresponds to the total amplitude of the EXAFS, since zeroes added to extend the $k$ range prior to the transform (see e.g. \cite{Lee}) ) cause a smoothing (convolution) of the FT-magnitude graph)."
 Peak positions (41) do not however translate directly to atomic distances. due to phase shifts in the scattering process.," Peak positions $R$ ) do not however translate directly to atomic distances, due to phase shifts in the scattering process."
 Phase shifts must be known beforehand. e.g. from theoretical calculations. in order to obtain true atomic distances.," Phase shifts must be known beforehand, e.g. from theoretical calculations, in order to obtain true atomic distances."
 A major problem is the adopted value for the edge energy E (?).., A major problem is the adopted value for the edge energy $E_0$ \citep{Lee}. .
 Although edge energies for many isolated atoms are known with sufficient precision. edge energies are subject to," Although edge energies for many isolated atoms are known with sufficient precision, edge energies are subject to"
To test the likelihood of LBCs being similar to these type of extremely dusty starbursts. we randomly assigned log IRN values in the 23.5 ranee to each LBC (hashed reeion of Fieure 2) aud followed the same aforeioeutioned procedure to predict the X-ray luminosities.,"To test the likelihood of LBGs being similar to these type of extremely dusty starbursts, we randomly assigned log IRX values in the 2–3.5 range to each LBG (hashed region of Figure 2) and followed the same aforementioned procedure to predict the X-ray luminosities."
 Our method predicts the mean N-vav huuinositv for the sample to be 27.WP eres + (Figure 3: Panel B).," Our method predicts the mean X-ray luminosity for the sample to be $2.7 \times
10^{43}\,$ $\,$ $^{-1}$ (Figure 3: Panel B)."
 This is two orders of maenituce larger than the observed value aud strongly suggests that LBGs are not hiding a significant amount of star formation behind a veil of dust., This is two orders of magnitude larger than the observed value and strongly suggests that LBGs are not hiding a significant amount of star formation behind a veil of dust.
 Iu fact. ~92% of the sample would have X-ray fluxes greater than the single source soft-band detection limit. with half being at least an order of magnitude Luger.," In fact, $\sim92$ of the sample would have X-ray fluxes greater than the single source soft-band detection limit, with half being at least an order of magnitude larger."
 Furthermore. if LBCs truly have ULIC-like IRN values hen the observed far-UV fluxes imply FIR luuinosities iu he 10124 10:57 L. range.," Furthermore, if LBGs truly have ULIG-like IRX values then the observed far-UV fluxes imply FIR luminosities in the $10^{12.4}$ $10^{14.7}$ $_{\odot}$ range."
 Using the method described w Adoelberger Steidel (2000) we estimate that of he saunple would have rest-frame A=200 Ὥτις densities greater than the 2 mJv detection limit for he IIDE-N subauilliieter (sub-nuau) survey conducted by IIughes et al. (, Using the method described by Adelberger Steidel (2000) we estimate that of the sample would have rest-frame $\lambda =200$ flux densities greater than the 2 mJy detection limit for the HDF-N sub-millimeter (sub-mm) survey conducted by Hughes et al. (
1998).,1998).
 LBCs. however. have so far proven o be elusive to stb observers (Blain et al.," LBGs, however, have so far proven to be elusive to sub-mm observers (Blain et al."
 2002: Chapman et al., 2002; Chapman et al.
 2000: IIughes et al. 1998).," 2000; Hughes et al, 1998)."
 The recent sub-nuustacked analysis of Τους by Webb et al. (, The recent sub-mm analysis of LBGs by Webb et al. (
2002) oxovides a emu sub-uua 26 detection of only 0.111 ids.,2002) provides a mean sub-mm $2\sigma$ detection of only 0.414 mJy.
 If LDCs cousist of carly generation stellar populations. then low metallicity (SMC-tvpo) dust may be appropriate for modeling their elobal far-IR ciission.," If LBGs consist of early generation stellar populations, then low metallicity (SMC-type) dust may be appropriate for modeling their global far-IR emission."
 This would be cousistent with the metallicity of the leused LBC MS 1512|36-cD58 (Z~1/1Z..) as constrained by Pettini et al. (, This would be consistent with the metallicity of the lensed LBG MS 1512+36-cB58 $Z \sim 1/4 Z_{\odot}$ ) as constrained by Pettini et al. (
2000).,2000).
 We test this idea is with the radiative trausfer dust models of Witt Cordon (2000)., We test this idea is with the radiative transfer dust models of Witt Gordon (2000).
 We compute the expected IRN aud. UV. spectral slope from Starburst99 (Leitherer et al., We compute the expected IRX and UV spectral slope from Starburst99 (Leitherer et al.
 1999) svuthetic starburst spectrum after applving extinction effects based on two Witt Gordon models for SMC-dust in a shell geometry., 1999) synthetic starburst spectrum after applying extinction effects based on two Witt Gordon models for SMC-dust in a shell geometry.
 The first model assmnues a homogeneous dust distribution iu the surrounding dust shell while the second iuvolves a non-homogencous chup! distribution., The first model assumes a homogeneous dust distribution in the surrounding dust shell while the second involves a non-homogeneous 'clumpy' distribution.
 The adopted Starburst99 spectrum is chosen to be consistent with the low aetallicity assumption., The adopted Starburst99 spectrum is chosen to be consistent with the low metallicity assumption.
 It is piruneterized by a continuous star formation rate. a Salpeter IAIF with slope a=—2.35. an upper mass lint of 100 AL... metallicity of Z=0.001. and a burst age of 100 Myr.," It is parameterized by a continuous star formation rate, a Salpeter IMF with slope $\alpha=-2.35$, an upper mass limit of 100 $_{\odot}$, metallicity of $Z=0.004$, and a burst age of 100 Myr."
 The bolometric dust huninosity is computed as the sum of the cnerev from extincted non-ioniziug photons plus the cnerey deposited from«4 Lava photons., The bolometric dust luminosity is computed as the sum of the energy from extincted non-ionizing photons plus the energy deposited from $\alpha$ photons.
 We estimate the Lya production. prior to αν extinction. by assunune that each ionizing photon generates one Lya photon (Osterbrock 1989).," We estimate the $\alpha$ production, prior to any extinction, by assuming that each ionizing photon generates one $\alpha$ photon (Osterbrock 1989)."
 The luuinosity in the FIR baudpass is estimated with DC., The luminosity in the FIR bandpass is estimated with $_{\rm dust}$.
 The resulting UV reddening relation for the homogeucous dust model is similar in shape to the / relation of MIIC99. but has a slightly less steep slope aud is offset to lower values of IRN for a values of ο>2 (dot-dash line of Figure 2).," The resulting UV reddening relation for the homogeneous dust model is similar in shape to the $\beta$ relation of MHC99, but has a slightly less steep slope and is offset to lower values of IRX for a values of $\beta > -2$ (dot-dash line of Figure 2)."
 The UV. reddening relation from the alternative chuupy dust distribution is also qualitatively similar to MIICO9 but. compared to the homogenucous inodoel. rises faster in IRN before it turus," The UV reddening relation from the alternative clumpy dust distribution is also qualitatively similar to MHC99 but, compared to the homogeneous model, rises faster in IRX before it turns"
(Vanture et al.,(Vanture et al.
 2011. in preparation).," 2011, in preparation)."
 We compare the list of S stars with and without Li detections to our FAST sample and analyze them for the Li feature., We compare the list of S stars with and without Li detections to our FAST sample and analyze them for the Li feature.
 Unfortunately. we find that this line cannot be reliably detected with spectra of our resolution and S/N. The AKARI satellite surveyed much of the sky in both near and far infrared bands.," Unfortunately, we find that this line cannot be reliably detected with spectra of our resolution and S/N. The AKARI satellite surveyed much of the sky in both near and far infrared bands."
 We use flux data collected by AKARI in the SOW and LI8W bandpasses to find infrared magnitudes for six objects in the FAST sample without available IRAS colors (Murakamietal.2007;Ishihara2010)..," We use flux data collected by AKARI in the S9W and L18W bandpasses to find infrared magnitudes for six objects in the FAST sample without available IRAS colors \citep{{2007PASJ...59S.369M},{2010A&A...514A...1I}}."
 The SOW and LI8W bandpasses are qualitatively similar to the IRAS 12 and 25 micron bandpasses., The S9W and L18W bandpasses are qualitatively similar to the IRAS 12 and 25 micron bandpasses.
 All available AKARI magnitudes are presented in reftab:mags.. for 52 stars (with two bands available for 35).," All available AKARI magnitudes are presented in \\ref{tab:mags}, for 52 stars (with two bands available for 35)."
 Since the zero magnitude fluxes for these bandpasses are not well established. all magnitudes are presented on the AB system.," Since the zero magnitude fluxes for these bandpasses are not well established, all magnitudes are presented on the AB system."
 In reffig:nearMidIReolors.. we show two color-color diagrams comparing intrinsic and extrinsic stars using K[9]. K-|15]. and [9]2|18] colors.," In \\ref{fig:nearMidIRcolors}, we show two color-color diagrams comparing intrinsic and extrinsic stars using $K-[9]$, $K-[18]$, and $[9]-[18]$ colors."
 S stars previously classified as intrinsic vs. extrinsic are shown in black. with others plotted in red.," S stars previously classified as intrinsic vs. extrinsic are shown in black, with others plotted in red."
 From the AKARI magnitudes and plots. we are able to identify an. additional two stars in the sample as intrinsic or extrinsic.," From the AKARI magnitudes and plots, we are able to identify an additional two stars in the sample as intrinsic or extrinsic."
 We identify 22315839+0201206 as an extrinsic S star., We identify 22315839+0201206 as an extrinsic S star.
 This star has a K—[18] value of —5.92 mag and a [K]—[9] value of —4.23 mag., This star has a $K-[18]$ value of $-5.92$ mag and a $[K]-[9]$ value of $-4.23$ mag.
 This places it in the extreme lower left corner of the color-color diagram comparing K—|9] color to K—[18] color. far away from any known intrinsic stars but close to many known extrinsic stars.," This places it in the extreme lower left corner of the color-color diagram comparing $K-[9]$ color to $K-[18]$ color, far away from any known intrinsic stars but close to many known extrinsic stars."
 Similarly. we are able to identify 1936493745011597 às an intrinsic. S star on the basis of color.," Similarly, we are able to identify 19364937+5011597 as an intrinsic S star on the basis of color."
 This star has a AK—[9] value of only —3.09 mag. and a K—[18] value of —4.01 mag.," This star has a $K-[9]$ value of only $-3.09$ mag, and a $K-[18]$ value of $-4.01$ mag."
 This places it in the upper right-hand corner of the plot comparing K—[9] and and K—-[18] color. far away from the cluster of extrinsic S stars.," This places it in the upper right-hand corner of the plot comparing $K-[9]$ and and $K-[18]$ color, far away from the cluster of extrinsic S stars."
 The four other stars for which we have no classification (035057044+0654325. 10505517+0429583. 132118734+4359136. and 16370314+0722207) cluster close to the transition between intrinsic and extrinsic S stars in all three color comparisons. meaning that we cannot confidently identify these with either class of stars.," The four other stars for which we have no classification (03505704+0654325, 10505517+0429583, 13211873+4359136, and 16370314+0722207) cluster close to the transition between intrinsic and extrinsic S stars in all three color comparisons, meaning that we cannot confidently identify these with either class of stars."
 We include our additional identifications in reftab:stars.. marked with an asterisk to distinguish them from those from Yangetal.(2006).," We include our additional identifications in \\ref{tab:stars}, marked with an asterisk to distinguish them from those from \citet{2006AJ....132.1468Y}."
 As mentioned before. S stars cover a wide range of spectral types and effective temperatures.," As mentioned before, S stars cover a wide range of spectral types and effective temperatures."
 However. they generally have effective temperatures similar to those of M giants.," However, they generally have effective temperatures similar to those of M giants."
 The starting point for classifying the spectral type and temperatures of our S stars. therefore. is to calculate a temperature index using M-giant eriterta (GrayandCorvally 2009)..," The starting point for classifying the spectral type and temperatures of our S stars, therefore, is to calculate a temperature index using M-giant criteria \citep{Gray09}. ."
 Houdasheltetal.(2000) use a grid of stellar models to calibrate a relation between color and temperature index for M stars., \citet{2000AJ....119.1424H} use a grid of stellar models to calibrate a relation between color and temperature index for M stars.
 Their analysis uses CIT/CTIO colors V—K and J—K., Their analysis uses CIT/CTIO colors $V-K$ and $J-K$.
 We find V magnitudes for some of the FAST sample using Simbad., We find $V$ magnitudes for some of the FAST sample using Simbad.
" We also convert the 2MASS K, magnitudes and J—K, colors using the following relations from We then use the temperature index/color relation to assign a preliminary temperature index to the stars in the FAST sample.", We also convert the 2MASS $_s$ magnitudes and $J-K_s$ colors using the following relations from We then use the temperature index/color relation to assign a preliminary temperature index to the stars in the FAST sample.
 Where possible. we use the (V—Κο relation. since this is specified by the authors as the most temperature sensitive.," Where possible, we use the $(V-K)_{CIT}$ relation, since this is specified by the authors as the most temperature sensitive."
 When there is no V. magnitude available. we use the (J—Κο relation (Houdasheltetal.2000)..," When there is no $V$ magnitude available, we use the $(J-K)_{CIT}$ relation \citep{2000AJ....119.1424H}."
 Results of this analysis are presentedin reftab:stars.., Results of this analysis are presentedin \\ref{tab:stars}.
 These temperature indices should be treated with caution. since many of the stars in the FAST sample are highly variable.," These temperature indices should be treated with caution, since many of the stars in the FAST sample are highly variable."
 Furthermore. differences in. C/O ratios. may lead to temperature errors up to KK (VanEcketal.2010)..," Furthermore, differences in C/O ratios, may lead to temperature errors up to K \citep{2010arXiv1011.2092V}."
 However. the preliminary classification gives us a rough idea of the relative effective temperatures of the S stars.," However, the preliminary classification gives us a rough idea of the relative effective temperatures of the S stars."
 We find that the average temperature index of the stars in the sample 1s 5. which in M giants corresponds to an effective temperature of roughly 3500 K (Houdasheltetal.2000)..," We find that the average temperature index of the stars in the sample is 5, which in M giants corresponds to an effective temperature of roughly 3500 K \citep{2000AJ....119.1424H}."
 In reftab:stars.. we also present known spectral types from Keenan&Boeshaar(1980).. which include temperature indices for the S stars.," In \\ref{tab:stars}, we also present known spectral types from \citet{1980ApJS...43..379K}, which include temperature indices for the S stars."
 We find reasonably good agreement between our calculated temperature indices and. those presented as part of the spectral type., We find reasonably good agreement between our calculated temperature indices and those presented as part of the spectral type.
 Differences between our temperature index and those included às part of the published spectral types are within the range of variability of the star., Differences between our temperature index and those included as part of the published spectral types are within the range of variability of the star.
 We also note that since we do not have a reliable color/temperature relation for stars with a temperature index greater than 7. we present all of these classes as 74.," We also note that since we do not have a reliable color/temperature relation for stars with a temperature index greater than 7, we present all of these classes as 7+."
 We also find reasonably good agreement (within one temperature index) between the values using (V—Κο and those derived using (Κο., We also find reasonably good agreement (within one temperature index) between the values using $(V-K)_{CIT}$ and those derived using $(J-K)_{CIT}$.
 We also conduct a preliminary analysis on. possible correlations between the intrinsic/extrinsie distinction and the temperature indices., We also conduct a preliminary analysis on possible correlations between the intrinsic/extrinsic distinction and the temperature indices.
 We find that the average temperature index of the intrinsic stars is 5.6c2.3. while the average temperature index of extrinsic stars is 4.3+2.2.," We find that the average temperature index of the intrinsic stars is $5.6\pm2.3$, while the average temperature index of extrinsic stars is $4.3\pm2.2$."
 Therefore. while the mean temperature index shows some differences. this measurement alone is not statistically significant.," Therefore, while the mean temperature index shows some differences, this measurement alone is not statistically significant."
 A larger sample would be needed to determine the validity of differences between average effective temperature between intrinsic and extrinsic S stars., A larger sample would be needed to determine the validity of differences between average effective temperature between intrinsic and extrinsic S stars.
 The temperature indices of S stars in general are insufficient to classify them as intrinsic or extrinsic. except for the reddest objects.," The temperature indices of S stars in general are insufficient to classify them as intrinsic or extrinsic, except for the reddest objects."
 Four of the stars in the original FAST sample have reliable parallax measurements (defined as a parallax detection at the 3c level) available from the Hipparcos survey (Perryman 1997).. so calculation of the absolute magnitude of these stars in the g and r bands is possible.," Four of the stars in the original FAST sample have reliable parallax measurements (defined as a parallax detection at the $3\,\sigma$ level) available from the Hipparcos survey \citep{1997A&A...323L..49P}, so calculation of the absolute magnitude of these stars in the $g$ and $r$ bands is possible."
" We calculate the error inour absolute magnitudes using the presented error in the parallax measurements and assuming apparent magnitude error values of c,=0.191 and a,= 0.192.", We calculate the error inour absolute magnitudes using the presented error in the parallax measurements and assuming apparent magnitude error values of $ \sigma{_g} = 0.191 $ and $ \sigma{_r} = 0.192 $ .
 Results of this analysis are given in reftab:plx.., Results of this analysis are given in \\ref{tab:plx}. .
 We note the calculated absolute g and r , We note the calculated absolute $g$ and $r$ 
Under the assumption. that the nonthermal emission originates from a central active nucleus heavily obscured by dust and gas. and that hot plasma has expanded into the outer parts of NGC 4410a. we fit the RS+PO model with different column density values for each component.,"Under the assumption, that the nonthermal emission originates from a central active nucleus heavily obscured by dust and gas, and that hot plasma has expanded into the outer parts of NGC 4410a, we fit the RS+PO model with different column density values for each component."
 One would expecta column density ηνoNica for the less obscured plasma outflow and a much higher προ for the AGN because of the intrinsic absorption within the NGC 4410 nucleus.," One would expect a column density $N_\mathrm{H,RS} \approx N_\mathrm{H,Gal}$ for the less obscured plasma outflow and a much higher $N_\mathrm{H,PO}$ for the AGN because of the intrinsic absorption within the NGC 4410 nucleus."
" While we apply Nips = πιο = 7 for the RS component. Nj,po for the PO component is set to 7."," While we apply $N_\mathrm{H,RS}$ = $N_\mathrm{H,Gal}$ = $^{-2}$ for the RS component, $N_\mathrm{H,PO}$ for the PO component is set to $^{-2}$."
 This yields the best fit for a lower plasma temperature of K and a very steep power-law for the central AGN with [ = 4.24 (see Fig., This yields the best fit for a lower plasma temperature of K and a very steep power-law for the central AGN with $\Gamma$ = 4.24 (see Fig.
 11)., 11).
 In the very soft range (0.1-0.3 keV) the spectrum is determined by the intrisically unobscured RS component., In the very soft range (0.1-0.3 keV) the spectrum is determined by the intrisically unobscured RS component.
 Raising the absorption for the PO component prohibits its contribution to the soft spectral range.," Raising the absorption for the PO component prohibits its contribution to the soft spectral range,"
The mass distribution of white dwarls (WDs) in the solar neighborhood peaks at ~0.6,The mass distribution of white dwarfs (WDs) in the solar neighborhood peaks at $\sim$ 0.6
As we have shown in Sect.,As we have shown in Sect.
 3. a warm absorber model represents the formally best description of the PSPC spectrum of13349+2438.," 3, a warm absorber model represents the formally best description of the PSPC spectrum of."
. The systematic structures in the residuals almost completely disappear and. in addition. the spectral shape of the intrinsic. X-ray continuum is consistent with the hard X-ray spectrum as observed with ASCA (D— 2.3).," The systematic structures in the residuals almost completely disappear and, in addition, the spectral shape of the intrinsic X-ray continuum is consistent with the hard X-ray spectrum as observed with ASCA $\Gamma\approx 2.3$ )."
 We further note that applying the dust-free warm absorber model we also obtain a viable description of the ASCA data. although with significantly different physical parameters for the warm absorber as compared to the ROSAT PSPC results.," We further note that applying the dust-free warm absorber model we also obtain a viable description of the ASCA data, although with significantly different physical parameters for the warm absorber as compared to the ROSAT PSPC results."
 The energy of the absorption edge is significantly lower in the ASCA data and consistent withVII. whereas the PSPC data clearly favorVII.," The energy of the absorption edge is significantly lower in the ASCA data and consistent with, whereas the PSPC data clearly favor."
.. Furthermore. the optical depth of the absorption edge is much higher in the PSPC data and. consequently. the column density of the warm absorber derived from the ROSAT observations (log Ay.=22.7d: 0.2) is abou= an order of magnitude higher than in the ASCA observatioαυ] dog Ny=21.590-2: Brandt et al.," Furthermore, the optical depth of the absorption edge is much higher in the PSPC data and, consequently, the column density of the warm absorber derived from the ROSAT observations (log $N_{\rm w} = 22.7\pm 0.2$ ) is about an order of magnitude higher than in the ASCA observation (log $N_{\rm w} = 
21.59^{+0.15}_{-0.26}$; Brandt et al."
 1997)., 1997).
 The rapid X-ray variability observed in undicates. changes in the ionizing continuum and thus a variable ionization state of the warm absorber is not unlikely., The rapid X-ray variability observed in indicates changes in the ionizing continuum and thus a variable ionization state of the warm absorber is not unlikely.
 This might explain the change in the absorption edge energy as wwas about a factor of four brighter in. X-rays during the second ROSAT observation (P2) as compared to the ASCA observation., This might explain the change in the absorption edge energy as was about a factor of four brighter in X-rays during the second ROSAT observation (P2) as compared to the ASCA observation.
 In the bright state. most of the oxygen Is ionized toVIEL.," In the bright state, most of the oxygen is ionized to."
 When the ionizing flux decreases. the lions recombine to aand the observed absorption edge energy decreases.," When the ionizing flux decreases, the ions recombine to and the observed absorption edge energy decreases."
 This kind of variation of the ionization state of the warm absorber has also been claimed for the Seyfert 1 galaxy MCG-06-30-15 (Reynolds et al. 1995::, This kind of variation of the ionization state of the warm absorber has also been claimed for the Seyfert 1 galaxy MCG–06–30–15 (Reynolds et al. \cite{reynolds};
 Otani et al. 1996))., Otani et al. \cite{otani}) ).
 The first PSPC observation (PT). when wwas In a state comparable to the ASCA observation. suffers from low photon statistics and although the resulting spectral parameters of the dust-free warm absorber model are consistent with P2 we note that the higher ra (1.05 compared to 0.84) might indicate spectral changes.," The first PSPC observation (P1), when was in a state comparable to the ASCA observation, suffers from low photon statistics and although the resulting spectral parameters of the dust-free warm absorber model are consistent with P2 we note that the higher $\chi^2_{\rm red}$ (1.05 compared to 0.84) might indicate spectral changes."
 Apart from changes in the ionization state. the differences between the ASCA and ROSAT spectra also require a change in the column density of the ionized material of at least 1.«107? > between the two observations. i.e. within about 3 years.," Apart from changes in the ionization state, the differences between the ASCA and ROSAT spectra also require a change in the column density of the ionized material of at least $4\times 10^{22}$ $^{-2}$ between the two observations, i.e. within about 3 years."
 One might speculate that isolated clouds of tonized material stripped off the torus and moving across the line of sight could be responsible for such a change in column density., One might speculate that isolated clouds of ionized material stripped off the torus and moving across the line of sight could be responsible for such a change in column density.
 A principal difficulty of any dust-free warm absorber model of course Is to explain the discrepancy between the observed amount of optical reddening and the absence of any cold X-ray absorption., A principal difficulty of any dust-free warm absorber model of course is to explain the discrepancy between the observed amount of optical reddening and the absence of any cold X-ray absorption.
 Apart from postulating atypical gas-to-dust ratios in wwe might think of two possible ways out: variable optical extinctiol and different paths for the optical and the X-ray radiation., Apart from postulating atypical gas-to-dust ratios in we might think of two possible ways out: variable optical extinction and different paths for the optical and the X-ray radiation.
 With regard to the first possibility we note that the X-ray and the optical observations were not simultaneous and therefore variable optical extinction cannot be excluded., With regard to the first possibility we note that the X-ray and the optical observations were not simultaneous and therefore variable optical extinction cannot be excluded.
 In fact. changes in the reddening of emission lines in Seyfert 1.8 galaxies on a time scale of years were reported by Goodrich (1989a.. 1990)) and interpreted in. terms of moving.cold obscuring material.," In fact, changes in the reddening of emission lines in Seyfert 1.8 galaxies on a time scale of years were reported by Goodrich \cite{goodrich89a}, \cite{goodrich90}) ) and interpreted in terms of moving obscuring material."
 On the other hand. no changes in the optical extinction have been observed up to now (Wills et al. 1992:;," On the other hand, no changes in the optical extinction have been observed up to now (Wills et al. \cite{wills};"
 Lanzetta et al. 1993)), Lanzetta et al. \cite{lanzetta}) )
 and the preliminary results of recent spectroscopic observations of (Leighly. priv.," and the preliminary results of recent spectroscopic observations of (Leighly, priv."
 com.:, com.;
 Papadakis. priv.," Papadakis, priv."
 com.), com.)
 are completely consistent with the original Wills et al. (1992)), are completely consistent with the original Wills et al. \cite{wills}) )
 results., results.
 Furthermore. the amount of cold absorption measured. with the ROSAT PSPC and ASCA is always consistent with the Galactic value and does not indicate variable cold absorption.," Furthermore, the amount of cold absorption measured with the ROSAT PSPC and ASCA is always consistent with the Galactic value and does not indicate variable cold absorption."
 Both results favor constant optical. extinction., Both results favor constant optical extinction.
.. Obviously. soft. X-ray and optical observations of aare required to ultimately decide whether variable optical extinction plays a role. but based on current observations this seems highly unlikely.," Obviously, soft X-ray and optical observations of are required to ultimately decide whether variable optical extinction plays a role, but based on current observations this seems highly unlikely."
 An alternative explanation for the apparent discrepancy between optical and cold X-ray absorption would be a special geometry. in which the optical and the X-ray continuum do not travel along the same paths to the observer.," An alternative explanation for the apparent discrepancy between optical and cold X-ray absorption would be a special geometry, in which the optical and the X-ray continuum do not travel along the same paths to the observer."
 Since the observed rapid X-ray variability of eeffectively excludes a significant contribution of scattered X-rays. one might invoke a partial covering geometry. where the optical continuum happens to pass through a lower total column density of obscuring material.," Since the observed rapid X-ray variability of effectively excludes a significant contribution of scattered X-rays, one might invoke a partial covering geometry, where the optical continuum happens to pass through a lower total column density of obscuring material."
 Although such a scenario might be constructed for a single object. this approach becomes increasingly contrived in the light of the growing number objects. for which a ‘simple’ dusty warm absorber provides a consistent explanation of the X-ray and optical properties (e.g.. NGC 3227. NGC 3786. IRAS 1702044544).," Although such a scenario might be constructed for a single object, this approach becomes increasingly contrived in the light of the growing number objects, for which a 'simple' dusty warm absorber provides a consistent explanation of the X-ray and optical properties (e.g., NGC 3227, NGC 3786, IRAS 17020+4544)."
 We therefore now turn to the dusty warm absorber hypothesis., We therefore now turn to the dusty warm absorber hypothesis.
 The prime argument for the presence of dust within the warm absorber is the apparent discrepancy between the observed optical extinction and the absence of cold absorption in the X-ray spectrum., The prime argument for the presence of dust within the warm absorber is the apparent discrepancy between the observed optical extinction and the absence of cold absorption in the X-ray spectrum.
 Furthermore. as we have shown in Sect.4.2. a self-consistent Galactic-ISM dusty warm absorber model ts a reasonable representation of the ASCA spectrum of aand the column density of the warm absorber determined by spectral fitting 1s consistent with the derived from optical reddening.," Furthermore, as we have shown in Sect.4.2, a self-consistent Galactic-ISM dusty warm absorber model is a reasonable representation of the ASCA spectrum of and the column density of the warm absorber determined by spectral fitting is consistent with the derived from optical reddening."
 We note. however. that the ASCA spectrum Is not very sensitive to the dustiness of the warm absorber. since the most important features (ike the Carbon absorption edge) are expected below 0.6 keV. Nevertheless. the absence of a strong," We note, however, that the ASCA spectrum is not very sensitive to the dustiness of the warm absorber, since the most important features (like the Carbon absorption edge) are expected below 0.6 keV. Nevertheless, the absence of a strong"
manv precise TOAs could be measured.,many precise TOAs could be measured.
 Timing solutions were constructed by performing a weighted fit to the data using (?) with the DE405 Solar Svstem ephemeris and TT(BIPM2011) time standard., Timing solutions were constructed by performing a weighted fit to the data using \citep{ehm06} with the DE405 Solar System ephemeris and TT(BIPM2011) time standard.
 All values are reported in Darvcentric Dynamical Time., All values are reported in Barycentric Dynamical Time.
 It is not uncommon for timing moclels to have a reduced \?>1 (424) even alter all parameters have been well measured., It is not uncommon for timing models to have a reduced $\chi^2 > 1$ $\chi^2\rmsub{red}$ ) even after all parameters have been well measured.
" When no systematic trends are present in the data. it is assumed that this value of AZ, is due to an underestimate of the error on individual TOAs."," When no systematic trends are present in the data, it is assumed that this value of $\chi^2\rmsub{red}$ is due to an underestimate of the error on individual TOAs."
" As is common practice. we deal with this situation by multiplying TOA errors by a small constant error [actor so that AZ,=1."," As is common practice, we deal with this situation by multiplying TOA errors by a small constant error factor so that $\chi^2\rmsub{red} = 1$."
 MSPs have a small intrinsic rate of spin-down >) that is usually heavily contaminated by accelerations within the potential of the cluster and Galaxy (?).., MSPs have a small intrinsic rate of spin-down $\dot{P}\rmsub{int}$ ) that is usually heavily contaminated by accelerations within the potential of the cluster and Galaxy \citep{phi93}.
 This makes it impossible {ο measure their spin-down related properties (surface magnetic field. spin-down luminosity. and characteristic age) directly.," This makes it impossible to measure their spin-down related properties (surface magnetic field, spin-down luminosity, and characteristic age) directly."
" Instead. we caleulate the limit where P is (he pulsar period. e444, and ec; are the accelerations due to the cluster ancl Galaxy. respectively. ji is the proper motion. D is the distance to the cluster. and e is the speed of light (the last termi accounts for the Shklovskii effect (2)))."," Instead, we calculate the limit where $P$ is the pulsar period, $a\rmsub{c,max}$ and $a\rmsub{G}$ are the accelerations due to the cluster and Galaxy, respectively, $\mu$ is the proper motion, $D$ is the distance to the cluster, and $c$ is the speed of light (the last term accounts for the Shklovskii effect \citep{shk70}) )."
" 2?9 showed that to within accuracy. for Ay,<2I. where o, is the central velocity dispersion. [ο is the core radius. and Ryo» is Che projected distance of the pulsar from the center of the cluster."," \citet{phi92,phi93} showed that to within accuracy, for $R\rmsub{psr} < 2 R\rmsub{c}$, where $\sigma_v$ is the central velocity dispersion, $R\rmsub{c}$ is the core radius, and $R\rmsub{psr}$ is the projected distance of the pulsar from the center of the cluster."
 Because all three of the clusters studied here are core collapsed. analvlical (?) απ numerical models are nol applicable. which is why we use the approximations of ?..," Because all three of the clusters studied here are core collapsed, analytical \citep{fhn+05} and numerical models are not applicable, which is why we use the approximations of \citeauthor{phi92}."
 These were developed for use with pulsars in M15. which is also core collapsed.," These were developed for use with pulsars in M15, which is also core collapsed."
 We use the values of A4 found in edition.., We use the values of $R\rmsub{c}$ found in \citet[2010 edition]{har96}.
 The following references are used for σε: ?.2010edition. lor M62: ? lor NGC 6544: and ? jor NGC 6624., The following references are used for $\sigma_v$: \citet[2010 edition]{har96} for M62; \citet{web85} for NGC 6544; and \citet{vor11} for NGC 6624.
 Table 2. lists the relevant properties of each cluster., Table \ref{table:gcs} lists the relevant properties of each cluster.
 The Galactic contribution is calculated under the approximation of a spherically svimmetric Galaxy. with a [lat rotation curve (2). and is, The Galactic contribution is calculated under the approximation of a spherically symmetric Galaxy with a flat rotation curve \citep{phi93} and is
In these units. velocity is measured in units of e]=ηHee (op equivalently: e7=η).,"In these units, velocity is measured in units of $[v] = n^{-1/2} c$ (or equivalently $c^2 = n$ )."
 The scaled equations are thus given simply bysetting G@=Al1 and e=n everywhere., The scaled equations are thus given simply bysetting $G=M=1$ and $c^2=n$ everywhere.
 This scaling ensures that the relativistic terms tend to zero when e (or n) is large and that the numerical values of p. pu and C are of order unity.," This scaling ensures that the relativistic terms tend to zero when $c$ (or $n$ ) is large and that the numerical values of $\rho$, $\rho
u$ and $U^r$ are of order unity."
 We thus specify the degree to which the eravity/eas dynamics is relativistic by specifving the value of à the proximity of the innermost radius. and thus the heating. to the Sebwarzschild radius. Ag=26Mfc).," We thus specify the degree to which the gravity/gas dynamics is relativistic by specifying the value of $n$ the proximity of the innermost radius, and thus the heating, to the Schwarzschild radius, $R_{\rm Sch} = 2GM/c^2$ )."
" We compute solutions corresponding to gas very close to a black hole (highly relativistic. η=2.0. or Ay=fg). neutron star (moderately relativistic. n=5. or By=Hs5Mο. which is equivalent to heating further out and. over a wider region around a black hole) and white dwarl/non-relativistic star (essentially non-relativistic. n=5000. or £2,=250044)."," We compute solutions corresponding to gas very close to a black hole (highly relativistic, $n=2.0$, or $R_* = R_{\rm Sch}$ ), neutron star (moderately relativistic, $n=5$, or $R_* = R_{\rm NS} = 5GM/c^2$, which is equivalent to heating further out and over a wider region around a black hole) and white dwarf/non-relativistic star (essentially non-relativistic, $n=5000$ , or $R_* = 2500 R_{\rm
Sch}$ )."
 Note that in the highly relativistic case although we scale the solution to η=2.0 such that the mass. length and time scales (and therefore the units of heating rate. energy ete.)," Note that in the highly relativistic case although we scale the solution to $n=2.0$ such that the mass, length and time scales (and therefore the units of heating rate, energy etc.)"
 correspond to those at r=fg. our numerical grid cannot begin at 7; as it does in the other cases.," correspond to those at $r=R_{\rm Sch}$, our numerical grid cannot begin at $R_*$ as it does in the other cases."
 We therefore set the lower bound on the racial grid to slightly below the heating shell (typically r=LOLA. where the heating begins at 1.111).," We therefore set the lower bound on the radial grid to slightly below the heating shell (typically $r =
1.01R_*$ where the heating begins at $1.1R_*$ )."
 Note that the above scaling is merely to ensure that the numerical solution is of order unity. since we scale in terms of dimensionless variables to compare with the non-relativistic solution.," Note that the above scaling is merely to ensure that the numerical solution is of order unity, since we scale in terms of dimensionless variables to compare with the non-relativistic solution."
 In order to solve the relativistic [uid equations numerically we use a method analogous to that used in the non-relativistic case (Figure Al))., In order to solve the relativistic fluid equations numerically we use a method analogous to that used in the non-relativistic case (Figure \ref{fig:scheme}) ).
 That is. we first compute C7 on the staggered (half) ericl and. use this to solve for p and py on the integer erid points.," That is, we first compute $U^r$ on the staggered (half) grid and use this to solve for $\rho$ and $\rho u$ on the integer grid points."
" Again the advective terms are cliseretizecl using upwinel dillerences (where the ""upsindedness! is determined from the sign of the co-ordinate velocity 0) and other derivatives are calculated using centred dillerences.", Again the advective terms are discretized using upwind differences (where the `upwindedness' is determined from the sign of the co-ordinate velocity $v^r$ ) and other derivatives are calculated using centred differences.
 As in the non-relativistic case. where a centred dilference is used. the quantities multiplving the derivative are interpolated onto the half grid. points if necessary.," As in the non-relativistic case, where a centred difference is used, the quantities multiplying the derivative are interpolated onto the half grid points if necessary."
 In equation (41)) we evaluate the OPὃν term using upwind differences.," In equation \ref{eq:relctyuse}) ) we evaluate the $\partial
P/\partial r$ term using upwind differences."
 We determine initial conditions for the relativistic case by setting (€=0 and 0/0E=0 in (39)). [rom which we have The pressure is thus caleulated as a function of p. & and P (where P=(+ Ίρις," We determine initial conditions for the relativistic case by setting $U^r = 0$ and $\partial/\partial t=0$ in \ref{eq:relmomuse}) ), from which we have The pressure is thus calculated as a function of $\rho$, $u$ and $P$ (where $P = (\gamma-1)\rho u$ )."
 We solve (48)) using the same assumptions as in the non-relativistic case refsec:nrinit)). that is an adiabatic atmosphere such that We therefore have which we solve using a first order (I2uler) cdiscretization to obtain a density profile.," We solve \ref{eq:reldPdr}) ) using the same assumptions as in the non-relativistic case \\ref{sec:nrinit}) ), that is an adiabatic atmosphere such that We therefore have which we solve using a first order (Euler) discretization to obtain a density profile."
 Phe pressure may then be caleulatec using (49)). however to ensure that hydrostatie equilibrium is enforced numerically we solve (48)) using the same cliscretization as in the fluid equations. integrating inwards from the outer boundary condition P(ru)=pira).," The pressure may then be calculated using \ref{eq:relpadiabatic}) ), however to ensure that hydrostatic equilibrium is enforced numerically we solve \ref{eq:reldPdr}) ) using the same discretization as in the fluid equations, integrating inwards from the outer boundary condition $P(r_{\rm max})=K\rho(r_{\rm max})^{\gamma}$."
" However in this case the pressure eracdient also depends on the pressure. so we use the pressure calculated from (49)) to caleulate the initial value of the specific enthalpy f and iterate the solution until converged P""1PEP""<10 101 "," However in this case the pressure gradient also depends on the pressure, so we use the pressure calculated from \ref{eq:relpadiabatic}) ) to calculate the initial value of the specific enthalpy $h$ and iterate the solution until converged $[P^{n+1}-P^n]/P^n < 10^{-10}$ )."
[In the black hole case the resulting pressure dilfers from that found using (49)) bv PIP~LO?., In the black hole case the resulting pressure differs from that found using \ref{eq:relpadiabatic}) ) by $\Delta P/P \sim 10^{-2}$.
 We choose A such that the central density is of order unity tvpically we use A=105/(5.—1) in the black hole case.," We choose $K$ such that the central density is of order unity – typically we use $K =
10\gamma/(\gamma-1)$ in the black hole case."
 Note that changing A simply changes the amount of matter presen in the atmosphere but does not alfect the temperature scaling and does not alfect the final results (although it significantly alloects the integration time since it determines the strength of the shock front and the amount of mass to be accelerated)., Note that changing $K$ simply changes the amount of matter present in the atmosphere but does not affect the temperature scaling and does not affect the final results (although it significantly affects the integration time since it determines the strength of the shock front and the amount of mass to be accelerated).
 Initial conditions caleulated in this manner for the black hole (2./Isa=n/2 1.0) and neutron star (IfBea= 2.5) atmospheres are shown in Figure 6.., Initial conditions calculated in this manner for the black hole $R_*/R_{\rm Sch} = n/2 =1.0$ ) and neutron star $R_*/R_{\rm Sch}=2.5$ ) atmospheres are shown in Figure \ref{fig:relinit}.
 Phe initial setup reduces to that of Figure 1. in the non-relativistic limit when the same value of A is used., The initial setup reduces to that of Figure \ref{fig:nrinit} in the non-relativistic limit when the same value of $K$ is used.
 We set the outer boundary at ff.=107. using 1335 radial grid points (again on a logarithmic grid)," We set the outer boundary at $r/R_* = 10^4$, using 1335 radial grid points (again on a logarithmic grid)."
 The results of a typical (n=2.0) relativistic simulation are shown in Figure 7 at /= 1000., The results of a typical (n=2.0) relativistic simulation are shown in Figure \ref{fig:relresults} at $t=1000$ .
 Again we observe that the wind structure reaches a quasi-steady state. with the velocityapproaching a steady value at large radii.," Again we observe that the wind structure reaches a quasi-steady state, with the velocityapproaching a steady value at large radii."
 Note that because the steady state density is higher than that of the surrounding medium no wide shock front is observed., Note that because the steady state density is higher than that of the surrounding medium no wide shock front is observed.
 Plotting3 the mass outflow rate AL=4x17fpC7. and the relativistic Bernoulli energv3. £4=i177fetole (see em.," Plotting the mass outflow rate $\dot{M} = 4\pi r^2\rho U^r$ and the relativistic Bernoulli energy $E_{\rm rel} = \frac{1}{2}\Gamma^2
h^2/c^2 - \frac{1}{2}c^2$ (see e.g."
 Plotting3 the mass outflow rate AL=4x17fpC7. and the relativistic Bernoulli energv3. £4=i177fetole (see em.3," Plotting the mass outflow rate $\dot{M} = 4\pi r^2\rho U^r$ and the relativistic Bernoulli energy $E_{\rm rel} = \frac{1}{2}\Gamma^2
h^2/c^2 - \frac{1}{2}c^2$ (see e.g."
Algol (Bachmann Hershey 1975). the LTT analysis can be complemented with astrometry to yield the orbital inclination and thus the actual mass and semi-major axis of the third body.,"Algol (Bachmann Hershey 1975), the LTT analysis can be complemented with astrometry to yield the orbital inclination and thus the actual mass and semi-major axis of the third body."
 Furthermore. with the orbital properties (P. ο and νο) known from the LTT analysis. only a small fraction of the astrometric orbit needs to be covered when using high-accuracy astrometry.," Furthermore, with the orbital properties $P$ , $e$ and $\omega$ ) known from the LTT analysis, only a small fraction of the astrometric orbit needs to be covered when using high-accuracy astrometry."
 In this paper we present the results of the combined LTT analysis and Hipparcos astrometry of the Algol-type eclipsing binary R CMa., In this paper we present the results of the combined LTT analysis and Hipparcos astrometry of the Algol-type eclipsing binary R CMa.
 The residuals of over 150 eclipse timings extending from 1887 to 2001 show a periodic (~93 yr) quasi- modulation., The residuals of over 150 eclipse timings extending from 1887 to 2001 show a periodic $\sim$ 93 yr) quasi-sinusoidal modulation.
 As previously shown by Radhakrishnan. Sarma. Abhyankar (1984) and Demirean (2000). these variations are best explained by the LTT effect arising from the gravitational influence of a third body.," As previously shown by Radhakrishnan, Sarma, Abhyankar (1984) and Demircan (2000), these variations are best explained by the LTT effect arising from the gravitational influence of a third body."
 The Hipparcos astrometry also shows the presence of small but significant acceleration terms in the proper motion components explicable by the reflex motion from a third body., The Hipparcos astrometry also shows the presence of small but significant acceleration terms in the proper motion components explicable by the reflex motion from a third body.
 Our study illustrates that with a well-defined LTT effect. only a few years of accurate astrometry are needed to constrain the orbital solution and determine the mass of the third body.," Our study illustrates that with a well-defined LTT effect, only a few years of accurate astrometry are needed to constrain the orbital solution and determine the mass of the third body."
 R Canis Majoris (HD 57167. HR 2788. HIP 35487) is a bright (Ving25.67 mag). semi-detached eclipsing binary having an orbital period of 1.1359 days.," R Canis Majoris (HD 57167, HR 2788, HIP 35487) is a bright $V_{\rm max}=5.67$ mag), semi-detached eclipsing binary having an orbital period of 1.1359 days."
 As pointed out by Varricatt Ashok (1999). R CMa holds special status among Algol systems in that it is the system with the lowest known total mass and hosting the least massive secondary star.," As pointed out by Varricatt Ashok (1999), R CMa holds special status among Algol systems in that it is the system with the lowest known total mass and hosting the least massive secondary star."
 Since the discovery of its variability in 1887 by Sawyer (1887). R CMa has been frequently observed and has well determined orbital and physical properties.," Since the discovery of its variability in 1887 by Sawyer (1887), R CMa has been frequently observed and has well determined orbital and physical properties."
 The major breakthrough in understanding the system came when Tomkin (1985) was able to measure the very weak absorption lines of the faint secondary star and determine the masses of the two stars from a double line radial velocity study., The major breakthrough in understanding the system came when Tomkin (1985) was able to measure the very weak absorption lines of the faint secondary star and determine the masses of the two stars from a double line radial velocity study.
" The analyses of its light and radial velocity curves (see Varricatt Ashok 1999) show that this system has a circular orbit and consists of a nearly spherical IV star (Mj= 1.0740.2M..R)=148400 R.: 1...=5.78+ 0.38) and a low mass. tidally-distorted K2-3 IV. star (M;20.170.02 M.. Ro=1.06+0.07 Ro: L;/L.,=0.43+ 0.10)."," The analyses of its light and radial velocity curves (see Varricatt Ashok 1999) show that this system has a circular orbit and consists of a nearly spherical F0-1 V star $M_1=1.07\pm0.2$ $_{\odot}$ ; $R_1=1.48\pm0.10$ $_{\odot}$; $L_1/{\rm 
L}_{\odot}=5.78\pm0.38$ ) and a low mass, tidally-distorted K2-3 IV star $M_2=0.17\pm0.02$ $_{\odot}$; $R_2=1.06\pm0.07$ $_{\odot}$; $L_2/{\rm 
L}_{\odot}=0.43\pm0.10$ )."
 Moreover. nearly every photometric study indicates that the cooler star fills its inner Lagrangian surface.," Moreover, nearly every photometric study indicates that the cooler star fills its inner Lagrangian surface."
 The relatively high space motions (S=67 km s) suggest that R CMa is a member of the old disk population and thus a fairly old (5-7 Gyr) star (Guinan [anna 1983)., The relatively high space motions $S=67$ km $^{-1}$ ) suggest that R CMa is a member of the old disk population and thus a fairly old (5–7 Gyr) star (Guinan Ianna 1983).
 The present state of the system is best explained as a low mass Algol system that has undergone mass exchange and extensive mass loss., The present state of the system is best explained as a low mass Algol system that has undergone mass exchange and extensive mass loss.
 Asymmetries in its light curves and subtle spectroscopic anomalies indicate that mass exchange and loss are still continuing but at a much diminished rate compared to most Algol systems., Asymmetries in its light curves and subtle spectroscopic anomalies indicate that mass exchange and loss are still continuing but at a much diminished rate compared to most Algol systems.
 The very low mass of the secondary star and old disk age indicate that R CMa is near the end of its life as an Algol system., The very low mass of the secondary star and old disk age indicate that R CMa is near the end of its life as an Algol system.
 As in the case of all Algol systems. the secondary star lies well above the main-sequence.," As in the case of all Algol systems, the secondary star lies well above the main-sequence."
 However. unlike most Algol systems. the primary star is too hot and overluminous for observed mass.," However, unlike most Algol systems, the primary star is too hot and overluminous for observed mass."
" Moreover. a recent analysis of older photometry of R CMa by Mkrtichian Gamarova (2000) indicates that the F star is a low-amplitude 6 Scuti variable with a B light amplitude of 9 millimagnitudes and a period of 68 minutes,"," Moreover, a recent analysis of older photometry of R CMa by Mkrtichian Gamarova (2000) indicates that the F star is a low-amplitude $\delta$ Scuti variable with a B light amplitude of 9 millimagnitudes and a period of 68 minutes."
 Hipparcos observed R CMa between March 9. 1990 and March 5. 1993.," Hipparcos observed R CMa between March 9, 1990 and March 5, 1993."
 There are 68 one-dimensional astrometric measurements corresponding to 35. different epochs in the Hippareos Intermediate Astrometric Data. which were obtained by the two Hipparcos Data Reduction Consortia (33 measurements from FAST and 35 from NDAC).," There are 68 one-dimensional astrometric measurements corresponding to 35 different epochs in the Hipparcos Intermediate Astrometric Data, which were obtained by the two Hipparcos Data Reduction Consortia (33 measurements from FAST and 35 from NDAC)."
 The astrometric data can be obtained from CD-ROM 5 of the Hippareos catalog (ESA 1997)., The astrometric data can be obtained from CD-ROM 5 of the Hipparcos catalog (ESA 1997).
 Unfortunately. the timespan of the Hipparcos observations is much smaller than the orbital period of the tertiary component. and this might eventually result in possible systematic errors in the orbital elements.," Unfortunately, the timespan of the Hipparcos observations is much smaller than the orbital period of the tertiary component, and this might eventually result in possible systematic errors in the orbital elements."
 To further constrain the solution additional older ground-based positions must be used., To further constrain the solution additional older ground-based positions must be used.
 Indeed. Tycho-2 proper motions were computed by combining Tycho-2 positions and ground-based astrometric catalogs.," Indeed, Tycho-2 proper motions were computed by combining Tycho-2 positions and ground-based astrometric catalogs."
 For R CMa. 17 epoch positions of ground-based catalogs used for the Tycho-2 proper motion computatior were kindly made available to us by Dr. Urban and are listed in Table ]..," For R CMa, 17 epoch positions of ground-based catalogs used for the Tycho-2 proper motion computation were kindly made available to us by Dr. Urban and are listed in Table \ref{tabastro}."
 These measurements span over one century anc so the Tycho-2 proper motions can be understood as the combination of the true proper motion and of a large fractior of the orbital motion., These measurements span over one century and so the Tycho-2 proper motions can be understood as the combination of the true proper motion and of a large fraction of the orbital motion.
 Consequently. the Tycho-2 proper motior of R CMa cannot itself be used in our analysis and only the individual positions contain valuable orbital information.," Consequently, the Tycho-2 proper motion of R CMa cannot itself be used in our analysis and only the individual positions contain valuable orbital information."
" [i contrast. a short-term proper motion determination. such as the one computed around 1980 by Guinan Tanna (1983). reveals itself to be very useful in constraming the astrometric solution,"," In contrast, a short-term proper motion determination, such as the one computed around 1980 by Guinan Ianna (1983), reveals itself to be very useful in constraining the astrometric solution."
 In the course of the astrometric data reduction of the Hippareos data. a test was applied to all the (apparently) single stars in order to check whether their motion was significantly non-linear.," In the course of the astrometric data reduction of the Hipparcos data, a test was applied to all the (apparently) single stars in order to check whether their motion was significantly non-linear."
 Most likely. a significant curvature of the photocenter motion is an indication of a possible duplicity.," Most likely, a significant curvature of the photocenter motion is an indication of a possible duplicity."
" As it turns out. R CMa is one of the 2622 ""acceleration"" solutions of the Double and Multiple Stars Annex of the Hippareos Catalogue. which provides a hint for the presence of a third body. independently from the LTT effect."," As it turns out, R CMa is one of the 2622 “acceleration” solutions of the Double and Multiple Stars Annex of the Hipparcos Catalogue, which provides a hint for the presence of a third body, independently from the LTT effect."
 R CMa has a long baseline of eclipse timings that extend from the present back to 1887., R CMa has a long baseline of eclipse timings that extend from the present back to 1887.
 Most of the early eclipse times were determined from visual estimates., Most of the early eclipse times were determined from visual estimates.
 Several period studies have been carried out., Several period studies have been carried out.
 Early studies of times of minimum light indicated a possible abrupt decrease in the period during 1914-15 (see Dugan Wright 1939: Wood 1946: Koch 1960: Guinan 1977)., Early studies of times of minimum light indicated a possible abrupt decrease in the period during 1914–15 (see Dugan Wright 1939; Wood 1946; Koch 1960; Guinan 1977).
 However. as more timings accumulated it became apparent that the long-term variations in the (O-C)’s of the system are periodic and thus best explained by the LTT effect produced by the presence of a third body.," However, as more timings accumulated it became apparent that the long-term variations in the (O–C)'s of the system are periodic and thus best explained by the LTT effect produced by the presence of a third body."
 The analysis of Radhakrishnan et al. (, The analysis of Radhakrishnan et al. (
1984). with eclipse timings from 1887 to 1982. and Demircan (2000). who includes timings up to 1998. make a strong case in support of the LTT scenario.,"1984), with eclipse timings from 1887 to 1982, and Demircan (2000), who includes timings up to 1998, make a strong case in support of the LTT scenario."
 Our photoelectric eclipse timing observations extend the time baseline up to early 2001., Our photoelectric eclipse timing observations extend the time baseline up to early 2001.
 The observations were obtained with the Four College 0.8-m Automatic Photoelectric Telescope located in Southern Arizonaduring 1995/96 and 2000/01., The observations were obtained with the Four College 0.8-m Automatic Photoelectric Telescope located in Southern Arizonaduring 1995/96 and 2000/01.
 Differential photometry was carried out using (vby Strómmgren filtersets., Differential photometry was carried out using $uvby$ Strömmgren filtersets.
 The mid-times of primary minimum and the (O-C)’sfor these are given in Table 2.. along with the corresponding uncertainties.," The mid-times of primary minimum and the (O–C)'sfor these are given in Table \ref{tabtim}, , along with the corresponding uncertainties."
 The (O-C)'s were computed using, The (O–C)'s were computed using
"recover the signature of reionisation late in the epoch of reionisation (22 7), by way of the 21-cm power spectrum, within the sensitivity limits of an instrument similar to the MWA.","recover the signature of reionisation late in the epoch of reionisation $z \approx 7$ ), by way of the 21-cm power spectrum, within the sensitivity limits of an instrument similar to the MWA."
" In addition to the statistical signature of cosmic reionisation, we have also shown that the tomographic image of the percolating IGM can be successfully cleaned of contamination."," In addition to the statistical signature of cosmic reionisation, we have also shown that the tomographic image of the percolating IGM can be successfully cleaned of contamination."
 We have applied our technique using a simple foreground model and a single thin Faraday screen., We have applied our technique using a simple foreground model and a single thin Faraday screen.
 We believe it is possible to extend the application of this technique to more complex and realistic foreground and Faraday screen models by performing the cleaning process iteratively., We believe it is possible to extend the application of this technique to more complex and realistic foreground and Faraday screen models by performing the cleaning process iteratively.
 This is an important improvement for lines of sight that have multiple Faraday-rotating screens or screens that are thick enough to be resolved by the instrument., This is an important improvement for lines of sight that have multiple Faraday-rotating screens or screens that are thick enough to be resolved by the instrument.
" For situations where a line of sight contains multiple screens, well separated in d$-space, the single iteration cleaning method used in this paper may be applied to each foreground peak in the effective Stokes J Faraday dispersion function."," For situations where a line of sight contains multiple screens, well separated in $\phi$ -space, the single iteration cleaning method used in this paper may be applied to each foreground peak in the effective Stokes $I$ Faraday dispersion function."
" Although contamination of the Stokes I signal due to very shallow Faraday screens (which have fluctuations in frequency-space on scale larger than the EoR signal) can be removed by simplya applyinga high-pass filter in ¢-space with minimal effect on the recovered cosmic signal, Faraday screens that lead to contamination that fluctuate on scales similar to the EoR signal (large |ó|) cannot, but can be easily removed using our method."," Although contamination of the Stokes $I$ signal due to very shallow Faraday screens (which have fluctuations in frequency-space on a scale larger than the EoR signal) can be removed by simply applyinga high-pass filter in $\phi$ -space with minimal effect on the recovered cosmic signal, Faraday screens that lead to contamination that fluctuate on scales similar to the EoR signal (large $|\phi|$ ) cannot, but can be easily removed using our method."
" It has already been shown that neither point sources, continuum DGSE nor instrumental noise will pose insurmountable obstacles tothe detection of the cosmic 21-cm signal (see,e.g.,????7).."," It has already been shown that neither point sources, continuum DGSE nor instrumental noise will pose insurmountable obstacles tothe detection of the cosmic 21-cm signal \citep[see, e.g.,][]{wang2006,geil2008b,jelic2008,bowman2009,liu2009}."
 Our results suggest that the cleaning of leaked polarised foregrounds will also be possible., Our results suggest that the cleaning of leaked polarised foregrounds will also be possible.
 Removing this contaminant will be a critical element in the removal of foregrounds that will be essential in order to detect the cosmological 21-cm signal., Removing this contaminant will be a critical element in the removal of foregrounds that will be essential in order to detect the cosmological 21-cm signal.
 'The authors would like to thank the anonymous referee for providing useful and detailed suggestions which has improved the manuscript., The authors would like to thank the anonymous referee for providing useful and detailed suggestions which has improved the manuscript.
" PMG acknowledges the support of an Australian Postgraduate Award and the hospitality of the University of Sydney, where part of this research was done."," PMG acknowledges the support of an Australian Postgraduate Award and the hospitality of the University of Sydney, where part of this research was done."
 JSBW acknowledges the support of the Australian Research Council., JSBW acknowledges the support of the Australian Research Council.
 BMG acknowledges the support of a Federation Fellowship from the Australian Research Council through grant FF0561298., BMG acknowledges the support of a Federation Fellowship from the Australian Research Council through grant FF0561298.
" The Centre for All-sky Astrophysics is an Australian Research Council Centre of Excellence, funded by grant CE11E0090."," The Centre for All-sky Astrophysics is an Australian Research Council Centre of Excellence, funded by grant CE11E0090."
 The visibility measurements of the next generation of low-frequency radio arrays will sample the instrumental response from an inherently three-dimensional volume of space at high redshift., The visibility measurements of the next generation of low-frequency radio arrays will sample the instrumental response from an inherently three-dimensional volume of space at high redshift.
" Only the fluctuating part of the signal contributes to an interferometric visibility, which we denote by AV(u,v,v), where u and v have their usual meaning (see,e.g., ?).."," Only the fluctuating part of the signal contributes to an interferometric visibility, which we denote by $\Delta V(u,v,\nu)$, where $u$ and $v$ have their usual meaning \citep[see, e.g.,][]{tms}. ."
" As discussed by ?,, there are three useful"," As discussed by \cite{morales2005}, , there are three useful"
Galaxies form [rom the interealactic medium (IGM). peeorocess such DEMeas into stars. ancl !possibly re-oject| a fraction of it. enriched by nucleosvnthetic products. back into. the interealactic space via powerful supernova-driven outLows (Mac Low Forrara 1999: Ferrara. Pettini Shchekinov 2000: Macau. Ferrara Rees 2001: Scannapieco. Ferrara Macau 2002: opPheuns 2002).,"Galaxies form from the intergalactic medium (IGM), process such gas into stars, and possibly re-eject a fraction of it, enriched by nucleosynthetic products, back into the intergalactic space via powerful supernova-driven outflows (Mac Low Ferrara 1999; Ferrara, Pettini Shchekinov 2000; Madau, Ferrara Rees 2001; Scannapieco, Ferrara Madau 2002; Theuns 2002)."
 opThe energy depositionun connected to these processes is: expected to leave at [east . . ↴⋅ ↿↓↥∢⊾↓≻∪⊳∖↓↿↓∪⊔⊳∖∪⇂↿↓↥∢⋅∟⊥≻≺⋅≱∖∖∖⊽↓↿↓⊔↓∐⊾∟∙∖⇁⋂⋜↧∣⋡⊳∖∪, The energy deposition connected to these processes is expected to leave at least some detectable imprints on the physical state of the IGM.
↓⋅↓≻⊔∪⊔↓↓⊔⋖⊾⊳∖↓⊔ o.it is .conceivable that. such signatures can: be studied :QSO QSO absorption. line. experiments.," Thus, it is conceivable that such signatures can be studied through QSO absorption line experiments."
". Naively.D. the(comoving) ry, of hot. outflowing gas. should result primarily inM thetwo . ellects: i] a decrease of the gas density and. di] an increase of the temperature caused: by shock-heating (acting in conjunction with photo-heating by the UV background) in a large (several hundreds kpe) region around the perturbing galaxy."," Naively, the presence of hot outflowing gas should result primarily in two effects: [i] a decrease of the gas density and [ii] an increase of the temperature caused by shock-heating (acting in conjunction with photo-heating by the UV background) in a large (several hundreds kpc) region around the perturbing galaxy."
 Both these occurrences would imply an increasingly more transparent Lya forest when approaching the galaxy. a galactic proximity effect.," Both these occurrences would imply an increasingly more transparent $\alpha$ forest when approaching the galaxy, a galactic proximity effect."
 Quantitative confirmation of this scenario has faced tremendous cilliculties. standing the complications of the physics of star formation. explosions and metal mixing in multiphase media.," Quantitative confirmation of this scenario has faced tremendous difficulties, standing the complications of the physics of star formation, explosions and metal mixing in multiphase media."
 Llence. most simulations to date had to rely on recipes for such processes.," Hence, most simulations to date had to rely on recipes for such processes."
 Nevertheless.. these ideas. have stimulated. the. first⋅ challenging. observations. aimed. at detecting. the imprints. of galaxy-LGAL interplay.," Nevertheless, these ideas have stimulated the first challenging observations aimed at detecting the imprints of galaxy-IGM interplay."
 Acdelberger (2002. A02) obtained high resolution spectra. of S. bright QSOs at 32<-4.1 and spectroscopicI.| redshifts.WO forup 431.dA Lyman-.break galaxies. (LBCs)) at lower redshifts.," Adelberger (2002, A02) obtained high resolution spectra of 8 bright QSOs at $3.1<z<4.1$ and spectroscopic redshifts for 431 Lyman-break galaxies (LBGs) at lower redshifts."
""" )By comparing. κ. ≱∖∪⊔↓⋖⋅∠⇂⋖⋅↿⋖⋅≼⇍↿⋜↧∣⋡↓∢⊾↓⊔↓↓≻↓⋅↓⊔⇂⊳∖∪⊔↿↓↕⋖⋅↓≻↓↥∙∖⇁⊳∖⊔⇍⋜↧↓≱∖⋯↿⋖⋅∪⇂↿⇂↥⋖⋅↓≺∣↳∖↓⊳""M . : : spectra.. indeed they⊀⊀ conelude that within =— 0.5/Πες.s Alpe⋅ of the. galaxies little. [li. present:; on through contrary. between 1 and 5h Alpe an Lt presence respect. to the LGAL mean. is detected."," By comparing the positions of the LBGs with the $\alpha$ absorption lines in QSO spectra, indeed they conclude that within $\approx 0.5 h^{-1}$ (comoving) Mpc of the galaxies little is present; on the contrary, between 1 and $h^{-1}$ Mpc an excess with respect to the IGM mean is detected."
wo This. ssimple with interpretation. might. be at odd with. the results of⋅ a VLP/UVES study of the forest in the vicinity of the LBG MS1512-0B58 showing the opposite trend (Savaglio 2002). an absorption excess close to the galaxy.," This simple interpretation might be at odd with the results of a VLT/UVES study of the forest in the vicinity of the LBG MS1512-cB58 showing the opposite trend (Savaglio 2002), an absorption excess close to the galaxy."
 Numerical simulations have also noticeable cdilliculties reproducing AO2 results as cliscussecl by Croft (2002) and Wwollmeicr (2002): however. these studies lack a sell-consistent treatment of multiphase gas structure and/or," Numerical simulations have also noticeable difficulties reproducing A02 results as discussed by Croft (2002) and Kollmeier (2002); however, these studies lack a self-consistent treatment of multiphase gas structure and/or"
SDME-Lite “chops” between the target aud cach of the refereuce stars.,"SIM-Lite “chops"" between the target and each of the reference stars."
 The chop sequence is target. reference. tarect. next reference. tarect. and so ou.," The chop sequence is target, reference, target, next reference, target, and so on."
 While the actual integration times depend ou stellar briehtuesses. a “typical” chop between two stars consists of 15 seconds on the target. 30 seconds on the reference. aud 15 seconds onu slews between the stars.," While the actual integration times depend on stellar brightnesses, a “typical” chop between two stars consists of 15 seconds on the target, 30 seconds on the reference, and 15 seconds on slews between the stars."
 This “dittercutial” tarect-reference lneasurement error is also plotted iu Figure 2..," This “differential"" target-reference measurement error is also plotted in Figure \ref{fig2}."
 Figure 23. shows the standard deviation. of ⋜↧↖↽↸∖↥⋅⋜↧∶↴∙⊾↸∖↴∖↴∪↕⊀∖↸⊳∐≺∏≻↴∖↴↖↽↸∖↥⋅↴∖↴∏↴∖↴↑∐↸∖↥⋅↸∖≺∏∐⋅↸∖≼⊔∐↑↸∖∶↴∙⊾↥⋅⋜↧⊓∪↕ nue. as Nis ⇁⋅⋅increased., Figure \ref{fig3} shows the standard deviation of averages of $N$ chops versus the required integration time as $N$ is increased.
 We- see that the standard ⋅⋅ . ≼∐∖↖↽↕⋜↧⊓∪∐∪↕↑↕∐∖≼∐⇡↽↸∖↥⋅↸∖∐⊓⋜↧↕⋯↸∖⋜↧↴∖↴⋯⋅↸∖⋯↸∖∐↑≼∐∖↸⊳↥⋅↸∖⋜↧↴∖↴↸∖↴∖↴⋅⋅⋅ as MVWI. aud from7 time. scales of 15 ---seconds) to 12. jours. the noise ⋅⋅in the differcutial⋅⋅⋅ measurement is⋅ rearly white.," We see that the standard deviation of the differential measurement decreases as $\sqrt{T}$, and from time scales of 45 seconds to 42 hours, the noise in the differential measurement is nearly white."
⋅ No- noise⋅ floor is⋅ observed down to 8 uas after about 12 hours., No noise floor is observed down to 8 nas after about 42 hours.
 Siuce the last value is obviously a downward fluctuation. we extrapolate .roni the mininuuaD iuteeration. time. of. 15 seconds o a white noise expectation of 21 nas at. 12 hours.," Since the last value is obviously a downward fluctuation, we extrapolate from the minimum integration time of 45 seconds to a white noise expectation of 24 nas at 42 hours."
 An important question in applying testbed results to SIM-Lite is how docs the thermal yvchavior of the relevaut parts of SIM-Lite on orbit colmpare with our ground testbed., An important question in applying testbed results to SIM-Lite is how does the thermal behavior of the relevant parts of SIM-Lite on orbit compare with our ground testbed.
 Within the estbed there were numerous temperature sensors hat recorded the temperature fluctuations of the optics aud mounts inside the παπα chamber., Within the testbed there were numerous temperature sensors that recorded the temperature fluctuations of the optics and mounts inside the vacuum chamber.
 We also conducted a very detailed thermal siuulatioun of the SIML-Lite spacecraft in orbit., We also conducted a very detailed thermal simulation of the SIM-Lite spacecraft in orbit.
 This multithousaud node thermal model was run for LOO hours of SIN-Lite operation. where he spacecraft attitude was allowed to change according a typical observing scenario.," This multi-thousand node thermal model was run for 100 hours of SIM-Lite operation, where the spacecraft attitude was allowed to change according a typical observing scenario."
 The simulation iucludes active thermal control. with the temperature uaintained near 20°C within the expected capabilities of SIM-Lite's thermal control system.," The simulation includes active thermal control, with the temperature maintained near $20^\circ$ C within the expected capabilities of SIM-Lite's thermal control system."
 As ciffereut »uwts of the spacecraft ire illmuinated by the Sun. the simulated thermal control svstem turus reaters on aud off in order to minimize temperature Huctuatious in the key opto-mechanicalenvironments.," As different parts of the spacecraft are illuminated by the Sun, the simulated thermal control system turns heaters on and off in order to minimize temperature fluctuations in the key opto-mechanical environments."
 Figure I shows the resulting predicted thermal Huctuatious of the SIN-Lite. beau combiner., Figure \ref{fig4} shows the resulting predicted thermal fluctuations of the SIM-Lite beam combiner.
 Also shown in the figure are measured testbed environment temperaturesunder conditious similar o those that yielded the results of Figure 3.., Also shown in the figure are measured testbed environment temperatures under conditions similar to those that yielded the results of Figure \ref{fig3}.
" We see that the actual thermal cuviroument of SIM-Lite should be better than the testbed. or conversely, that the test results are conservative with respect to thermal dit."," We see that the actual thermal environment of SIM-Lite should be better than the testbed, or conversely, that the test results are conservative with respect to thermal drift."
 To directly compare the stability of SIN-Lite thermal cnviromment to the testbed. we need to extract statistical quantities. that describe the stability of the two thermal euvironnieuts," To directly compare the stability of SIM-Lite thermal environment to the testbed, we need to extract statistical quantities that describe the stability of the two thermal environments."
 One such quantity is the power spectrum of the thermal fluctuations. shown in Figure 5..," One such quantity is the power spectrum of the thermal fluctuations, shown in Figure \ref{fig5}."
 SIMLLite on orbit is seen to be more thermally stable than our current testbed environment., SIM-Lite on orbit is seen to be more thermally stable than our current testbed environment.
 ↖↖∐↕↸∖↑↕∐↴∖↴↻⋜⋯↸∖↥⋅≼∐∖⋜↧↴∖↴↻↥⋅∐⊔⋜∐⋅∏⋅↖↽↖↖↽↕↑∐↕∐↴∖↴⊓⋅⋯⊔↸∖∐↑⋜↧↕a. . . ⋅⋅ error sources. we have also extensively⋅ studied⋅ ⋜↧↴∖↴⊓⋅≺∪∐↖↽↴∖↴∐⊳⋜↧↕↸∖∐⋅∪↥⋅↴∖↴↖↖↽∐≼⊳∐↖↖⇁↸∖↴∖↴," While this paper deals primarily with instrumental error sources, we have also extensively studied astrophysical errors which we summarize here."
∏⋯⋯⋜∐⋅↕∑↸∖↕∐∖↕⋅⋜∖⋅⋅ ⋅ ⋅⋅ The↴ two major. astrophysical⋅ errors ii⋅ astrometry are stellar activity⋅⋅ and companions⋅ to refercuce. stars., The two major astrophysical errors in astrometry are stellar activity and companions to reference stars.
'M A typical sunspot the arca of the Sun will in the worst case shift the plhotocenter of the Sin by επ0.25 aat LO pe and produce a radial velocity bias of 1 m/s., A typical sunspot the area of the Sun will in the worst case shift the photocenter of the Sun by 0.25 at 10 pc and produce a radial velocity bias of 1 ${\rm m}/{\rm s}$ .
 A shift of 0.25 Hs well below the sinele-epoch precision of SIALLite., A shift of 0.25 is well below the single-epoch precision of SIM-Lite.
 Star spot noise will not average down with integration time until that time is comparable to l/l- 1/2 the rotation period of the star or the can sunspot lifetime., Star spot noise will not average down with integration time until that time is comparable to 1/4 - 1/2 the rotation period of the star or the mean sunspot lifetime.
DEN The presence of planets orbiting reference stars is another astrophysical noise source., The presence of planets orbiting reference stars is another astrophysical noise source.
 RV vetting of reference stars will eliniuate binary stars and planets down to about Jupiter mass., RV vetting of reference stars will eliminate binary stars and planets down to about Jupiter mass.
 With multiple refercuce stars. it is possible to detect aud assieu the remaining plauets to a specific reference star.," With multiple reference stars, it is possible to detect and assign the remaining planets to a specific reference star."
 A nore detailed treatiuent will appear iu a subsequent. paper., A more detailed treatment will appear in a subsequent paper.
 For planet fiuding. the dominant error experienced S an astrometric interferometer is the thermally induced drift of the metrology with respect to the starlight.," For planet finding, the dominant error experienced by an astrometric interferometer is the thermally induced drift of the metrology with respect to the starlight."
 The testbed results show that. eve in he presence of a harsher thermal cuviroument han SIM-Lite will experience iu space. chopping )etween the target aud reference stars reuders this error nearly “white” with a uoise floor below 21 las after 12 hours of averaging.," The testbed results show that, even in the presence of a harsher thermal environment than SIM-Lite will experience in space, chopping between the target and reference stars renders this error nearly “white” with a noise floor below 24 nas after 42 hours of averaging."
 This is below the 35 nas required to detect au Earth in the habitable zone of the nearest GO stars., This is below the 35 nas required to detect an Earth in the habitable zone of the nearest $\sim60$ stars.
 While investigation of the uext-level uoise sources is coutinuine.these," While investigation of the next-level noise sources is continuing,these"
Dark matter haloes are often broadly categorised as residing in Ποια. ‘group’. and ‘cluster’ environments based solely on their mass.,"Dark matter haloes are often broadly categorised as residing in `field', `group', and `cluster' environments based solely on their mass."
 In. Figure 1.. for example. haloes of mass A—LOYAL.) 102777AZ... and 1077AZ. approximately correspond to these environment. bins. respectively.," In Figure \ref{fig:pop}, for example, haloes of mass $M\sim10^{12}M_\odot$, $10^{13.5}M_\odot$, and $10^{15}M_\odot$ approximately correspond to these environment bins, respectively."
 Many environment analyses use this categorisation. although as we have seen. the distinctions between them can often be blurred. in detail.," Many environment analyses use this categorisation, although as we have seen, the distinctions between them can often be blurred in detail."
 Some studies also attempt to explicitly identify ealaxies that are isolated or in groups or rich clusters. for example using friends-of-friends. &roup-finding algorithms (c.g.Derlindctal.2006:Yanget2007).," Some studies also attempt to explicitly identify galaxies that are isolated or in groups or rich clusters, for example using friends-of-friends group-finding algorithms \citep[e.g.][]{Berlind06, Yang07}."
. Analvses using group catalogues are complementary to studies with nearest neighbour or fixed aperture measures. or with galaxy clustering (c.g.Weinmannctal.2006: 2011).," Analyses using group catalogues are complementary to studies with nearest neighbour or fixed aperture measures, or with galaxy clustering \citep[e.g.][]{Weinmann06, Martinez06, Blanton07, Bosch08, Balogh09, Skibba11}."
. Work focused on galaxy clusters have also vielded complementary results (e.g.Pogeiantictal.2008:Itucdnicketal. 2009).," Work focused on galaxy clusters have also yielded complementary results \citep[e.g.][]{Poggianti08, Rudnick09, Bamford09, Wolf09, Gallazzi09}."
. Importantly. the way a galaxy formis. ancl evolves. is clearly related to its environment.," Importantly, the way a galaxy forms and evolves is clearly related to its environment."
 Some galaxy properties. such as luminosity. colour. and stellar mass. are directly correlated with the large-scale environment through the host dark matter halo (c.g.Zehavictal.2005:Li2006).," Some galaxy properties, such as luminosity, colour, and stellar mass, are directly correlated with the large-scale environment through the host dark matter halo \citep[e.g.][]{Zehavi05, Li06}."
. Other galaxy properties. such as structure. are to some extent only indirectly correlated with the environment (e.g. 2007).," Other galaxy properties, such as structure, are to some extent only indirectly correlated with the environment \citep[e.g.][]{Kauffmann04, Blanton05, Cassata07}."
. Indeed. a number of authors report that. for many aspects of the galaxy population. environmental dependence is often weak once stellar mass is fixed (vandenDoschetal.canietal. 2011).," Indeed, a number of authors report that, for many aspects of the galaxy population, environmental dependence is often weak once stellar mass is fixed \citep{Bosch08, Bosch08b, Scodeggio09, Bolzonella10, Vulcani11}."
. In any case. these studies highlight the fact that it is important to carefully determine how a galaxys environment is characterised. anc to identify. anc navigate 1e potential aspects of the environment analysis that may bias the results.," In any case, these studies highlight the fact that it is important to carefully determine how a galaxy's environment is characterised, and to identify and navigate the potential aspects of the environment analysis that may bias the results."
 The kev consideration when picking an environment measure is the scale that is being probed., The key consideration when picking an environment measure is the scale that is being probed.
" The term environment is very general but in fact. breaks down into wo main regions. and we argue that the community should agree on a standard. terminology for clarity ancl to. avoid ""uture confusion."," The term environment is very general but in fact breaks down into two main regions, and we argue that the community should agree on a standard terminology for clarity and to avoid future confusion."
 The first region is the ‘local environment which corresponds to scales internal to a halo., The first region is the `local environment' which corresponds to scales internal to a halo.
 Phese are yest probed using nearest neighbour methods. but the value of n is important.," These are best probed using nearest neighbour methods, but the value of $n$ is important."
 When η is larger than the number of ealaxies likely to reside within the halo the usefulness. of his environment measure can weaken., When $n$ is larger than the number of galaxies likely to reside within the halo the usefulness of this environment measure can weaken.
 The second. region ies external to the halo. the ‘large-scale environment’.," The second region lies external to the halo, the `large-scale environment'."
 The arge-scale environment is best. probed using aperture based methods., The large-scale environment is best probed using aperture based methods.
 In. general. there is no simple way. to probe all environments with a single method. and one should consider carefully the best tool to answer the questions at hand.," In general, there is no simple way to probe all environments with a single method, and one should consider carefully the best tool to answer the questions at hand."
 This paper marks the first in a series exploring the meaning and methods of galaxy environment. as measured in the current literature.," This paper marks the first in a series exploring the meaning and methods of galaxy environment, as measured in the current literature."
 In. the present work we have focused. on using a clean sample of mock galaxies. to quantify how selected properties of the galaxy population correlate with different environment methods. ancl how these methods themselves: compare.," In the present work we have focused on using a clean sample of mock galaxies to quantify how selected properties of the galaxy population correlate with different environment methods, and how these methods themselves compare."
 Future work will include investigating the detrimental ellects of survey geometry. edges anc holes (such as those caused by stars) on environment and techniques that can be applied. to successfully overcome them.," Future work will include investigating the detrimental effects of survey geometry, edges and holes (such as those caused by stars) on environment and techniques that can be applied to successfully overcome them."
 Furthermore. the relationship between galaxy. halo and dark matter environment warrants additional exploration. as does the redshift dependence of a galaxvs environment (defined. in various ways). what the cifferent environment methods tell us about galaxy evolution. and how these can best be applied to the noisy data of the high redshift’ Universe.," Furthermore, the relationship between galaxy, halo and dark matter environment warrants additional exploration, as does the redshift dependence of a galaxy's environment (defined in various ways), what the different environment methods tell us about galaxy evolution, and how these can best be applied to the noisy data of the high redshift Universe."
 The authors wish to thank Llanni Lux and 101 Zehavi for useful discussions and the referee. Christian Wolf. for improving the quality of the paper.," The authors wish to thank Hanni Lux and Idit Zehavi for useful discussions and the referee, Christian Wolf, for improving the quality of the paper."
 DIC acknowledges receipt of a QI Fellowship by the Australian Research Council., DJC acknowledges receipt of a QEII Fellowship by the Australian Research Council.
 IBA thanks NRE for the research grant 2010-0023319., HBA thanks NRF for the research grant 2010-0023319.
 NBC is supported by a CLERA Postdoctoral Fellowship., NBC is supported by a CIERA Postdoctoral Fellowship.
 MEG. is supported by an STEC' Advanced Fellowship., MEG is supported by an STFC Advanced Fellowship.
 Phe Dark Cosmology Contre is funded bv the Danish National Research Foundation., The Dark Cosmology Centre is funded by the Danish National Research Foundation.
 The Millennium. Simulation used. in this paper was carried out by the Virgo Supercomputing Consortiun at the Computing Centre of the Alax-Planck Society in Garching., The Millennium Simulation used in this paper was carried out by the Virgo Supercomputing Consortium at the Computing Centre of the Max-Planck Society in Garching.
 The halo merger trees used. in the paper are publicly available through the CAVO. interface. found. at htt/ww.mpa-garching.mpe.cde/millennium pz/The mock ealaxy catalogue generated. from. the Millennium Simulation trees can be downloaded. from the Theoretical Astrophysical Observatory (PAO) repository: httpz/tao.it.swin.edu.au/mock-galaxy-factory," The halo merger trees used in the paper are publicly available through the GAVO interface, found at http://www.mpa-garching.mpg.de/millennium/. The mock galaxy catalogue generated from the Millennium Simulation trees can be downloaded from the Theoretical Astrophysical Observatory (TAO) repository: http://tao.it.swin.edu.au/mock-galaxy-factory/."
matrix elements but the templates (dust aud Los MIIZ enission) are fitted separately.,matrix elements but the templates (dust and 408 MHz emission) are fitted separately.
 The vector 7 coutains the concatenated data for all channels ϱ data points per channel)., The vector $\vec{y}$ contains the concatenated data for all channels $N$ data points per channel).
 It is therefore a (onuSIN) vector., It is therefore a $(n_{chan}\times N)$ vector.
" The coadded Q-band and coadded Ix,-baud data are shown in Fig. 2..", The coadded Q-band and coadded $_a$ -band data are shown in Fig. \ref{data_simu}.
 The covariance matrix is sn (ngu\NYS(nounsUN) matrix.," The covariance matrix is an $(n_{chan}\times
N)\times(n_{chan}\times N)$ matrix."
 The No ταῖς contains the template simulated signal (one for cach channel) as well as a constant term and a eradieut term for cach channel. in order to account for the fact that such terms were removed from the SP9L data.," The $X$ matrix contains the template simulated signal (one for each channel) as well as a constant term and a gradient term for each channel, in order to account for the fact that such terms were removed from the SP94 data."
 The matrix [X is therefore a ωνsUN)(Εμμ\3) matrix., The matrix $X$ is therefore a $(n_{chan}\times N)\times(n_{chan}\times 3)$ matrix.
 Ina eiven column (correspouding to a eiven channel). X contaius mostly zeros. except for the rows corresponding to that chanucl where it contaius the template simulated signal.," In a given column (corresponding to a given channel), $X$ contains mostly zeros, except for the rows corresponding to that channel where it contains the template simulated signal."
 The vost estinate. of @ is ἑeiven through the 475 minimization along with its covariance matrix: We obtain a correlation coefficient for cach channel but those are highly correlated according to the covariance matrix X., The best estimate of $\vec{a}$ is given through the $\chi^2$ minimization along with its covariance matrix: We obtain a correlation coefficient for each channel but those are highly correlated according to the covariance matrix $\Sigma$.
 The correlation coefficieuts cannot therefore be averaged in a straightforward manner., The correlation coefficients cannot therefore be averaged in a straightforward manner.
 We estimate the average of the correlation cocficieuts via: where Lis a vector whose clemenuts are all equal to 1., We estimate the average of the correlation coefficients via: where $\vec{1}$ is a vector whose elements are all equal to 1.
 The best estimate of à is then obtained by: where the Total. function returus the stun of all eleiieuts of a matrix or vector., The best estimate of $\bar{a}$ is then obtained by: where the $\mathrm{Total}$ function returns the sum of all elements of a matrix or vector.
 This is equivaleut to a weighted average. though iu this case we also account for correlations between the differcut nieasures.," This is equivalent to a weighted average, though in this case we also account for correlations between the different measures."
" The emvor-bar on e is then: We do this for the I,- and Q-hands separately. aud for the combination of the to."," The error-bar on $\bar{a}$ is then: We do this for the $_a$ - and Q-bands separately, and for the combination of the two."
 The results are shown iu Table 2.., The results are shown in Table \ref{tabcorrel}.
 Equations &..9 and 10 nuplicitle suppose that the dust-correlated compoucut las a flat spectrum(e has a spectral iudex à= 0).," Equations \ref{chisqa}, \ref{aval} and \ref{aerr} implicitly suppose that the dust-correlated component has a flat spectrum has a spectral index $n=0$ )."
 As was mentioned before. results from other experiments teud to favor spectral indices close tonc 2similar to free-free cussion.," As was mentioned before, results from other experiments tend to favor spectral indices close to $n\simeq-2$ similar to free-free emission."
 In order to account for a non-zero spectral iudex. we model the eunission as: where vy is a reference frequency and uot an additional deeree of freedom.," In order to account for a non-zero spectral index, we model the emission as: where $\nu_0$ is a reference frequency and not an additional degree of freedom."
 Equation & then becomes: where mis a vector with 7 elements 1;=(5)., Equation \ref{chisqa} then becomes: where $\vec{m}$ is a vector with 7 elements $m_i=\left(\frac{\nu_i}{\nu_0}\right)^n$.
 This VPA is not linearH iftq oue lets à vary as a free. parameter., This $\chi^2$ is not linear if one lets $n$ vary as a free parameter.
 We- therefore munimize it nuuericallv for a exid of 300 values of η between -5 aud 5., We therefore minimize it numerically for a grid of 300 values of $n$ between -5 and 5.
 We compute correlations between the SP91 aud both dust aud svuchrotron templates shown in Fig., We compute correlations between the SP94 and both dust and synchrotron templates shown in Fig.
 2 aud Table 2.., \ref{data_simu} and Table \ref{tabcorrel}.
 Those results are also plotted as a function of ie frequency in Fie. 3.., Those results are also plotted as a function of the frequency in Fig. \ref{figres}.
" The results we obtain show a nareinal correlation of the OQ-band data with the dust IRAS/DIRDBE uplate whereas there is no correlation iu 16 I, baud.", The results we obtain show a marginal correlation of the Q-band data with the dust IRAS/DIRBE template whereas there is no correlation in the $_a$ -band.
 No siguificaut positive correlation is found im either baud with the ITaslai template., No significant positive correlation is found in either band with the Haslam template.
" The uncertainty on 16 combined Q-band aud Is,,-band correlation cocficicuts is not as uch smaller than that of the Q-band or I;-baud doue as one Ισ! naively expect.", The uncertainty on the combined Q-band and $_a$ -band correlation coefficients is not as much smaller than that of the Q-band or $_a$ -band alone as one might naively expect.
 In fact. this is due to 1ο contribution of the CMD covariance matrix.," In fact, this is due to the contribution of the CMB covariance matrix."
 For cach Tiauncl. the CMD covariance matrix is comparable to the roise one aud therefore combining the data reduces the roise contribution but not the CAIB one that becomes dominant.," For each channel, the CMB covariance matrix is comparable to the noise one and therefore combining the data reduces the noise contribution but not the CMB one that becomes dominant."
 Tn Table 2.. we also show the result for the analysisallowing the spectral iudex to vary as a free parameter.," In Table \ref{tabcorrel}, we also show the result for the analysisallowing the spectral index to vary as a free parameter."
" Combining the I, chaunels did not lead to any realistic value for the spectral index (the best fit. η=5.0. was at the edge of the range we searched)."," Combining the $_a$ channels did not lead to any realistic value for the spectral index (the best fit, $n=5.0$, was at the edge of the range we searched)."
 Combining the xuid data leads to a best fit for the spectral iudex of po—O8+£2.0., Combining the Q-band data leads to a best fit for the spectral index of $n=0.8\pm 2.0$.
" Combining all I, and Q data together cads ton=2.1c1.0.", Combining all $_a$ and Q data together leads to $n=2.1\pm 1.0$.
 It is there clear hat positive values are preferred., It is there clear that positive values are preferred.
" This is not a surprise. however. as the Q-ας data obviously correlate with the IRAS data better han the Ix,, does."," This is not a surprise, however, as the Q-band data obviously correlate with the IRAS data better than the $_a$ does."
 We stuumarize in Fig., We summarize in Fig.
 l1 the ucasureimeuts performed up to now of the correlation with the vibrational cust raced by IRAS/DIRDE 100/142: SPOL correspouds to he present article. the Tenerife measurements have beeu mblished in two ciffereut articles (deOliveira-Costaetal.1999:Mukhlerjeeetab.2000) 4porting slightly differeut results obtained with almost the same data.," \ref{resume_mes} the measurements performed up to now of the correlation with the vibrational dust traced by IRAS/DIRBE $100\mu\mathrm{m}$: SP94 corresponds to the present article, the Tenerife measurements have been published in two different articles \cite{doc_spindust,mukherjee00} reporting slightly different results obtained with almost the same data."
" We plot oth measurements, the lower values were obtaimed bv (deOliveiva-Costaetal.1999) aud considered. as a possible evidence for the presence of spinning dust vecause of the fall at LO CIIz."," We plot both measurements, the lower values were obtained by \cite{doc_spindust} and considered as a possible evidence for the presence of spinning dust because of the fall at 10 GHz."
 The upper measurements (Mukherjeeetal.2000) were published more recently and mitigated the euthusiasni for spinning dust., The upper measurements \cite{mukherjee00} were published more recently and mitigated the enthusiasm for spinning dust.
 As the values in this region are under question now. we plotted a square around these points.," As the values in this region are under question now, we plotted a square around these points."
 OVRO ieasured one poiut in this region at 11.5 Giz (Leitchetab.1997) that seenus to favour upper values of the correlation., OVRO measured one point in this region at 14.5 GHz \cite{leich97} that seems to favour upper values of the correlation.
" Saskatoon data are taken from (deOliveira-Costaetal...1997) aud show a lo detection iu the IX,,-baud (not significant) and a 1.90 detection in the Q-hband.", Saskatoon data are taken from \cite{doc_saskatoon} and show a $1\sigma$ detection in the $_a$ -band (not significant) and a $1.9\sigma$ detection in the Q-band.
 The 19 Giz (whole sky survey) data were taken from (deOliveira-Costaetal. 1998)., The 19 GHz (whole sky survey) data were taken from \cite{doc19ghz}. .
. The result from PythouV at 11 CIIz was taken, The result from PythonV at 41 GHz was taken
the total number of stars. the average stellar age. and the age spread.,"the total number of stars, the average stellar age, and the age spread."
 The second (refined) approach models each of the 5 subgroups separately with these three parameters., The second (refined) approach models each of the 5 subgroups separately with these three parameters.
 In the third method. we directly use the observed massive stars with their parameters. together with estimates of those that have already exploded as supernovae.," In the third method, we directly use the observed massive stars with their parameters, together with estimates of those that have already exploded as supernovae."
 In our population synthesis. stellar-evolution tracks are evaluated/interpolated to find the mass loss and kinetic energy from the stellar winds as a function of time.," In our population synthesis, stellar-evolution tracks are evaluated/interpolated to find the mass loss and kinetic energy from the stellar winds as a function of time."
 The supernova contribution is added as stellar evolution terminates. assuming a canonical ejection energy of 10°! erg.," The supernova contribution is added as stellar evolution terminates, assuming a canonical ejection energy of $10^{51}$ erg."
 The UV emission versus time is found from matching stellar atmosphere models with the stellar parameters at a given time., The UV emission versus time is found from matching stellar atmosphere models with the stellar parameters at a given time.
 In addition to caleulating the cumulative stellar outputs for the entire population. we estimate the statistical deviations. caused by the random sampling of the IMF.," In addition to calculating the cumulative stellar outputs for the entire population, we estimate the statistical deviations, caused by the random sampling of the IMF."
 Discussions of the shape of the distributions caused by this can be found in Cervino&Luridiana(2006);Vossetal.(2009);Gounelle (2009).," Discussions of the shape of the distributions caused by this can be found in \citet{Cervino2006,Voss-popsyn,Gounelle2009}."
. We compare two ways: Án analytical formula developed by Cervino&Luridiana(2006).. and Monte Carlo. sampling.," We compare two ways: An analytical formula developed by \citet{Cervino2006}, and Monte Carlo sampling."
 Our method was found consistent both with results from the code (Leithereretal.1999;Vazquez& 2005).. and with the results of a similar but different population synthesis implementation by Cerviiioetal.(2000).," Our method was found consistent both with results from the code \citep{Leitherer1999,Vazquez2005}, and with the results of a similar but different population synthesis implementation by \citet{Cervino2000}."
. In Vossetal.(2009). different stellar-model inputs were analyzed and compared., In \citet{Voss-popsyn} different stellar-model inputs were analyzed and compared.
 In the following. we use three different stellar models. in order to represent the possible spread from theoretical predictions.," In the following, we use three different stellar models, in order to represent the possible spread from theoretical predictions."
 For all three models we use stellar-wind velocities according to (Lamersetal.1995;Niedzielskirzynski2002) and the (Kurucz1992;Martins2005;Smithetal.2005) stellar atmosphere models.," For all three models we use stellar-wind velocities according to \citep{Lamers1995,Niedzielski2002}
 and the \citep{Kurucz1992,Martins2005,Smith2005}
 stellar atmosphere models."
 We compare three different models for Orion's. stellar population:, We compare three different models for Orion's stellar population:
-.8 true ID. The companion paper introduces the idea of mesolensing. in which a single lens has a high probability of producing a detectable event Stefano 2006a).,"-.8 true in The companion paper introduces the idea of mesolensing, in which a single lens has a high probability of producing a detectable event Stefano 2006a)."
 Nearby stellar remnants are examples of mesolenses., Nearby stellar remnants are examples of mesolenses.
 Consider. e.g.. a neutron star located 100 pe from us. traveling with a transverse speed of 100 km s! in front of M31.," Consider, e.g., a neutron star located $100$ pc from us, traveling with a transverse speed of $100$ km $^{-1}$ in front of M31."
" Over the course of twenty to thirty years. the Einstein ring of the neutron star will traverse an area of roughly 0.02”«(4—6)"". In most regions of M31. this area will contain several hundred stars."," Over the course of twenty to thirty years, the Einstein ring of the neutron star will traverse an area of roughly $0.02'' \times (4-6)''.$ In most regions of M31, this area will contain several hundred stars."
 It is likely that one or more of these stars is bright enough that. when it is magnified. the integrated Juminosity from a square aresecond region around it will increase by 10%.," It is likely that one or more of these stars is bright enough that, when it is magnified, the integrated luminosity from a square arcsecond region around it will increase by $10\%$."
 During the same interval. there may also be several smaller magnifications. producing jitter in the baseline light.," During the same interval, there may also be several smaller magnifications, producing jitter in the baseline light."
" In addition. astrometric shifts of ~0.001"" may occur and be detectable in the images of several stars Lying in an even larger swath across the sky."," In addition, astrometric shifts of $\sim 0.001''$ may occur and be detectable in the images of several stars lying in an even larger swath across the sky."
" These lensing effects could potentially lead. through a monitoring program. to the discovery of a ""new"" neutron star. one whose presence is not yet known."," These lensing effects could potentially lead, through a monitoring program, to the discovery of a “new"" neutron star, one whose presence is not yet known."
 Alternatively. if there is a known pulsar or X-ray emitter along the direction to M31. the region behind the mass can be targeted for repeated deep. high-resolution observations.," Alternatively, if there is a known pulsar or X-ray emitter along the direction to M31, the region behind the mass can be targeted for repeated deep, high-resolution observations."
 Such observations would have the potential to measure the mass of the neutron star. determine its proper motion. and probe for evidence of companions.," Such observations would have the potential to measure the mass of the neutron star, determine its proper motion, and probe for evidence of companions."
 This type of argument can be applied to other dark and dim masses located within roughly à kpe. ranging from the relatively rare isolated black hole. to the more ubiquitous low-mass dwarfs.," This type of argument can be applied to other dark and dim masses located within roughly a kpc, ranging from the relatively rare isolated black hole, to the more ubiquitous low-mass dwarfs."
 If the lensing action of such objects can be detected. gravitational lensing will become a valuable tool to discover a larger fraction of them and to study their properties. including their masses and multiplicities.," If the lensing action of such objects can be detected, gravitational lensing will become a valuable tool to discover a larger fraction of them and to study their properties, including their masses and multiplicities."
 The primary goal of this paper is to study applications of mesolensing., The primary goal of this paper is to study applications of mesolensing.
 We focus exclusively on photometric effects. although astrometric effects are also expected.," We focus exclusively on photometric effects, although astrometric effects are also expected."
 The necessary background is covered in 32., The necessary background is covered in 2.
 Section 3 focuses on computing the event rates due to nearby stars: low-mass dwarfs. white dwarfs (WDs). neutron stars (NSs). and black holes (BHs).," Section 3 focuses on computing the event rates due to nearby stars: low-mass dwarfs, white dwarfs (WDs), neutron stars (NSs), and black holes (BHs)."
 These forms of matter are known to exist., These forms of matter are known to exist.
 The predicted rates are high enough to provide a guaranteed signal in past. ongoing. and future monitoring programs.," The predicted rates are high enough to provide a guaranteed signal in past, ongoing, and future monitoring programs."
 This signal can be used to study these nearby populations in a way that has not so far been possible., This signal can be used to study these nearby populations in a way that has not so far been possible.
 Even if the primary goal of a monitoring program is to study dark matter. the signal due to nearby masses must be identified so that events due to nearby lenses can be subtracted from the total lensing signal to determine the true contribution of other lens populations. such as MAssive Compact Halo Objects (MACHOs).," Even if the primary goal of a monitoring program is to study dark matter, the signal due to nearby masses must be identified so that events due to nearby lenses can be subtracted from the total lensing signal to determine the true contribution of other lens populations, such as MAssive Compact Halo Objects (MACHOs)."
 In $4. attention turns to forms of nearby matter for which there Is às yet no direct evidence.," In 4, attention turns to forms of nearby matter for which there is as yet no direct evidence."
 Specifically. we consider (1) intermediate-mass black holes (IMBHs). (2) disk dark matter 1n the form of free-streaming planet-mass objects. and (3) possible planets in the outer regions (71000 AU) of the solar system.," Specifically, we consider (1) intermediate-mass black holes (IMBHs), (2) disk dark matter in the form of free-streaming planet-mass objects, and (3) possible planets in the outer regions $> 1000$ AU) of the solar system."
 Section 5 is a summary of the conclusions., Section 5 is a summary of the conclusions.
 Lensing events have been discovered by monitoring programs. each of which regularly observes a dense background field at intervals of one to several days.," Lensing events have been discovered by monitoring programs, each of which regularly observes a dense background field at intervals of one to several days."
 Attention so far has focused on the Galactic Bulge and the Magellanic Clouds., Attention so far has focused on the Galactic Bulge and the Magellanic Clouds.
 M31 has also been subjected to regular monitoring., M31 has also been subjected to regular monitoring.
 The monitoring programs are designed to discover evidence of lensing by masses lying in front of the background: the presence of the specific masses that eventually produce events is not generally known prior to the observations., The monitoring programs are designed to discover evidence of lensing by masses lying in front of the background; the presence of the specific masses that eventually produce events is not generally known prior to the observations.
 Monitoring observations can therefore discover and probe the properties of a population of dark or dim objects., Monitoring observations can therefore discover and probe the properties of a population of dark or dim objects.
" The monitored field can be viewed as a composite of many small subfields. each with linear dimensions 0,,,,: where the value of 0,,,, has typically been on the order of an aresecond."," The monitored field can be viewed as a composite of many small subfields, each with linear dimensions $\theta_{mon},$ where the value of $\theta_{mon}$ has typically been on the order of an arcsecond."
" The term “monitored region"". for a specific lens. refers to a box centered on the lens with area (yon\0,,,,. It was necessary to develop a mode of analysis that considers monitored regions. rather than individual stars. because the dense fields we observe always have multiple stars within each resolution element Stefano Esin 1995)."," The term “monitored region"", for a specific lens, refers to a box centered on the lens with area $\theta_{mon} \times \theta_{mon}.$ It was necessary to develop a mode of analysis that considers monitored regions, rather than individual stars, because the dense fields we observe always have multiple stars within each resolution element Stefano Esin 1995)."
 Although the details of the analysis can be complex. the basic idea is that the image of the region obtained at time £ is compared with an appropriately averaged image of the field. and differences are identified.," Although the details of the analysis can be complex, the basic idea is that the image of the region obtained at time $t$ is compared with an appropriately averaged image of the field, and differences are identified."
 The value of this difference Imaging approach is that variations of an individual star can be discovered. even when the field is so," The value of this difference imaging approach is that variations of an individual star can be discovered, even when the field is so"
so [ar about planets orbiting intermediate-nmiass Παsequence stars.,so far about planets orbiting intermediate-mass main-sequence stars.
 Recent models of planet formation (e.g. &Lin 2005: Ixennedy.&Ixenvon 2008)) suggest that formation mav peak among the late B stars., Recent models of planet formation (e.g. \citealt{ida2005}; ; \citealt{kennedy2008snowline}) ) suggest that gas-giant formation may peak among the late B stars.
 Itacdial-velocity searches. for planets orbiting stars in this mass range become feasible only once the star has evolved. into a late-twpe giant. (Llatzesetal.2005: Johnsonetal. 2007:: Satoetal. 2008)). by which time any closc-orbiting planets are likely to have been engulfed.," Radial-velocity searches for planets orbiting stars in this mass range become feasible only once the star has evolved into a late-type giant \citealt{hatzes2005giant}; \citealt{johnson2007giants}; \citealt{sato2008giants}) ), by which time any close-orbiting planets are likely to have been engulfed."
 Transit signals have been reported. for main-sequence A-I-tvpe stars. suggesting the possible presence of close-in planets (Christianctal.2006:kaneetal. 2008).. but measuring the small reflex motion that would. confirm their planetary. origin is generally not possible for these line-poor. fast-rotating stars.," Transit signals have been reported for main-sequence A-F-type stars, suggesting the possible presence of close-in planets \citep{christian2006,lister2007,street2007,clarkson2007,kane2008}, but measuring the small reflex motion that would confirm their planetary origin is generally not possible for these line-poor, fast-rotating stars."
 Lhe hottest star known to passes a transiting planet until now is OGLE2-TR-LO (Snellenctal.2009).. which at spectral type F3 and esing=33 km  is still not far from solar-tvpe.," The hottest star known to passes a transiting planet until now is OGLE2-TR-L9 \citep{snellen2009}, which at spectral type F3 and $v\sin i=33$ km $^{-1}$ is still not far from solar-type."
" As a result. we know very little vet about the frequency of giant-planet formation around earlier-tvpe stars. with their harder radiation fields. more distant. snow-lines and greater disc Masses,"," As a result, we know very little yet about the frequency of giant-planet formation around earlier-type stars, with their harder radiation fields, more distant snow-lines and greater disc masses."
 lere. we use the established technique of Doppler imaging to confirm the presence of a transiting planet around the bright. fast-rotating star LID 15082 (V=SX: Sp.," Here we use the established technique of Doppler imaging to confirm the presence of a transiting planet around the bright, fast-rotating star HD 15082 $V=8.3$; Sp."
 type ASm. esini=S6 kms +).," type A5m, $v \sin i = 86$ km $^{-1}$ )."
 The travelling spectral signature of a planet transiting the disc of the star during the flight minimum. vields information on the properties of the planet and its orbit., The travelling spectral signature of a planet transiting the disc of the star during the light minimum yields information on the properties of the planet and its orbit.
 Phis complements or supplements that derived. from standard. photometric analyses. notably its size. retrograde orbit. ancl non-alignment of the stellar and orbital spin axes.," This complements or supplements that derived from standard photometric analyses, notably its size, retrograde orbit, and non-alignment of the stellar and orbital spin axes."
 LID 15082 (WASP-33) is an early-type star in which Lat-rottomed. planct-like transits recurring every 1.22. dass were discovered. by Christianctal.(2006). in the WASP survey (Pollaecoetal.2006).," HD 15082 (WASP-33) is an early-type star in which flat-bottomed, planet-like transits recurring every 1.22 days were discovered by \citet{christian2006} in the WASP survey \citep{pollacco2006}."
. However. it rotates too rapicllv o permit straightforward confirmation of the planet. from orecise radial-velocity observations. and so was selected for he more sophisticated analysis reported here.," However, it rotates too rapidly to permit straightforward confirmation of the planet from precise radial-velocity observations, and so was selected for the more sophisticated analysis reported here."
 Our first step was tofollow up the WASD discovery with dedicated photometric observations of LLD 15082 to improve he definition of the transit light curve., Our first step was tofollow up the WASP discovery with dedicated photometric observations of HD 15082 to improve the definition of the transit light curve.
 A partial transit was observed in the 2 band on 2006 November 13 using the CCD camera of the 0.95-m James Gregory Telescope (JL) at the St Andrews. University Observatory., A partial transit was observed in the $R$ band on 2006 November 13 using the CCD camera of the 0.95-m James Gregory Telescope (JGT) at the St Andrews University Observatory.
 One complete and one partial 2-band transit were observed. with the 60-cm telescope and CCD camera of the University of Ixeele (Pollaccoetal.2008) on 2006 December 11 and 2007 Alarch 20., One complete and one partial $R$ -band transit were observed with the 60-cm telescope and CCD camera of the University of Keele \citep{pollacco2007_wasp-3} on 2006 December 11 and 2007 March 20.
 Finally. complete transits were observed in 2 and { bands with the 35-cm Schmidt-Cassegrain telescope and CCD camera at the University of London Observatory. Mill LLL (Fossev.Waldmann.&Ixipping2009) on the nights of 2007 November 14 and. 2008 September 20.," Finally, complete transits were observed in $R$ and $I$ bands with the 35-cm Schmidt-Cassegrain telescope and CCD camera at the University of London Observatory, Mill Hill \citep{fossey2009hd80606} on the nights of 2007 November 14 and 2008 September 20."
 In all three instruments the unvignetted. field. of view includes. several bright reference stars. which were used to derive the transit light curves shown in Fig.," In all three instruments the unvignetted field of view includes several bright reference stars, which were used to derive the transit light curves shown in Fig."
 1 using cdilferential. aperture photometry., \ref{fig:followup_phot} using differential aperture photometry.
 The total transit. duration is 272 hours from first to last contact: ingress and egress last 16 minutes. and the transit depth is 0.015 mag in both bands.," The total transit duration is 2.72 hours from first to last contact; ingress and egress last 16 minutes, and the transit depth is 0.015 mag in both bands."
 Preliminary raclial-velocity. (RV) measurements of HD 15082 were obtained at the Thürringer. Landessternwarte ‘Tautenburg (PLS) in order to determine the mass of the planet. from the host. stars orbital rellex. motion., Preliminary radial-velocity (RV) measurements of HD 15082 were obtained at the Thürringer Landessternwarte Tautenburg (TLS) in order to determine the mass of the planet from the host star's orbital reflex motion.
 Observations were made during the periods 2006 November 30 December 12 and 2007 February 04 2007. March 05. using the coudé'ecchelle: spectrograph of the 22m. Alfred. Jenseh telescope ab a resolving power of AfAA=67.000. covering the wavelength range from 4700 to 7400.," Observations were made during the periods 2006 November 30 – December 12 and 2007 February 04 – 2007 March 05, using the coud\'e\\'ecchelle spectrograph of the 2-m Alfred Jensch telescope at a resolving power of $\lambda/\Delta\lambda=67,000$, covering the wavelength range from 4700 to 7400."
Α.. WASDP-33 is) part of the Tautenburg search. for extrasolar planets (c.g. Cuentheret.al. 20093)., WASP-33 is part of the Tautenburg search for extrasolar planets (e.g. \citealt{guenther2009}) ).
 Raclial-velocity measurements are obtained using an iodine cell., Radial-velocity measurements are obtained using an iodine cell.
 As described in detail bv Llatzesetal.(2005)... we fit an initial elobal wavelength solution to all orders of the spectrum of a FhAr lamp. then use the lines from the iodine cell to determine the instrumental profile (LP) and the instrumental shift simultaneously with the observations.," As described in detail by \citet{hatzes2005giant}, we fit an initial global wavelength solution to all orders of the spectrum of a ThAr lamp, then use the lines from the iodine cell to determine the instrumental profile (IP) and the instrumental shift simultaneously with the observations."
 An accuracy of 121017 m tis achieved for bright slowlv-rotating stars (Llatzes&Zechmoelster2007)., An accuracy of 1.2 to 1.7 m $^{-1}$ is achieved for bright slowly-rotating stars \citep{hatzes2007}.
. In the case of WASP-33. however. the reduced. stellar spectra show extreme rotational broadening. with esin’c90+10 km f.," In the case of WASP-33, however, the reduced stellar spectra show extreme rotational broadening, with $v\sin i \simeq 90 \pm 10$ km $^{-1}$."
 This precludes the direct. determination of precise racial velocities relative to the iodine spectrum., This precludes the direct determination of precise radial velocities relative to the iodine spectrum.
 ]nsteac. relative radial velocities were computed. by cross-correlation with the template spectrum of the star outside the iodine spectral region.," Instead, relative radial velocities were computed by cross-correlation with the template spectrum of the star outside the iodine spectral region."
 The results are listed together with the signal-to-noise ratios (SNIU of the individual spectra in Table 1.. and the racial-velocity curve is plotted in Fig. 2..," The results are listed together with the signal-to-noise ratios (SNR) of the individual spectra in Table \ref{tab:rvorbit}, and the radial-velocity curve is plotted in Fig. \ref{fig:RVcurve}. ."
 Phere is a long- trend in the radial velocities over the 05-day span of these observations. corresponding to a radial acceleration of Wt3ms itd?in the centre of mass of the transiting pair.," There is a long-term trend in the radial velocities over the 95-day span of these observations, corresponding to a radial acceleration of $-18\pm 3$ m $^{-1}$ $^{-1}$in the centre of mass of the transiting pair."
 Although most of the stars in the “Tautenburg surveys do not exhibit trends at this level, Although most of the stars in the Tautenburg radial-velocity surveys do not exhibit trends at this level
Coronal flares are known to be very couples phenomena. and to iuvolve inultiple coronal structures. iltiple spectral bands aud multiple physical mechanisius at a iue.,"Coronal flares are known to be very complex phenomena, and to involve multiple coronal structures, multiple spectral bands and multiple physical mechanisms at a time."
 Furthermore. if is very difficult to define a typical coronal flare pattern (e.g. Golub Pasachof 1997).," Furthermore, it is very difficult to define a typical coronal flare pattern (e.g. Golub Pasachoff 1997)."
" A “standard” classification, of sola coronal flares divides loui into two main categories. based fundamentally on he of topologythe involved structures: compact flares and ong-cudurimg events (Pallaviciui et al."," A “standard” classification, of solar coronal flares divides them into two main categories, based fundamentally on the topology of the involved structures: compact flares and long-enduring events (Pallavicini et al."
 1977)., 1977).
 Compact Hares occur mostlv inside single loops whose shape and volume do not change siguificantly during the flare., Compact flares occur mostly inside single loops whose shape and volume do not change significantly during the flare.
 Long-—enduring events. instead. occur in loop arcades. and uigher aud higher loops ave typically iuvolved as the flare oogresses.," Long-enduring events, instead, occur in loop arcades, and higher and higher loops are typically involved as the flare progresses."
 The arcade footpoiuts. best seen in the Πα ine. appear as two rlbbous getting more distant with iue.," The arcade footpoints, best seen in the $\alpha$ line, appear as two ribbons getting more distant with time."
 Long-eudunus events are eenerallv more eradual and louger-lsting than compact flares. but exceptions exist.," Long-enduring events are generally more gradual and longer-lasting than compact flares, but exceptions exist."
" The soft N-ray light curve of fares consists generally, of a steep rising phase. a well-defined peak and a slower ecnerally expoucutial decay."," The soft X-ray light curve of flares consists, generally, of a steep rising phase, a well-defined peak and a slower – generally exponential – decay."
 A gradual rise or a decay conrposed. by segments with different e-foldiug times (6.8. Osten Brown 1999) cau also occur., A gradual rise or a decay composed by segments with different e-folding times (e.g. Osten Brown 1999) can also occur.
 Stellar flares are spatially unresolved and we have direct information. on∙∙∙ the morphology of the∏⋜∐⋅↕∐∶↴∙⊾↕∪∪↻↴∖↴∙↕⊰↸∖⋜↧↕↸∖↸∖↑⋜↧↕⋅∐≝↭∏≺↧↸∖∏↖↽↸∖≼↧⋜⋯↸∖∐∏≻∐⋅↕↸⊳⋜↧↕ coronal structures. involved. except iu the presence of eclipses cavingdne theEH flareo (C1 Favataaxta 1999).," Stellar flares are spatially unresolved and we have no direct information on the morphology of the coronal structures involved, except in the presence of eclipses during the flare (Schmitt Favata 1999)."
1OOC The. rentsimilarityαταΈτ oft solar and stellar X-ray (Schuttfares. however. suggests that also stellar flares involve plasma confined in closed structures.," The similarity of solar and stellar X-ray flares, however, suggests that also stellar flares involve plasma confined in closed structures."
 Empirical methods have been developed to infer the size of the flaring structures from the e-folding decay time οἳ light curves (Kopp Poletto 1951. White et al.," Empirical methods have been developed to infer the size of the flaring structures from the e-folding decay time of light curves (Kopp Poletto 1984, White et al."
 1986. Poletto et al.," 1986, Poletto et al."
 1985. yan den Oord Alewe 1989. Pallavicini et al.," 1988, van den Oord Mewe 1989, Pallavicini et al."
 1990. Tlawley ct al.," 1990, Hawley et al."
 1995. Reale et al.," 1995, Reale et al."
 1997. Reale Micela 1998. see Reale 2002 for an extensive review of these methods).," 1997, Reale Micela 1998, see Reale 2002 for an extensive review of these methods)."
 In the livpothesis of fares occurring inside closed coronal structures. the decay time of the N-ray emission roughly scales as the plasma cooling time.," In the hypothesis of flares occurring inside closed coronal structures, the decay time of the X-ray emission roughly scales as the plasma cooling time."
 In turn. the cooling time scales with the leneth of the structure which confines the plasma: the loneer the decay. the larger is the structure (c.¢. Haisch 1983).," In turn, the cooling time scales with the length of the structure which confines the plasma: the longer the decay, the larger is the structure (e.g. Haisch 1983)."
 A loop thermodynamic decay time has beenderived (van den Oord Mee 1989. Serio et al.," A loop thermodynamic decay time has been derived (van den Oord Mewe 1989, Serio et al."
 1991) as: where Lo and Tz are the loop halfleneth aud the πιααι temperature of the flaring plasima. in units of 10? cmi and 10* Is. respectively.," 1991) as: where $L_9$ and $T_7$ are the loop half-length and the maximum temperature of the flaring plasma, in units of $10^9$ cm and $10^7$ K, respectively."
 The timescale above. is derived. πιλος the hypothesis of impulsive heat released at the beeiunins of the flare., The timescale above is derived under the hypothesis of impulsive heat released at the beginning of the flare.
 However. a significant heat released the decay may increase the decay fine. and therefore duringlead to overestinate the loop leugth. if not correctly diagnosed. (Reale et al.," However, a significant heat released during the decay may increase the decay time, and therefore lead to overestimate the loop length, if not correctly diagnosed (Reale et al."
 1997. Reale 2002).," 1997, Reale 2002)."
 Dx means of extensive livdrodyvnuauic simmlatious of decaving uo ," By means of extensive hydrodynamic simulations of decaying flaring loops, Reale et al. ("
forumla for the loop leugth. combining the inforination from the light curve and the trajectory of the flare in the deusity-temperature. diaeram.3: where Tee: is the decay tine derived from the leht curve.,"1997) derived an empirical formula for the loop length, combining the information from the light curve and the trajectory of the flare in the density-temperature diagram: where $\tau_{LC}$ is the decay time derived from the light curve."
 This formmla can be obtained from the expression, This formula can be obtained from the expression
They then extrapolate the deprojection mass to f?sqy. the radius where ο/η=500: the extrapolated mass is Magy=4.06xLO!5.1M. within 0.855.+ Mpe.,"They then extrapolate the deprojection mass to $R_{500}$, the radius where $\rho/\rho_{crit}=500$; the extrapolated mass is $M_{500}=4.06\times10^{14}\:h^{-1}\:M_\odot$ within $0.85\:h^{-1}$ Mpc."
 Our caustic mass estimate is consistent with the X-ray data at both radii., Our caustic mass estimate is consistent with the X-ray data at both radii.
 Figure LL shows the differential /-bancl huninosityv funetion of AlG44., Figure \ref{fig-lf} shows the differential -band luminosity function of A1644.
 In the bins with complete spectroscopy (47.< 13) redshifts determine cluster membership., In the bins with complete spectroscopy $H<13$ ) redshifts determine cluster membership.
 At the faint end we estimate (he number of field galaxies because we do not have spectra., At the faint end we estimate the number of field galaxies because we do not have spectra.
 We moclel the nunmber of field galaxies in each magnitude bin by a power law of the form where Cis a normalization constant., We model the number of field galaxies in each magnitude bin by a power law of the form where $C$ is a normalization constant.
 We assume the background slope of 0.67 determined bv Gardner.Cowie.&Weoinseoat(1993) [rom a compilation of A-band field survevs., We assume the background slope of 0.67 determined by \citet{gar93} from a compilation of -band field surveys.
" As our best estimate of (he background. we normalize the power law by integrating equation 7 [rom Il——oc lo Hf=14 and equating the left haud side with the number of field galaxies in the direction of the cluster: there are 5+2 field galaxies deg? with 7<14 in our photometric region,"," As our best estimate of the background, we normalize the power law by integrating equation \ref{power-law} from $H=-\infty$ to $H=14$ and equating the left hand side with the number of field galaxies in the direction of the cluster; there are $5\pm2$ field galaxies $^{-2}$ with $H<14$ in our photometric region."
 Our off-cluster survey contains 3946 bright galaxies per square degree. and Garcner οἱ al. (," Our off-cluster survey contains $39\pm6$ bright galaxies per square degree, and Gardner et al. ("
1993) and Szokolvetal.(1998). observe roughly 1343 and 23+6 galaxies * in this magnitude range.,1993) and \citet{szo98} observe roughly $13\pm3$ and $23\pm6$ galaxies $^{-2}$ in this magnitude range.
 Although these field counts are statistically consistent with our esimale. (he large varialions in (he normalization can produce a rising. flat. or declining faint end of the A1644 cluster LF.," Although these field counts are statistically consistent with our estimate, the large variations in the normalization can produce a rising, flat, or declining faint end of the A1644 cluster LF."
 Alter subtracting the background fit normalized by our redshift survey [rom the total number of faint galaxies identified by the SExtractor SSTAR parameter. we characterize the data with a Schechter luminosity function.," After subtracting the background fit normalized by our redshift survey from the total number of faint galaxies identified by the SExtractor STAR parameter, we characterize the data with a Schechter luminosity function."
 We fit to the Schechter(1976) [orm of the luminosity finetion where a is the faint-enclslope. L is a characteristic Iuminosity. and »* is a normalization constant.," We fit to the \citet{sch76} form of the luminosity function where $\alpha$ is the faint-endslope, $L^*$ is a characteristic luminosity, and $n^*$ is a normalization constant."
 In terms of absolute magnitude AM the luminosity [unction is where &=(In10/2.5) and M is Che absolute magnitude corresponding to L* 1995).., In terms of absolute magnitude $M$ the luminosity function is where $k\equiv(\ln10/2.5)$ and $M^*$ is the absolute magnitude corresponding to $L^*$ \citep{kas95}. .
 At the mean redshift of our cluster Mj;=m—35.78+5log h., At the mean redshift of our cluster $M_H=m_H-35.78+5\log h$ .
"where R,. is the effective radius. containing of the total Light of the bulge and 44. is the surface brightuecss at R..","where $R_e$ is the effective radius, containing of the total light of the bulge and $\mu_e$ is the surface brightness at $R_e$."
 We fit the disk component usiug where fy is the central surface brightuess aud 7 is the scaleleneth of the disk., We fit the disk component using where $\mu_0$ is the central surface brightness and $h$ is the scalelength of the disk.
 The resits of this bulge-disk decompostion can be ποσα in Figur el and Table 1., The results of this bulge-disk decompostion can be seen in Figure \ref{decompose} and Table 4.
 We assign masses to the disk axd bulee components using a range of stellar mass-to-light ratios from Bell de Jong (2001)., We assign masses to the disk and bulge components using a range of stellar mass-to-light ratios from Bell de Jong (2001).
 Specifically. 1 our rotation curve models we allow mass-to-lisht raticS of CUL)=1.0.1.3 and 1.6 (measured in D band soluw units). aud use our photometrically-derived disk aud bulge light profiles Ln=Lagudp to dotermuue the stellar inass contribution to cach Lauigerotation curve: AM.=(M/L)Lpg.," Specifically, in our rotation curve models we allow mass-to-light ratios of $(M/L) = 1.0, 1.3$ and $1.6$ (measured in B band solar units), and use our photometrically-derived disk and bulge light profiles $L_{B} = L_{disk} + L_{bulge}$ to determine the stellar mass contributuion to each rotation curve: $M_{*} = (M/L) L_{B}$."
 We now explore a rauge of allowed dark matter halo masses and deusitv profiles. adopting two extreme models for disk galaxy formation.," We now explore a range of allowed dark matter halo masses and density profiles, adopting two extreme models for disk galaxy formation."
 In the first. we assuue that the dark matter halos surrounding these galaxies have not responded significautlv to the formation of the disks. i.e. adiahatic contraction (AC) does not occur.," In the first, we assume that the dark matter halos surrounding these galaxies have not responded significantly to the formation of the disks, i.e. adiabatic contraction (AC) does not occur."
 We refer to this as our “non-AC™ model., We refer to this as our “non-AC” model.
 In this case. the dark matter coutributuion to cach galaxy rotation curve is described by a density profiles that nirrors those found in dark matter smulatious: where ro is a characteristic “inner” radius. aud py a corresponding inner density.," In this case, the dark matter contributuion to each galaxy rotation curve is described by a density profiles that mirrors those found in dark matter simulations: where $r_s$ is a characteristic “inner"" radius, and $\rho_s$ a corresponding inner density."
 Tere we have adopted the profile shape of Navarro. Frenk White (1996: hereafter NEW).," Here we have adopted the profile shape of Navarro, Frenk White (1996; hereafter NFW)."
" The NEW profile is à two-parameter function and is completely specified by choosing wo independent parauters. e.g. the virial mass Mya, {or virial radius Tha ) aud concentration e;—Br, chune the profile cona]etelv (see Bullock et 22001b. tf Yon CLISCUSSIO1)."," The NFW profile is a two-parameter function and is completely specified by choosing two independent paramters, e.g. the virial mass $M_{\rm vir}$ (or virial radius $R_{\rm vir}$ ) and concentration $c_{\rm vir} \equiv R_{\rm vir}/r_s$ define the profile completely (see Bullock et 2001b, for a discussion)."
 Simuarly. eiven a virial mass AM aud he dark matter circular velocity at any radius. the halo οςonicentration eo 15 cOupletely determined.," Similarly, given a virial mass $M_{\rm vir}$ and the dark matter circular velocity at any radius, the halo concentration $c_{\rm vir}$ is completely determined."
" Iu the second class of inodels we adopt the scenario of ""adiabatic coutraction (AC) discussed by. BIumenutha et al (", In the second class of models we adopt the scenario of “adiabatic contraction” (AC) discussed by Blumenthal et al. (
1986: see also Bullock et al.,1986; see also Bullock et al.
 2001a. Pizaguo et 2005).," 2001a, Pizagno et 2005)."
 Tere we assume that the barvons anc dark matter initially follow au NEW profile aud. that the barvous cool aud settle iuto the halo ceuter slowly compared to a typical orbital time., Here we assume that the baryons and dark matter initially follow an NFW profile and that the baryons cool and settle into the halo center slowly compared to a typical orbital time.
 This slow infal provokes an adiabatic contraction in the halo deusitv distributuion and gives rise to a more conceutratec dark matter profile., This slow infall provokes an adiabatic contraction in the halo density distributuion and gives rise to a more concentrated dark matter profile.
" The idea of adiabatic contraction was originally discussed as to explain the ""conspiracv between dark halos aud disk sizes which gives rise to a", The idea of adiabatic contraction was originally discussed as to explain the “conspiracy” between dark halos and disk sizes which gives rise to a
FasATTNO.. although this line is wach narrower than the luur?5? line.,"as, although this line is much narrower than the 787 line."
 These lines cannot be redshifted. higher order Lyman lines. because the corresponding Lya lines are not detected in the longer wavelength UV spectra obtained with COURS/STIS.," These lines cannot be redshifted, higher order Lyman lines, because the corresponding $\alpha$ lines are not detected in the longer wavelength UV spectra obtained with GHRS/STIS."
 Associated absorption by lam9977. Llunll391. LL11518.1550. LL11032.1038 as well as several members of the Lyman series of lydrogen have been detected in T1821|613 bv Savage.Tripp&Lu(1998) aud Penton.Stocke&Shull (2000).," Associated absorption by 977, 1394, 1548,1550, 1032,1038 as well as several members of the Lyman series of hydrogen have been detected in H1821+643 by \citet{savage98} and \citet{penton00}."
. The FUSE aud UST observations combined show a broad range of ionization iu the associated absorber(s) iucludiueOV and .," The FUSE and HST observations combined show a broad range of ionization in the associated absorber(s) – including, and ."
 However. no low ionization species such as oor thas been observed.," However, no low ionization species such as or has been observed."
 We see uo evidence for LL7770.780 absorption iu the FUSE data at i4;= 296712.," We see no evidence for 770,780 absorption in the FUSE data at $z_{abs}=0.29673$ ."
 There are 23Pa possible sites of associated absorption in the III8211613. spectrum: (1) the host galaxw of he QSO. (2) the intracluster iuediun (CAD. or (3) a cluster ealaxy or galaxies along the line of sight to he QSO.," There are 3 possible sites of associated absorption in the H1821+643 spectrum: (1) the host galaxy of the QSO, (2) the intracluster medium (ICM), or (3) a cluster galaxy or galaxies along the line of sight to the QSO."
 Absorbing gas which is near the QSO central engine i8 often called “intrinsic” absorption., Absorbing gas which is near the QSO central engine is often called “intrinsic” absorption.
 Tn many specific cases. there is strong spectroscopic evidence that associated NÀLs are iutrinsic.," In many specific cases, there is strong spectroscopic evidence that associated NALs are intrinsic."
 The evidence iucludes: (1) time variable line streneths. (2) smooth absorption that is broad compared to the thermal line width. (3) partial covering of the contin source. and 1) presence of excited-state absorption (IEauauu&Ferland2000).," The evidence includes: (1) time variable line strengths, (2) smooth absorption that is broad compared to the thermal line width, (3) partial covering of the continuum source, and (4) presence of excited-state absorption \citep{hamann00}."
. None of these properties convincingly describes the T1821|613 associated absorber., None of these properties convincingly describes the H1821+643 associated absorber.
 Time-variability of absorption lines has not been reported. and cannot be addressed with this dataset.," Time-variability of absorption lines has not been reported, and cannot be addressed with this dataset."
 The liue is broader than its thermal line width. but is narrower than most iutriusic svstems. which typically have widths of 500," The line is broader than its thermal line width, but is narrower than most intrinsic systems, which typically have widths of $\sim 500$."
 The associated Lyo line observed in the IIST/STIS spectrum obtained by Tripp.Savage&Jenkis(2000) is black at the line ceuter (T. AL Tripp. private conumnumnication).," The associated $\alpha$ line observed in the HST/STIS spectrum obtained by \citet{tripp00} is black at the line center (T. M. Tripp, private communication)."
 This requires full) coverage of the continuum: source., This requires full coverage of the continuum source.
 Finally. excited-state absorption is not observed.," Finally, excited-state absorption is not observed."
 All of this evidence points to the associated absorber in II1821]6123 being unlike normal “trinsic” absorbers., All of this evidence points to the associated absorber in H1821+643 being unlike normal “intrinsic” absorbers.
 Nevertheless. we still thins that a likely origin of the associated absorption lies iu the nearby environs of the IM82116123 host galaxy.," Nevertheless, we still think that a likely origin of the associated absorption lies in the nearby environs of the H1821+643 host galaxy."
 Halos of cluster galaxies will be ranrpressure stripped by their passage through the itracluster medium., Halos of cluster galaxies will be ram-pressure stripped by their passage through the intracluster medium.
 Cas in the ICM is extremely hot (T~ 10K) and will have neslisible ionic fractious of aad.," Gas in the ICM is extremely hot $T\sim10^7$ K), and will have negligible ionic fractions of and."
 I£ a cooling flow exists in the cluster. then the aad less ionized species formed in this cooling eas would exist close to the cD ealaxy at the cluster center — the host of T18211613," If a cooling flow exists in the cluster, then the and less ionized species formed in this cooling gas would exist close to the cD galaxy at the cluster center – the host of H1821+643."
 The photoionization models preseuted bw Taman(1997) indicate that an ionization paraueter of (—0.1 (for a wide range of coutimaiun shapes) is needed to simultaneously produce aud but then the fractional ionization of wwill be much too low to explain the absorption we detect.," The photoionization models presented by \citet{hamann97} indicate that an ionization parameter of $U \sim 0.1$ (for a wide range of continuum shapes) is needed to simultaneously produce and, but then the fractional ionization of will be much too low to explain the absorption we detect."
 IIeuce. a iiultiplase model is required to explain broad ranec of ionization present in the IT1821|613 sorptiontMbsorbor.," Hence, a multiphase model is required to explain the broad range of ionization present in the H1821+643 absorber."
 Multiple sites for the formation of the al is also consistent with the Lhuurrsi hne width., Multiple sites for the formation of the absorption is also consistent with the 787 line width.
 This work is based ou data obtained for the παντατοσα Time Team by the NASA-CNES-CSA FUSE 1uissiou, This work is based on data obtained for the Guaranteed Time Team by the NASA-CNES-CSA FUSE mission
The following relations then apply: assuming equal scale-heights for clouds and stellar mass.,The following relations then apply: assuming equal scale-heights for clouds and stellar mass.
" If the clouds are self-gravitating, then pj?= where x~10 is an estimate of the pressure enhancement due to self-gravity of interstellar clouds."," If the clouds are self-gravitating, then $p_{cl} ^{sg}= \pi \chi G {\Sigma_{cl}}^2 , $ where $\chi\sim 10$ is an estimate of the pressure enhancement due to self-gravity of interstellar clouds."
" We redefine p7=χρα, and can now write Sa=(pe/Pg)!/?(StotDg)/?. The covering factor S; of clouds in the disk is directly inferred to be δει=(Mo/Ma)fa, where fa is the gas fraction in clouds."," We redefine $p_{cl} ^{sg}=\chi p_{cl} ,$ and can now write $\Sigma_{cl} = (p_{cl}/p_{g})^{1/2}(\Sigma_{tot} \Sigma_g)^{1/2}.$ The covering factor $S_{cl}$ of clouds in the disk is directly inferred to be $ S_{cl}= {\left(\Sigma_g / \Sigma_{cl}\right)}f_{cl} ,$ where $f_{cl} $ is the gas fraction in clouds."
" We rewrite this as S4=PP. Here is the total (cloudfa(ps/pa) plus (Xdiffuse)/Yau) gas surface X,mass density.", We rewrite this as $ S_{cl}= f_{cl}{\left(p_{g}/p_{cl}\right)}^{1/2}{\left(\Sigma_g / \Sigma_{tot} \right)}^{1/2}.$ Here $\Sigma_{g}$ is the total (cloud plus diffuse) gas surface mass density.
" The cloud collision time-scale is teow=(XaH)/(Mgfaog), where the scale height Ho=(παΣιοι)/σῇ, and og is the cloud velocity dispersion."," The cloud collision time-scale is $t_{coll}=({\Sigma_{cl}H})/({\Sigma_{g}f_{cl}\sigma_g}),$ where the scale height $H^{-1}=({\pi G\Sigma_{tot}})/{\sigma_g^2}$, and $\sigma_g$ is the cloud velocity dispersion."
" The collision time can also be expressed aS teo=Sei'teross With toross=H/og, which becomes teol)=Ρα More generally, inclusion of more realistic 3D(H/o,). cloud kinematics (cf. (2008)))"," The collision time can also be expressed as $t_{coll} = {S_{cl}}^{-1} t_{cross}$ with $t_{cross} = {H/{\sigma_g}},$ which becomes $ t_{coll} =f_{cl}^{-1}(p_{cl}/p_{g})^{1/2}{\left( {\Sigma_{tot} / \Sigma_g}\right)^{1/2} \left(H / \sigma_g\right)} .$ More generally, inclusion of more realistic 3D cloud kinematics (cf. \citet{tas08}) )"
 yields correction factors of order unity., yields correction factors of order unity.
 We now assume the disk star formation rate is self-regulated by supernova feedback which drives the cloud velocity dispersion., We now assume the disk star formation rate is self-regulated by supernova feedback which drives the cloud velocity dispersion.
" While this assumption has a long history Firmani&Tutukov (1992))),"," While this assumption has a long history (c.f. \cite{firm92}) ),"
 it remains controversial., it remains controversial.
(c.f. Numerical simulations| certainly demonstrate that supernovae provide negative feedback into star-forming clouds by driving turbulence (Jou," Numerical simulations certainly demonstrate that supernovae provide negative feedback into star-forming clouds by driving turbulence \citep{jou06,tas06,koy08a, koy08b, kim07, jou08}."
"ng role in regulating star formation, via controlling the porosity of supernova remnant-driven bubbles (51142001) as well as the molecular hydrogen fraction (Blitz&"," Turbulent pressure plays an important role in regulating star formation, via controlling the porosity of supernova remnant-driven bubbles \citep{sil01} as well as the molecular hydrogen fraction \citep{bli06}."
" At the same time, global shear also plays a role in ∙∙controlling cloud peculiar velocities, especially for massive clouds (Gammieetal][1991)."," At the same time, global shear also plays a role in controlling cloud peculiar velocities, especially for massive clouds \citep{gam91}."
". Since global gravitational instabilities ultimately drive cloud formation, and hence control star formation, the common origin of competitive turbulence drivers means that effects of shear and supernovae in self-regulating cloud turbulence are not easily separated in 2-dimensional models (Shetty&Ostriker|2008)."," Since global gravitational instabilities ultimately drive cloud formation, and hence control star formation, the common origin of competitive turbulence drivers means that effects of shear and supernovae in self-regulating cloud turbulence are not easily separated in 2-dimensional models \citep{she08}."
". However fully three-dimensional high resolution models of self-consistent star-forming disks embedded within dark halos demonstrate that non-axisymmetric gravitational instabilities dominate the observed turbulence of ~10km/s at low star formation rates, but that supernova feedback will be important via the intermediary of the hot gaseous phase at a star formation rate in excess of 10-4Mpe""yr "," However fully three-dimensional high resolution models of self-consistent star-forming disks embedded within dark halos demonstrate that non-axisymmetric gravitational instabilities dominate the observed turbulence of $\sim 10 \rm km/s$ at low star formation rates, but that supernova feedback will be important via the intermediary of the hot gaseous phase at a star formation rate in excess of $10^{-3} \rm M_\odot kpc^{-2}yr^{-1}$ \citep{age09, tam09}."
Let ⋅⋅mgyw be the mass in stars formed in order to result in a Type II supernova., Let $m_{SN}$ be the mass in stars formed in order to result in a Type II supernova.
 This is just a function of the adopted IMF., This is just a function of the adopted IMF.
" Momentum balance gives Here f. is the cloud volume filling factor, which can be expressed in terms of porosity Q as f,=e9. Also, Egn is the kinetic energy of a SNe II and v. is the velocity at the onset of strong cooling of the SNe II remnant."," Momentum balance gives Here $f_c$ is the cloud volume filling factor, which can be expressed in terms of porosity $Q$ as $f_c=e^{-Q}.$ Also, $E_{SN}$ is the kinetic energy of a SNe II and $v_c$ is the velocity at the onset of strong cooling of the SNe II remnant."
 Canonical numbers used throughout are mgy=150M (for a Chabrier IMF) and v.=400kms.," Canonical numbers used throughout are $m_{SN} = 150 \rm M_{\odot}$ (for a Chabrier IMF) and $v_c= 400\, \rm kms^{-1}$."
 We can rewrite the star formation rate per unit volume as with esy=(pg/pa)/?. This formulation is commonly (mswveog)EsN used as a star formation rate prescription in semi-analytical modeling of galaxy formation., We can rewrite the star formation rate per unit volume as with $\epsilon_{SN}=({m_{SN}v_c\sigma_g}){E_{SN}}^{-1}({p_g}/{p_{cl}})^{1/2}.$ This formulation is commonly used as a star formation rate prescription in semi-analytical modeling of galaxy formation.
" It may be more relevant to rewrite this formulation for disks: where 3,,,=X,+Uy. Here the disk gas fraction is fg~0.1, and we use the disk scale-height -to-radius relation H/R=(o,/v,;)? for a disk rotating at v, with Q?=GY,4/R. Remarkably, although the preceding formula ignores the multi-phase nature of the interstellar medium and the possibility of gas outflows (see below), one nevertheless manages to fit the Schmidt-Kennicutt relation."," It may be more relevant to rewrite this formulation for disks: where $\Sigma_{tot} =\Sigma_{g} +\Sigma_\ast.$ Here the disk gas fraction is $f_g \sim 0.1$, and we use the disk scale-height -to-radius relation $H/R=(\sigma_g/v_r)^2$ for a disk rotating at $v_r$ with $\Omega^2=G\Sigma_{tot}/R.$ Remarkably, although the preceding formula ignores the multi-phase nature of the interstellar medium and the possibility of gas outflows (see below), one nevertheless manages to fit the Schmidt-Kennicutt relation."
" We write the observed Schmidt-Kennicutt (SK) law as oy=CskYl* and obtain the SK law coefficient Inserting typical parameter values, we find that 'This demonstrates that we get the correct normalization at, say, 3 kpc, the scale length of the molecular gas in the Milky Way, where the scale-height is around 100 pc, the gas fraction is around 0.2, and the molecular gas covering fraction around3096."," We write the observed Schmidt-Kennicutt (SK) law as $\dot\Sigma_\ast=C_{SK}\Sigma_{g}^{3/2},$ and obtain the SK law coefficient Inserting typical parameter values, we find that This demonstrates that we get the correct normalization at, say, 3 kpc, the scale length of the molecular gas in the Milky Way, where the scale-height is around 100 pc, the gas fraction is around 0.2, and the molecular gas covering fraction around."
. The observed star formation efficiency in inner spiral disks is found to be fairly robust and for [Es alone amounts to 5.25c2.510”!9yr! (Leroyetal.|2008)., The observed star formation efficiency in inner spiral disks is found to be fairly robust and for $H_2$ alone amounts to $5.25 \pm 2.5 10^{-10 } \rm yr^{-1}$ \citep{le08}.
". This compares well with the Kennicutt law, both locally and at z~2 in shape (X.€32/2) and in normalization (for egy& 0.02) (Bouché2007)."," This compares well with the Kennicutt law, both locally and at $z\sim 2$ in shape $\dot\Sigma_\ast \simpropto \Sigma_{gas}^{3/2}$ ) and in normalization (for $ \epsilon_{SN} \approx
0.02$ ) \citep{bou07}."
" For the luminous starbursts at z~2, theet al]turbulence is enhanced (og~ 40km/s), but the scale height is thickened."," For the luminous starbursts at $z\sim 2, $ the turbulence is enhanced $\sigma_g\sim 40\rm km/s $ ), but the scale height is thickened."
" One reason is that egyοςog and (R/H)!?«x1/σᾳ for disks with varying amounts of turbulence, as might be induced by minor mergers."," One reason is that $\epsilon_{SN}\propto\sigma_g$ and $(R/H)^{1/2}\propto 1/\sigma_g$ for disks with varying amounts of turbulence, as might be induced by minor mergers."
" If the covering factor increases, it is not obvious if the star formation rate in a cloud collision model would increase."," If the covering factor increases, it is not obvious if the star formation rate in a cloud collision model would increase."
" To lowest order, these effects all cancel at fixed Σο, and we can hence understand how starbursts remain on the local Schmidt-Kennicutt law."," To lowest order, these effects all cancel at fixed $\Sigma_{tot}$, and we can hence understand how starbursts remain on the local Schmidt-Kennicutt law."
 Supernova feedback effectively keeps star formation inefficient., Supernova feedback effectively keeps star formation inefficient.
" Of course, we need to better understand how starbursts satisfy the same scaling law as quiescent disks."," Of course, we need to better understand how starbursts satisfy the same scaling law as quiescent disks."
" One hint is that while the gas velocity dispersion may vary in starbursts depending on the merging history, Xo; satisfies Freeman's law and is approximately constant for star-forming disk galaxies."," One hint is that while the gas velocity dispersion may vary in starbursts depending on the merging history, $\Sigma_{tot}$ satisfies Freeman's law and is approximately constant for star-forming disk galaxies."
" The observed dispersion in the Schmidt-Kennicutt law may arise from the dispersion in total surface density and molecular as well as total gas fraction f,.", The observed dispersion in the Schmidt-Kennicutt law may arise from the dispersion in total surface density and molecular as well as total gas fraction $f_g$ .
 Suetal.2010)) ⋝∏⋝↕≼∖⋠∖⋯↕⊺⋠↕↾↕⋮↕∩∩≼⊲∎⋠∖∖⇁↕↓∏↓≼∖↕⋯↓⋠∖↕o ~i507 (~10 iu etal.2011iereafter &Aliaroniau(2011)sugeested imuples a more recent transient event., \citealt{dobler10}; \citealt{su10}) $1\lesssim E_{\gamma}\lesssim 100$ $\sim 50^{\circ}$ $\sim 10$ $40^{\circ}$ \citealt{dobler11} \citet{crocker11} implies a more recent transient event.
" Iun contrast. Dobler)obleretal.(2010)(2010 audand SuSuetetal.(2010)(2010 arguedargue that the enission may —be dominated by upscatteriug— of p1 onthethe mitersteliariü radiation.ation Sell"" GRE)ISLE andrt tic cosmic jotonismicrowaven backeround by CR electrons. whose ↴∖↴⋅↖↽∐↸⊳↕∐⋅∪⊓⋅∪∐↸∖∐∐↴∖↴↴∖↴↕∪∐↕⊔⋜↧⋅↖↽∐⋜∏⇁↸∖⋜↧∐⋅↸∖⋜∥∙↖⇁↴⋝↸∖↸∖∐≼∐∖↑↸∖↸⊳↑↸∖≼↧ ∙∙ at tens: of (ΤΠ.GITz by- theà (WMAP: Finkbeiner2001: Dobler&Fin"," In contrast, \citet{dobler10} and \citet{su10} argued that the emission may be dominated by upscattering of photons in the interstellar radiation field (ISRF) and the cosmic microwave background by CR electrons, whose synchrotron emission may have already been detected at tens of GHz by the (WMAP; \citealt{finkbeiner04a}; \citealt{dobler08}) )."
"kbeiner Cheng etae that periodic me ougitiude. AS ‘""»D ACN MM$ed d.Itfo Ἡι-l nSeununua-ray OBI US ”-”- winds 10 iuto the n » The Fermi ntbbleswithin a few 2 UMIvrs."," \citet{cheng11} argued that periodic star capture processes by the Galactic supermassive black hole, Sgr $^{*}$, release AGN winds into the Galactic halo, producing the bubbles within a few Myrs."
"Zubovas ot.al.the(2011)suggested |that the near-spherical out BowThe a quasar event of Ser AY 6 Myr ago may . the5 origin"" ofB the »bbles", \citet{zubovas11} suggested that the near-spherical outflow from a quasar event of Sgr $^{*}$ around $6$ Myr ago may explain the origin of the bubbles.
" bulue conpanion pepe (Co ©NoMatüewsMat""Tdiffused denoted as Paper V). we performed the20: first of1 ani 1iWe""mfotos The5 EE Mαπ, VNclaimedk . S. A anNI nami AR Utm 1: »feature).with originated TOMmines o: Myr ago can the the Ferm: oSrwith roughly 1-3the observed ei Ocation. size. avl shape."," In a companion paper \citealt{guo12}; hereafter denoted as “Paper I""), we performed the first numerical simulation following the dynamical evolution of the bubbles, and showed that a recent AGN jet event originated from Sgr $^{*}$ around $1$ - $3$ Myr ago can reproduce the bubbles with roughly the observed location, size, and shape."
 Our jet model is inspired * inany extragalactic AGN jets. which are clearly xoduciug CR-filled bubbles seen iu radio observations (AIcNamara&Nulseu2007).," Our jet model is inspired by many extragalactic AGN jets, which are clearly producing CR-filled bubbles seen in radio observations \citep{mcnamara07}."
. In our model. the opposing jets. dominated by kinetic energy aud over-pressured by either CR or thermal pressure. were active for 0.1 - 0.5 Abvr and moderately light.," In our model, the opposing jets, dominated by kinetic energy and over-pressured by either CR or thermal pressure, were active for $\sim 0.1$ - $0.5$ Myr and moderately light."
 We also showthat theveep»ibble edges require that CR diffusion across thebubble edges is suppressed significantlybelow the CR diffusion rate estimated in the solar vicinity., We also showthat thesharpbubble edges require that CR diffusion across the bubble edges is suppressedsignificantly below the CR diffusion rate estimated in the solar vicinity.
follows the light profile.,follows the light profile.
 We thus add three constraints to the model: the PA of the galaxy. its ellipticity ¢ and effective radius Roy; (see Table 3)).," We thus add three constraints to the model: the PA of the galaxy, its ellipticity $e$ and effective radius $R_{eff}$ (see Table \ref{gal7}) )."
 Due to the limited number of observational constraints. isothermal mass profiles are assumed to be spherically symmetric (SIS. re. Singular Isothermal Sphere) when modeling doubles.," Due to the limited number of observational constraints, isothermal mass profiles are assumed to be spherically symmetric (SIS, i.e. Singular Isothermal Sphere) when modeling doubles."
 This 1s not a strong asumption as the quadrupole term of the potential modifies only slightly the time delays of doubly imaged quasars (22)..," This is not a strong asumption as the quadrupole term of the potential modifies only slightly the time delays of doubly imaged quasars \citep{Kochanek2002, Wucknitz2002}."
 For quads. we allow the ellipticity of the isothermal mass distribution (SIE. te. Singular Isothermal Ellipsoid) to deviate from the ellipticity of the light profile.," For quads, we allow the ellipticity of the isothermal mass distribution (SIE, i.e. Singular Isothermal Ellipsoid) to deviate from the ellipticity of the light profile."
 This enables to account for dark matter halos that would be rounder then the light distribution (?).., This enables to account for dark matter halos that would be rounder then the light distribution \citep{Ferreras2008}.
 The position angle of the total mass distribution can be constrained as the one of the light profile as these two distributions might only be slightly misaligned (??)..," The position angle of the total mass distribution can be constrained as the one of the light profile as these two distributions might only be slightly misaligned \citep{Keeton1997a, Ferreras2008}."
 Finally. we also assume that the center of the total mass distribution and the one of the light profile are identical within the error bars.," Finally, we also assume that the center of the total mass distribution and the one of the light profile are identical within the error bars."
 This is supported by the work of ?) who found. for 4 lensed quasars with an Einstein ring. that the offset between the light and the total mass distribution is limited to a few mas.," This is supported by the work of \citet{Yoo2006} who found, for 4 lensed quasars with an Einstein ring, that the offset between the light and the total mass distribution is limited to a few mas."
 Calculating the number of degree(s) of freedom (d.o.f.).," Calculating the number of degree(s) of freedom (d.o.f.),"
 which ts the difference between the number of model parameters and observable quantities. we find 0 d.o.f.," which is the difference between the number of model parameters and observable quantities, we find 0 d.o.f."
 when modeling doubly imaged quasars and 2 (resp., when modeling doubly imaged quasars and 2 (resp.
 3) d.o.f., 3) d.o.f.
 when modeling quads with SIE (resp., when modeling quads with SIE (resp.
 de Vaucouleurs) + external shear., de Vaucouleurs) + external shear.
 The search for the best model and estimate of uncertainties is performed in two steps., The search for the best model and estimate of uncertainties is performed in two steps.
 First. we generate an initial sample of 2000 different models with parameters distributed over the whole parameter space and optimize them.," First, we generate an initial sample of 2000 different models with parameters distributed over the whole parameter space and optimize them."
 This method is efficient to find the best models and identify local minima., This method is efficient to find the best models and identify local minima.
 Then. in order to estimate the model uncertainties. we sample the posterior probability. distribution of the parameter space using an adaptive Metropolis Hastings Monte-Carlo Markov Chain (MCMC) algorithm.," Then, in order to estimate the model uncertainties, we sample the posterior probability distribution of the parameter space using an adaptive Metropolis Hastings Monte-Carlo Markov Chain (MCMC) algorithm."
 This technique is implemented in LENSMODEL and described in ?).., This technique is implemented in LENSMODEL and described in \citet{Fadely2010}.
" In practice. an ensemble of 15 different chains are run, each chain consisting of a sequence of trial steps drawn from a multivariate gaussian distribution of width estimated thanks to the first step of the process."," In practice, an ensemble of 15 different chains are run, each chain consisting of a sequence of trial steps drawn from a multivariate gaussian distribution of width estimated thanks to the first step of the process."
 The sampling of the parameter space is optimised by using the covariance matrix., The sampling of the parameter space is optimised by using the covariance matrix.
 In of the steps. the covariance matrix 18 diagonal. allowing to use a large step along one of the axis and better escape local minima in the y surface.," In of the steps, the covariance matrix is diagonal, allowing to use a large step along one of the axis and better escape local minima in the $\chi^2$ surface."
 We use the same criterion as 2). to assess that any MCMC run has converged., We use the same criterion as \citet{Fadely2010} to assess that any MCMC run has converged.
 Finally. for each point of the MCMC. we calculate the relative likelihood of a parameter p based on the y statistics (i.e. L(D|p)= exp(—y7/2)). and calculate a confidence interval for each parameter.," Finally, for each point of the MCMC, we calculate the relative likelihood of a parameter $p$ based on the $\chi^2$ statistics (i.e. $L(D|p) = exp(-\chi^2/2)$ ), and calculate a confidence interval for each parameter."
 The parameters of the best fit models are displayed in Table 4.., The parameters of the best fit models are displayed in Table \ref{lensmodel7}.
" The columns display the following items: the name of the object. the type of mass distribution used (CDV"" stands for profile). the mass scale parameter (the angular Einstein radius Rp; 1n areseconds). the mass distribution ellipticity e and its orientation 8, in degrees positive East of North. the effective radius R,;; in areseconds in the case of a de Vaucouleurs model. the intensity of the shear y and its orientation 9, in degrees (East of North). the number of degree(s) of freedom (d.o.f.)."," The columns display the following items: the name of the object, the type of mass distribution used (“DV” stands for ), the mass scale parameter (the angular Einstein radius $R_{Ein}$ in arcseconds), the mass distribution ellipticity $e$ and its orientation $\theta_{e}$ in degrees positive East of North, the effective radius $R_{eff}$ in arcseconds in the case of a de Vaucouleurs model, the intensity of the shear $\gamma$ and its orientation $\theta_{\gamma}$ in degrees (East of North), the number of degree(s) of freedom (d.o.f.),"
 the y of the fit and the predicted time delays in days when the lens redshift is known., the $\chi^{2}$ of the fit and the predicted time delays in days when the lens redshift is known.
 For the quads and in the same column as the y. we also give the Vm which ts the contribution of the lensed Images position to the (C. and U which is the contribution of the lens galaxy position to the y.," For the quads and in the same column as the $\chi^{2}$, we also give the $\chi^{2}_{im}$ which is the contribution of the lensed images position to the $\chi^{2}$, and $\chi^{2}_{l}$ which is the contribution of the lens galaxy position to the $\chi^{2}$."
" Let us note that Ary,> 0 means that the flux of A varies before the one of B. The median value of each parameter along with confidence level is shown in Table 5..", Let us note that $\Delta t_{AB} >$ 0 means that the flux of A varies before the one of B. The median value of each parameter along with confidence level is shown in Table \ref{MCMC7}.
 For the doubly imaged quasars. both SIS+shear and DV+shear models can reproduce the image configuration as well as the flux ratio. even with our constraints on the shape of the galaxy in the case of a de Vaucouleurs profile.," For the doubly imaged quasars, both SIS+shear and DV+shear models can reproduce the image configuration as well as the flux ratio, even with our constraints on the shape of the galaxy in the case of a de Vaucouleurs profile."
 Two systems require a large amount of shear (Le. y>0.1 for both mass models) to reproduce the lens configuration: SDSS J1226-0006 and SDSS J1155+6346., Two systems require a large amount of shear (i.e. $\gamma > 0.1$ for both mass models) to reproduce the lens configuration: SDSS J1226-0006 and SDSS J1155+6346.
" For SDSS J1226-006. the HST/NIC2 images actually reveal a galaxy Go at RA=177153 and DEC=371710 from image A (3744 from the main deflector). about 15° off the direction of &,."," For SDSS J1226-006, the HST/NIC2 images actually reveal a galaxy $\rm G_{2}$ at $\rm RA=1\farcs7153$ and $\rm DEC=3\farcs1710$ from image A 4 from the main deflector), about $^{\circ}$ off the direction of $\theta_{\gamma}$."
 This galaxy. which type is unknown. is likely not the only source of shear.," This galaxy, which type is unknown, is likely not the only source of shear."
" Indeed. the luminosity ratio between G» and the lens is να,=4.8."," Indeed, the luminosity ratio between $\rm G_{2}$ and the lens is $L_{lens}/L_{G_{2}}=4.8$ ."
 Assuming we can use the Faber-Jackson relation (L&ot.?). this ratio leads to Crens/OG.=1.5. Tens and σα. being respectively the velocity dispersion of the lens and of Gs.," Assuming we can use the Faber-Jackson relation \citep[L $\propto \sigma^{4}$, this ratio leads to $\sigma_{lens}/\sigma_{G_{2}}=1.5$, $\sigma_{lens}$ and $\sigma_{G_{2}}$ being respectively the velocity dispersion of the lens and of $\rm G_{2}$."
" The isothermal model allows us to translate Rrj, of the lens to cj,4;.", The isothermal model allows us to translate $R_{Ein}$ of the lens to $\sigma_{lens}$.
 We find ση=212 km/s and thus σος=141 km/s. Using formula A.20 of ?) and supposing Go ts at the same redshift as the lens. this induces a shear of y=0.039. more than 2 times smaller than the one predicted by the SIS model.," We find $\sigma_{lens}=212$ km/s and thus $\sigma_{G_{2}}=141$ km/s. Using formula A.20 of \citet{Momcheva2006} and supposing $\rm G_{2}$ is at the same redshift as the lens, this induces a shear of $\gamma=0.039$, more than 2 times smaller than the one predicted by the SIS model."
 Other galaxies 1n the field are probably responsible for the remaining shear., Other galaxies in the field are probably responsible for the remaining shear.
 A more dramatic case is SDSS J1155+6346. for which models predict a shear as large as 0.4 to reproduce the observed configuration.," A more dramatic case is SDSS J1155+6346, for which models predict a shear as large as 0.4 to reproduce the observed configuration."
 This is one of the largest shears needed to reproduce a lensed quasar system., This is one of the largest shears needed to reproduce a lensed quasar system.
 On some larger field images of this object (obtained with ACS onboard HST. PE: ο. Kochanek). we do not see any bright galaxy in its vicinity.," On some larger field images of this object (obtained with ACS onboard HST, PI: C.S. Kochanek), we do not see any bright galaxy in its vicinity."
 We thus suspect that a massive galaxy cluster lies outside the ACS field. though nothing is clearly visible on the SDSSdata®.," We thus suspect that a massive galaxy cluster lies outside the ACS field, though nothing is clearly visible on the SDSS."
. Deeper images would be necessary to infirm or confirm the existence of this cluster., Deeper images would be necessary to infirm or confirm the existence of this cluster.
" In the case of HE 0047-175. a diffuse component lies at RA=-0""0434 and DEC=-2'93505 from image A (156 from the lens). in the direction of the shear (see Fig. 1))"," In the case of HE 0047-175, a diffuse component lies at $\rm RA=-0\farcs0434$ and $\rm DEC=-2\farcs3393$ from image A $1\farcs56$ from the lens), in the direction of the shear (see Fig. \ref{dec_NICMOS7}) )"
 unregarding the employed model., unregarding the employed model.
 Although very faint (about 2 mag fainter than the lens). this galaxy is likely the major contribution to the shear in this system.," Although very faint (about 2 mag fainter than the lens), this galaxy is likely the major contribution to the shear in this system."
 Indeed.a SIS with c=88km/s would produce the observed amount of shear. if located at the position of this faint companion (assuming Zeomp=Zions 0.407).," Indeed,a SIS with $\sigma = 88 \ \rm km/s$ would produce the observed amount of shear, if located at the position of this faint companion (assuming $\rm z_{comp} = \rm z_{lens} = 0.407$ )."
wih which they cross hat part of the color-magnitude diagram. should likely inprove he results and possildv CXend its applicability to metal-poor stars.,"with which they cross that part of the colour-magnitude diagram, should likely improve the results and possibly extend its applicability to metal-poor stars."
 Rotation changes he position of the stars in the COour-uaenitudoe diagrau (Maceer Pevtremann 1970)., Rotation changes the position of the stars in the colour-magnitude diagram (Maeder Peytremann 1970).
" Typically. the position o La star rotating at ~200 kn 1 wi] change by 0.10.3 nag in M, aud 2ο250 I in τμ."," Typically, the position of a star rotating at $\sim 200$ km $^{-1}$ will change by 0.1–0.3 mag in $M_v$ and 200–250 K in $T_{\rm eff}$."
 Therefore. for high rotaional velocities. has to be takeu iuto account before appvine the procedure described here.," Therefore, for high rotational velocities, has to be taken into account before applying the procedure described here."
 It is possible to eet better B.V colotro estiniatfes than those compiled in the catalogue., It is possible to get better B–V colour estimates than those compiled in the catalogue.
" The caibratiou of IEunmanec (1998) amakes it possible to accurately estimate the V aud D colours from the V aud D iudices together with the II, iunaguitudes.", The calibration of Harmanec (1998) makes it possible to accurately estimate the V and B colours from the $-$ V and $-$ B indices together with the $H_p$ magnitudes.
 Besides. the BV colours listed iu the catalogue can be refined by conibiuσα18o them) wih Earh-hased measurements. as proved by Clementini e al. (," Besides, the B–V colours listed in the catalogue can be refined by combining them with Earth-based measurements, as proved by Clementini et al. ("
1999).,1999).
 We have selected the set of isochrones ¢erived roni the evolutionary calculations ο: Bertell et al. (, We have selected the set of isochrones derived from the evolutionary calculations of Bertelli et al. (
1991) because hey are one of the most houxSOLO ale coniprehensive azione those publicly availade in electronic format.,1994) because they are one of the most homogeneous and comprehensive among those publicly available in electronic format.
 I is of interest to check wnher the lise of alternative uodeIs woulL lead to the saue conclusions., It is of interest to check whether the use of alternative models would lead to the same conclusions.
 Consideringo he particuir case of stars between 0.8 ix 1.25 AL. of Civ., Considering the particular case of stars between 0.8 and 1.25 $_{\odot}$ of 4 Gyr.
 age. we cau compare the caleulations «of VandeuBere (1985) with those of Bertelli ct al. ," age, we can compare the calculations of VandenBerg (1985) with those of Bertelli et al. ("
©991).,1994).
 Fieure 7 displavs such a comparison iu both. f1ο theoretica (logy Tot) aud observational (AL). BV) planes.," Figure \ref{Figl} displays such a comparison in both, the theoretical $\log g - T{\rm eff}$ ) and observational $M_v -$ B–V) planes."
 The poiuts iu tI| isochrones corresponding equal nisses (left-side panels: 0.8. 1.0. 1.25 AD.) or raH Gieht-huux panels: 0.83. 1.20. 2.0. 2.51 Rk. ) have heen iuked by solic seemeuts.," The points in the isochrones corresponding to equal masses (left-side panels; 0.8, 1.0, 1.25 $_{\odot}$ ) or radii (right-hand panels; 0.83, 1.20, 2.0, 2.51 $_{\odot}$ ) have been linked by solid segments."
 Differences in the theoretical plajo may be the (ffect of one or more of the different iugredieuts iu the calculations. such as convection tfreatiuenr or radiative Qowities (Los Alamos Opacity Library vs. OPAL). as well as shehbtly citfereu asstuned metallicities (Z=0.0169 vs. 0.02). or lass fracion of Lelimm (Y=0.25 vs. 0.28).," Differences in the theoretical plane may be the effect of one or more of the different ingredients in the calculations, such as convection treatment or radiative opacities (Los Alamos Opacity Library vs. OPAL), as well as slightly different assumed metallicities (Z=0.0169 vs. 0.02), or mass fraction of helium (Y=0.25 vs. 0.28)."
 The agreement is better for the dwarfs with lower effective temperatures and ects poorer for lower eravitics., The agreement is better for the dwarfs with lower effective temperatures and gets poorer for lower gravities.
 However. the discrepajicies in fi6 observational plane )oconie 11010 sienificaut and systenatic. and could iuduce nuportant differences 1ji the resuts.," However, the discrepancies in the observational plane become more significant and systematic, and could induce important differences in the results."
 Even though there are details μιch as discordant assuniptious for the Suus )olonmetrie crection 0.12. vs. 0.08). the different uodoel atiunosshores employed iu tjo frauslation frou he heoretical magnitudes iust play a major role.," Even though there are details such as discordant assumptions for the Sun's bolometric correction $-0.12$ vs. $-0.08$ ), the different model atmospheres employed in the translation from the theoretical magnitudes must play a major role."
 The more recent mode oO ⋜↧↑⋯∪↴∖↴↻∐↸∖↥⋅↸∖↴∖↴≺↕↘⊽↿∐⋅↿cz 1992) eniplowed bx Bertelli et al., The more recent model atmospheres (Kurucz 1992) employed by Bertelli et al.
 ↻↸∖↥⋅↕≯∪↥⋅⋯⋜∥∐∖≺∣∏⋜↧↑↸∖↕⋅↖↽∙⋜↧↴∖↴↴∖↴∏∶↴∙⊾∶↴∙⊾↸∖↴∖↴↑↸∖≺↧↴⋝∙↖↽ he conclusions i ," perform adequately, as suggested by the conclusions in 3."
T16 positions in the logyTar plane predicted by the calcuatiois of Schaller et al. (, The positions in the $\log g - T_{\rm eff}$ plane predicted by the calculations of Schaller et al. (
1992) without overshootiig.oO shown wihi filled circles in the left-side upper paucl of Fig.,"1992) without overshooting, shown with filled circles in the left-side upper panel of Fig."
 7 for 0.5. 1.0. and 1.25 AI... do not exactly overlap neither with the predictions derived from Bertelli et al," \ref{Figl} for 0.8, 1.0, and 1.25 $_{\odot}$, do not exactly overlap neither with the predictions derived from Bertelli et al."
is calculatiois nor with those of VaudeuBerg (1985). vet even so they include the sine radiative opacities (LAOL: IIucbner et al.,"'s calculations, nor with those of VandenBerg (1985), yet even so they include the same radiative opacities (LAOL; Huebner et al."
 1977) aid assume the same value for the mixiue-leusth a as VavdeuBere’s models., 1977) and assume the same value for the mixing-length $\alpha$ as VandenBerg's models.
 Again. slightly cliffereit valies for Z... ων and details iu the treatiuneut of envelope convection uist be responsible.," Again, slightly different values for $_{\odot}$, $_{\odot}$, and details in the treatment of envelope convection must be responsible."
 The open circle correspond. to a 1.25 model with overshooting., The open circle correspond to a 1.25 $_{\odot}$ model with overshooting.
 Daona (1901) made use of the calibration of Balona Shu)bbrook (1981) o estimate absolute magnitudes from he svuthetic SStrónuueren indices computed by Lester ot al. (, Balona (1994) made use of the calibration of Balona Shobbrook (1984) to estimate absolute magnitudes from the synthetic Strömmgren indices computed by Lester et al. (
1956) based ou Iurucz (1979) moclel atiiosoieres.,1986) based on Kurucz (1979) model atmospheres.
 Ie derived effective teiiperatures. eravitics. and luminosities from the model atmospheres. and used the Togs and luninosities to interpolate in the models of stellar evolution by Claret Camenez (1992) aud Schaller et al. (," He derived effective temperatures, gravities, and luminosities from the model atmospheres, and used the $T_{\rm eff}$ s and luminosities to interpolate in the models of stellar evolution by Claret Gimenez (1992) and Schaller et al. ("
1992) and tjen cstimate evavitics.,1992) and then estimate gravities.
 The comparison showed that the eravitics were arecr than the eravitics from the model atinosphlieres. for stars with logg<1. and the discrepancy was increasing owards lower eravitics.," The comparison showed that the gravities were larger than the gravities from the model atmospheres for stars with $\log g < 4$, and the discrepancy was increasing towards lower gravities."
 Besides. the situation appeared ο be reversed for stars with logg>1.," Besides, the situation appeared to be reversed for stars with $\log g > 4$."
 The evolutionary caleulations used here tend to unuderpredict he stellar uasses for low-eravity stars., The evolutionary calculations used here tend to underpredict the stellar masses for low-gravity stars.
 However. this effect is much s3inaller aud in opposite seuse to the huge differeuces found w Balona (1991) that were as large as 0.5 dex for logg (evolutionary) ~3.5.," However, this effect is much smaller and in opposite sense to the huge differences found by Balona (1994) that were as large as 0.5 dex for $\log g$ ) $\sim 3.5$."
 The explanation is still unclear. mt we note that the comparison of the eravitics from LTE Quodelatmospheres) spectroscopic analysis (iron lonization equilibria) with those obtaimed combining paralaxes and evolutiomary unocdels secum to agree reasonably well (Allende Prieο et al.," The explanation is still unclear, but we note that the comparison of the gravities from LTE (model-atmospheres) spectroscopic analysis (iron ionization equilibrium) with those obtained combining parallaxes and evolutionary models seem to agree reasonably well (Allende Prieto et al."
 1999: see also Fulu1iianun 1998)., 1999; see also Fuhrmann 1998).
 Gravitational redshifts are proportional to the mass-radius ratio aix systematically affect measurements of stellar radial vekcities (Dravius et al., Gravitational redshifts are proportional to the mass-radius ratio and systematically affect measurements of stellar radial velocities (Dravins et al.
 1999)., 1999).
 Photospheric spectral lines are shifted bv rougilv 600 us + for a star like the Sin. and by more than 1000 m + for more massive stars m the main seqence.," Photospheric spectral lines are shifted by roughly 600 m $^{-1}$ for a star like the Sun, and by more than 1000 m $^{-1}$ for more massive stars in the main sequence."
" The curpirically deternüned errors for masses aud radi derived from the »oxition of a star iu the colouraAnagnuitude diagram make it possible to estimate its gravitational redshift with au ποai vo ""the order of 100 ms 1", The empirically determined errors for masses and radii derived from the position of a star in the colour-magnitude diagram make it possible to estimate its gravitational redshift with an uncertainty of the order of 100 m $^{-1}$.
 A precise knowledge of the stellar radius iud the disance o the star combine ogether to translate the measured stellar flux to he fhx at the star's surface. a quantity that can be σοιxwed with svuthetic spectra from i1uodel atux]olieres.," A precise knowledge of the stellar radius and the distance to the star combine together to translate the measured stellar flux to the flux at the star's surface, a quantity that can be compared with synthetic spectra from model atmospheres."
 Spectrophotometry is already available for the large sa11dle of stars observed by IUE. UST. anc μα. ofier missions. and their mvestigation wil likely provide valuable inforiuatiou on the stellar content of he Calactic «isc in the solar neighbourhood and bevoud.," Spectrophotometry is already available for the large sample of stars observed by IUE, HST, and many other missions, and their investigation will likely provide valuable information on the stellar content of the Galactic disc in the solar neighbourhood and beyond."
of V1494 Aql and that has initiated a careful re-check of the literature and previous data.,of V1494 Aql and that has initiated a careful re-check of the literature and previous data.
 All observations were reduced with in a standard fashion., All observations were reduced with in a standard fashion.
 Spectroscopic reductions included bias. flat and sky background corrections.," Spectroscopic reductions included bias, flat and sky background corrections."
 Aperture extraction and wavelength calibrations were done with the task utilizing CuAr spectral lamp exposures taken before and after every ten stellar exposures., Aperture extraction and wavelength calibrations were done with the task utilizing CuAr spectral lamp exposures taken before and after every ten stellar exposures.
 The flux calibration used a spectrum of LTT 7379. a GO-type spectroscopic. standard.," The flux calibration used a spectrum of LTT 7379, a G0-type spectroscopic standard."
 Time-series direct images were corrected with bias and sky-flat frames. while instrumental R-band magnitudes were calculated with simple aperture photometry (the diameter of the aperture was set to 6755) in respect to comparison stars located within 100.," Time-series direct images were corrected with bias and sky-flat frames, while instrumental $R$ -band magnitudes were calculated with simple aperture photometry (the diameter of the aperture was set to 5) in respect to comparison stars located within 0."
 Following Barsukova Goranskit 2003. the main comparison was GSC 0473-4227.," Following Barsukova Goranskii 2003, the main comparison was GSC 0473–4227."
" Typical photometric accuracy was 0901—0""02.", Typical photometric accuracy was $\pm0\fm01-0\fm02$.
 The original purpose of making sharp images on October 18. 2003 was checking the presence or absence of a resolvable nova shell.," The original purpose of making sharp images on October 18, 2003 was checking the presence or absence of a resolvable nova shell."
 The predicted angular radius of the shell 3.8 years after the outburst is 07994 (following Kiss Thomson 2000, The predicted angular radius of the shell 3.8 years after the outburst is 94 (following Kiss Thomson 2000
"mean value of —2.0, there are pointings that exhibit more structure in the PDS around 0.01 Hz with multiple peaks just below the significance level.","mean value of $-$ 2.0, there are pointings that exhibit more structure in the PDS around 0.01 Hz with multiple peaks just below the significance level."
" 'To identify the state of the system when these PDSs arise, we calculated the fraction of data as a function of phase whose root-mean square values are above the level of a standard deviation 4- the median rms value of all the data (see Fig. 1,,"," To identify the state of the system when these PDSs arise, we calculated the fraction of data as a function of phase whose root-mean square values are above the level of a standard deviation $+$ the median rms value of all the data (see Fig. \ref{fig-1},"
 black histogram)., black histogram).
" In addition, each fraction was further divided among different radio/X-ray states (coloured histograms in Fig. 1))."," In addition, each fraction was further divided among different radio/X-ray states (coloured histograms in Fig. \ref{fig-1}) )."
 Quiescent radio/X-ray states are not shown in Fig., Quiescent radio/X-ray states are not shown in Fig.
 1 as they have lower rms values., \ref{fig-1} as they have lower rms values.
 Fig., Fig.
" 1 shows that most of the rms variation is due to the rms-flux relation (tracing the orbital modulation), but two anomalous peaks show up at phases 0.3-0.4 and 0.6-0.7."," \ref{fig-1} shows that most of the rms variation is due to the rms-flux relation (tracing the orbital modulation), but two anomalous peaks show up at phases 0.3–0.4 and 0.6–0.7."
 The first peak is due to only the FHXR state and the second peak results from the excesses in the FIM/FSXR states., The first peak is due to only the FHXR state and the second peak results from the excesses in the FIM/FSXR states.
 These states and related phases are the same states and phases where the QPOs discussed in this work are found., These states and related phases are the same states and phases where the QPOs discussed in this work are found.
 Fig., Fig.
 2 and Table 2 show the PDSs and significances (based on the Monte-Carlo analysis referred to in Section 2) respectively of the QPOs we have identified in this subset of data with Fig., \ref{fig-2} and Table \ref{table-2} show the PDSs and significances (based on the Monte-Carlo analysis referred to in Section 2) respectively of the QPOs we have identified in this subset of data with Fig.
 3 highlighting the data from the 2000 Apr 3 observation., \ref{fig-3} highlighting the data from the 2000 Apr 3 observation.
" As noted in Table 2,, the QPOs occurred during the flaring states — particularly in the FSXR/FHXR states."," As noted in Table \ref{table-2}, the QPOs occurred during the flaring states – particularly in the FSXR/FHXR states."
" In the context of phase, we note that the QPOs occurred between phase 0.2-0.7."," In the context of phase, we note that the QPOs occurred between phase 0.2–0.7."
" Interestingly, the QPOs discussed in vanderKlis&Jansen(1985) all appear exclusively in the phase interval 0.0—0.75 that corresponds to the rising"," Interestingly, the QPOs discussed in \citet{vanderklis} all appear exclusively in the phase interval 0.0–0.75 that corresponds to the rising"
remaining alter fillering is about 10 Ix for filter width of one pixel. decreasing to 1.7 Ix for the ten pixel filter.,"remaining after filtering is about 10 K for filter width of one pixel, decreasing to 1.7 K for the ten pixel filter."
" Also shown on figure 1 is the continuum. using a region 1.42 ""square centered on (1.b)2(331.43.0.56) that includes both diffuse continuum and a lew bright sources."," Also shown on figure 1 is the continuum, using a region 1.42 square centered on (l,b)=(331.43,0.56) that includes both diffuse continuum and a few bright sources."
 The continuum is only weakly affected by the filtering lor filter widths less than about five pixels. but progressively more strongly attenuated Lor filler widths ten pixels or more.," The continuum is only weakly affected by the filtering for filter widths less than about five pixels, but progressively more strongly attenuated for filter widths ten pixels or more."
 On the basis of figure L we choose a ten pixel filter [passing spatial frequencies higher than (3.5 arc ! which preserves angular sizes smaller than about 4/]]. since filtering more heavily begins to reduce the continuum as much as the line emission.," On the basis of figure 1 we choose a ten pixel filter [passing spatial frequencies higher than (8.5 arc $^{-1}$ which preserves angular sizes smaller than about ], since filtering more heavily begins to reduce the continuum as much as the line emission."
 Already. with this fillering the total continuum flux of our background sources is less (han it is on the unfiltered map. since they are extended objects. (hus we are beginning to lose signal to noise on the absorption spectra.," Already with this filtering the total continuum flux of our background sources is less than it is on the unfiltered map, since they are extended objects, thus we are beginning to lose signal to noise on the absorption spectra."
" We (abulate below these filtered continuum peak values since they determine the noise level in (he absorption spectra. but these should not be used to estimate the flux densities of the continuum sources,"," We tabulate below these filtered continuum peak values since they determine the noise level in the absorption spectra, but these should not be used to estimate the flux densities of the continuum sources."
 In addition io removing (he emission toward the continuum sources to obtain the absorption spectra as described in the last paragraph. we need to interpolate the emission from nearby beam areas in order (0 estimate the emission spectrmu which would be seen in the direction of the continuum source if there were no absorption.," In addition to removing the emission toward the continuum sources to obtain the absorption spectra as described in the last paragraph, we need to interpolate the emission from nearby beam areas in order to estimate the emission spectrum which would be seen in the direction of the continuum source if there were no absorption."
 This we do bv a spatial interpolation on the unfiltered cube. which includes information from all the short uv spacings.," This we do by a spatial interpolation on the unfiltered cube, which includes information from all the short uv spacings."
 The technique is described by MeClIure-Griffitlis et al. (, The technique is described by McClure-Griffiths et al. (
2001): we construct for each spectral channel a bi-Hnear function fitted to the pixels around the background source for which the continuum brightness is below a threshold set at. of its peak value ,2001); we construct for each spectral channel a bi-linear function fitted to the pixels around the background source for which the continuum brightness is below a threshold set at of its peak value on-source.
We use the off-source pixels so defined both for the fitting and to estimate the error ol the fitted [Iunction: the latter is given by the rms of the data minus the fit averaged over the set of off-source pixels., We use the off-source pixels so defined both for the fitting and to estimate the error of the fitted function; the latter is given by the rms of the data minus the fit averaged over the set of off-source pixels.
 That rms should be an overestimate of the likely error in the interpolated spectrum in the direction of the background source. since (he area covered by the off-«ource pixels is much larger than that of the source itself.," That rms should be an overestimate of the likely error in the interpolated spectrum in the direction of the background source, since the area covered by the off-source pixels is much larger than that of the source itself."
 The error envelope defined (his way is indicated above and below (he emission profiles on figures 2-8., The error envelope defined this way is indicated above and below the emission profiles on figures 2-8.
 The absorption speclra are constructed by averaging spectra toward (he pixels for which the ratio of the continuum brightness to the continuum peak is above8056.. weighting bv the square of this ratio. (," The absorption spectra are constructed by averaging spectra toward the pixels for which the ratio of the continuum brightness to the continuum peak is above, weighting by the square of this ratio. ("
The continuum map used to determine this weighting has also been spatially liltered in the same wav as the spectral line cube.),The continuum map used to determine this weighting has also been spatially filtered in the same way as the spectral line cube.)
 Note that we do not need to subtract (he interpolated emission from (he spectrum Coward the continuum to obtain the absorption spectrum. since (he spatial lillering process has already. accomplished that step.," Note that we do not need to subtract the interpolated emission from the spectrum toward the continuum to obtain the absorption spectrum, since the spatial filtering process has already accomplished that step."
 This is the difference between (he analysis performed here and that of MeChire-Grilliths et al. (, This is the difference between the analysis performed here and that of McClure-Griffiths et al. (
2001).,2001).
 Comparing the spectra in figure 8 of that paper with (he corresponding spectra in figures 2 and 3 below. we see that the effects of emission fInctuations have been attenuated bv a [actor of two to three by the spatial filtering step described above.," Comparing the spectra in figure 8 of that paper with the corresponding spectra in figures 2 and 3 below, we see that the effects of emission fluctuations have been attenuated by a factor of two to three by the spatial filtering step described above."
 The accuracy. of both, The accuracy of both
and their likely progenitors.,and their likely progenitors.
 S.V. aud A.IK. ire supported by GA AV erant που» TAA300030908 and LAASO01630901. respectively. aud bv GÀ CRR erant uuuber P209/10/0967.," S.V. and A.K. are supported by GA AV grant numbers IAA300030908 and IAA301630901, respectively, and by GA ČRR grant number P209/10/0967."
 ALIN. also acknowledges support frou the Centre for Theoretical Astrophysics (LCO06011)., A.K. also acknowledges support from the Centre for Theoretical Astrophysics (LC06014).
 RT. aud INS acknowledge support frou NSF evant AST-0708810., J.R.T. and J.N.S acknowledge support from NSF grant AST-0708810.
. A.P. and 2.1. acknowledge Polish MINISZW eraut N N203 302635., A.P. and Z.K. acknowledge Polish MNiSzW grant N N203 302635.
 This research has made use of the VizieR catalogue access tool (CDS. Strasbourg. France). aud of data products from the Two Micron. All Sky Survey which is a joint. project of the University of Massachusetts aud the Iufrared Processing and Analysis Center/California Institute of Technology. funded bv the National Aeronautics and Space Achuinistration and the National Science Foundation.GALEN..Mavall..," This research has made use of the VizieR catalogue access tool (CDS, Strasbourg, France), and of data products from the Two Micron All Sky Survey which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation.,."
were taken near transit to aid the interpretation of the parallax data.,were taken near transit to aid the interpretation of the parallax data.
 Relative photometry between 2MASS 1207 and the 12 brightest stars in the field gives an average variability of c=0.03 mag., Relative photometry between 2MASS 1207 and the 12 brightest stars in the field gives an average variability of $\sigma=0.03$ mag.
" Given that the differential magnitude between 2MASS 1207 A and b is 7.8 in the similar NICMOS F090M filter (?),, this variability must be completely dominated by 2MASS 1207 A's intrinsic variability."," Given that the differential magnitude between 2MASS 1207 A and b is 7.8 in the similar NICMOS F090M filter \citep{2006ApJ...652..724S}, this variability must be completely dominated by 2MASS 1207 A's intrinsic variability."
" The variability is smaller than the error bars of published relative photometry of 2MASS 1207 b (seeforexample?),, which legitimizes 2MASS 1207 A's use as a photometric calibrator for 2MASS 1207 b (although as we describe in Section D.2], the nearby background star 2MASS 12073400-3932586 is a better calibrator for variability studies)."," The variability is smaller than the error bars of published relative photometry of 2MASS 1207 b \citep[see for example][]{2004AA...425L..29C}, which legitimizes 2MASS 1207 A's use as a photometric calibrator for 2MASS 1207 b (although as we describe in Section \ref{VLT/NACO}, the nearby background star 2MASS 12073400-3932586 is a better calibrator for variability studies)."
 Variations in the I-band magnitude of 2MASS 1207 with respect to its average I-band value are plotted in Figure D]., Variations in the I-band magnitude of 2MASS 1207 with respect to its average I-band value are plotted in Figure \ref{A variability}.
 Error bars are calculated empirically from the multiple frames taken on each individual night., Error bars are calculated empirically from the multiple frames taken on each individual night.
 A possible explanation for 2MASS 1207 b’s under-luminosity is that it is being partially extincted by a near edge-on disk of large (gray-extincting) dust grains (??).. ," A possible explanation for 2MASS 1207 b's under-luminosity is that it is being partially extincted by a near edge-on disk of large (gray-extincting) dust grains \citep{2007ApJ...657.1064M,2010AA...517A..76P}. ."
"Such a disk must produce ~2.5 mags of extinction at J-band, with nearly gray extinction."," Such a disk must produce $\sim$ 2.5 mags of extinction at J-band, with nearly gray extinction."
 The disk must create only moderate photometric variability., The disk must create only moderate photometric variability.
 The disk may not have an extremely unlikely viewing angle/geometry., The disk may not have an extremely unlikely viewing angle/geometry.
 And the disk properties should be consistent with our current picture of disk evolution., And the disk properties should be consistent with our current picture of disk evolution.
" Additionally, any dust around 2MASS 1207 b will have its emission constrained by our 8.7 um photometry."," Additionally, any dust around 2MASS 1207 b will have its emission constrained by our 8.7 $\micron$ photometry."
" In this section, we discuss the viability of the near edge-on disk hypothesis, with respect to these conditions."," In this section, we discuss the viability of the near edge-on disk hypothesis, with respect to these conditions."
" We used the RADMC radiative transfer code (?) and RAYTRACE, a post-processing tool, to calculate the emerging spectral energy distribution (SED) of a hypothetical disk around 2MASS 1207 b. The primary input parameters of the RADMC/RAYTRACE codes are the SED and mass (Ma) of a central source, and the inner radius (Ri,), outer radius (Hai), inclination (i), and mass (Mai) of its disk."," We used the RADMC radiative transfer code \citep[]{2004AA...417..159D} and RAYTRACE, a post-processing tool, to calculate the emerging spectral energy distribution (SED) of a hypothetical disk around 2MASS 1207 b. The primary input parameters of the RADMC/RAYTRACE codes are the SED and mass $M_{\rm star}$ ) of a central source, and the inner radius $R_{\rm in}$ ), outer radius $R_{\rm disk}$ ), inclination $i$ ), and mass $M_{\rm disk}$ ) of its disk."
" Other relevant parameters include the disk’s vertical flaring geometry (described below), and a dust grain distribution with associated optical properties."," Other relevant parameters include the disk's vertical flaring geometry (described below), and a dust grain distribution with associated optical properties."
" As we will show later in this section, our Gemini/T-ReCS 8.7m photometry upper-limit is not sensitiveenough to detect the presence of a disk around 2MASS 1207 b. Consequently,"," As we will show later in this section, our Gemini/T-ReCS $\micron$ photometry upper-limit is not sensitiveenough to detect the presence of a disk around 2MASS 1207 b. Consequently,"
aud the second one flatter.,and the second one flatter.
 The two power laws cross at about the values of the breaks found with the BPL model., The two power laws cross at about the values of the breaks found with the BPL model.
 As apparent from the best-fit fluxes reported in 22. caving the second observation the source was weaker.," As apparent from the best-fit fluxes reported in 2, during the second observation the source was weaker."
 We checked if the amount of variability was different at, We checked if the amount of variability was different at
"Iu the previous section. we discussed results for several quantities that emerged from our analysis of the VLBA nuages. uamely: the source flux density. the source structure index. the source compactuess, and the time variability of each of these quautitics.","In the previous section, we discussed results for several quantities that emerged from our analysis of the VLBA images, namely: the source flux density, the source structure index, the source compactness, and the time variability of each of these quantities."
 In this section. we compare the source structure index to the compactucss in order to verity that the two quantities are related.," In this section, we compare the source structure index to the compactness in order to verify that the two quantities are related."
 Iu addition. we compare both the structure index aud the compactuess to two astrometric quantities derived in Paper L uamely: the formal position uucertaiutfies aud position variability of the sources.," In addition, we compare both the structure index and the compactness to two astrometric quantities derived in Paper I, namely: the formal position uncertainties and position variability of the sources."
 These comparisous were made to determine whether the reduced structure effects seen at high frequency correspond to more precise astrometric positions., These comparisons were made to determine whether the reduced structure effects seen at high frequency correspond to more precise astrometric positions.
 As an initial test of the source compactucss. we compared € to the source structure index. 57. at cach of the two frequencies.," As an initial test of the source compactness, we compared $\bar C$ to the source structure index, $SI$, at each of the two frequencies."
 She»vu in Figure 12 are the distributions of the mean source compactuess for the 27 sources damaged at K band separated iu terms of uaxinuniL source structure iudex., Shown in Figure \ref{FIG:K_COMPACT_SI} are the distributions of the mean source compactness for the 274 sources imaged at K band separated in terms of maximum source structure index.
 Figure 13 shows similar distributious for the 132 sources imaged at Q xad., Figure \ref{FIG:Q_COMPACT_SI} shows similar distributions for the 132 sources imaged at Q band.
" The three panels in cach &Sgure show οὐ = 1. 2 and 23 sources. respectively,"," The three panels in each figure show $SI$ = 1, 2 and 3 sources, respectively."
 There are two sources at Iv wand and one source at OQ band with 57=1 that are rot shown in the figures., There are two sources at K band and one source at Q band with $SI=4$ that are not shown in the figures.
 Tn both figures. it is evident hat the distributions in compactucss among the three structure indices are quite different with the distribution or Sf=l being strougly peaked at both frequencies. and the distributions broadening with increasing values of S7.," In both figures, it is evident that the distributions in compactness among the three structure indices are quite different with the distribution for $SI = 1$ being strongly peaked at both frequencies, and the distributions broadening with increasing values of $SI$."
 Within cach panel of Figures 12 and 13. the mean and median of the distribution are given., Within each panel of Figures \ref{FIG:K_COMPACT_SI} and \ref{FIG:Q_COMPACT_SI} the mean and median of the distribution are given.
 These values are also sunuuarzed in Table 5.., These values are also summarized in Table \ref{TAB:COMPACT_SI}.
 From the table we see that for both frequencies. the mean aud mecca source colmpactuess is directly related to structure index.," From the table we see that for both frequencies, the mean and median source compactness is directly related to structure index."
 The correspondence between SL aud C is not unexpected. since both quantities provide au indication of the source structure as derived from the VEDI imagine.," The correspondence between $SI$ and $\bar C$ is not unexpected, since both quantities provide an indication of the source structure as derived from the VLBI imaging."
 We also compared the compactuess variability iudex to the source structure index aud the results are shown iu Figure LL., We also compared the compactness variability index to the source structure index and the results are shown in Figure \ref{FIG:K_COMPACT_VAR_SI}.
 Plotted iu the figure is σεις at IX baud as a function of cach of the three structure indices. $7 = 1.2 and 3.," Plotted in the figure is $\sigma_C/\bar{C}$ at K band as a function of each of the three structure indices, $SI$ = 1, 2 and 3."
 Recall that the compactuess variability iudex was deteruiued for oulv those sources observed i more than one session (235 sources at I& band aud 82 sources at Q band)., Recall that the compactness variability index was determined for only those sources observed in more than one session (235 sources at K band and 82 sources at Q band).
 The equivalent plot for the Q baud data was uot produced because of the greatly reduced umber of sources., The equivalent plot for the Q band data was not produced because of the greatly reduced number of sources.
 As in the case of the source compactuecss. the variability iu the conipactuess shows a clear treud with ST. with the σε” distribution being the most narrow for Sf=1 aud the broadest for Sf=3.," As in the case of the source compactness, the variability in the compactness shows a clear trend with $SI$, with the $\sigma_C/\bar{C}$ distribution being the most narrow for $SI = 1$ and the broadest for $SI=3$."
" The mean (amecian) values for cach distribution are 0.01 (0.0413. 0.08 (0.07) and 0.15 (0.11) for the 57 — 1. 2 aud 3 sources. respectively,"," The mean (median) values for each distribution are 0.04 (0.04), 0.08 (0.07) and 0.15 (0.14) for the $SI$ = 1, 2 and 3 sources, respectively."
 A variability iudex oefC=0 indicates no variability iu the source conipactuess froni one session to the next., A variability index $\sigma_C/\bar{C} = 0$ indicates no variability in the source compactness from one session to the next.
 This relationship between the compactuess variability iudex aud the structure index suggests that the sources with the most structure as measured by SI exhibit increased variability iu their structure as jiueasured by oc., This relationship between the compactness variability index and the structure index suggests that the sources with the most structure as measured by $SI$ exhibit increased variability in their structure as measured by $\sigma_C/\bar{C}$.
 The impact of source structure on the hieli-frequenucy CRE can be further studied bv comparing structure index with the formal precision of the source positions colmprising a potential CRE., The impact of source structure on the high-frequency CRF can be further studied by comparing structure index with the formal precision of the source positions comprising a potential CRF.
 The formal position nucertaimtics were taken from the [K-baud astrometric solution detailed in Paper L For this solution. we usec the CALC/SOLVE software package maintained by the NASA (ιοατα Space Flight Ceuter (GSFC) to perform a least-squares astrometric solution for the Ik-hand data.," The formal position uncertainties were taken from the K-band astrometric solution detailed in Paper I. For this solution, we used the CALC/SOLVE software package maintained by the NASA Goddard Space Flight Center (GSFC) to perform a least-squares astrometric solution for the K-band data."
 The 10 diurnal I-baud experiments euconipassed 82.921 measurements of bandwidth svuthesis (group) delay and phase. delay rate.," The 10 diurnal K-band experiments encompassed 82,334 measurements of bandwidth synthesis (group) delay and phase delay rate."
" Geodetic parameters estimated for cach session iuclude: station positions. 20-minute piecewise linear continuous troposphere zenith xuwanmieters, tropospheric eracicuts iu the eastwest aud rorthsouth directions. lear in time. estimated once or 21 hr session. quadratic clock polvnomials to model he eross clock behavior. and G0-1àniuute piecewise linear continuous clock parameters."," Geodetic parameters estimated for each session include: station positions, 20-minute piecewise linear continuous troposphere zenith parameters, tropospheric gradients in the east–west and north–south directions, linear in time, estimated once per 24 hr session, quadratic clock polynomials to model the gross clock behavior, and 60-minute piecewise linear continuous clock parameters."
 Corrections for ionospheric refraction drawn from Global Positioning System (CPS) otal electron content (TEC) maps were applied to I&-xuid data as discussed in Paper I. Positious for sources laving three or more measurements of eroup delay were he only elobal parameters that were estimated., Corrections for ionospheric refraction drawn from Global Positioning System (GPS) total electron content (TEC) maps were applied to K-band data as discussed in Paper I. Positions for sources having three or more measurements of group delay were the only global parameters that were estimated.
 The EK-baud catalog derived from the astrometric solution is comprised of positious aud associated formal nucertaitics for 268 sources., The K-band catalog derived from the astrometric solution is comprised of positions and associated formal uncertainties for 268 sources.
 Because there were too few sources at Q-baud (131) to separate iuto the four structure index. categories. we chose only to compare the ατα unecrtainties with structure index and colmpactness.," Because there were too few sources at Q-band (131) to separate into the four structure index categories, we chose only to compare the K-band uncertainties with structure index and compactness."
 An initial comparison of all 268 sources showed the position uncertainties plotted as a function of Sf category to be scusitive to a few outlicrs with relatively few observations., An initial comparison of all 268 sources showed the position uncertainties plotted as a function of $SI$ category to be sensitive to a few outliers with relatively few observations.
 We. therefore. decided to restrict the comparison to sources with 100 or more eroup delay measurements.," We, therefore, decided to restrict the comparison to sources with 100 or more group delay measurements."
 This same restriction was used by Fey&Charlot(2000) ina simular study performed at X baud., This same restriction was used by \cite{FC:00} in a similar study performed at X band.
 Shown in Figure 15. are the distributious of tle formal position uncertziufies ia) ocosó and b) à for 193 sources with 100 or more group delay nieasureineuts at Is baud., Shown in Figure \ref{FIG:POS_UNCER_HIST_100} are the distributions of the formal position uncertainties ina) $\alpha\cos\delta$ and b) $\delta$ for 193 sources with 100 or more group delay measurements at K band.
 The distributions are separated iuto the three SI categories 1. 2. and 3.," The distributions are separated into the three $SI$ categories 1, 2, and 3."
 There were two SZ= [sources with ereater than 100 delay measurements that are not shown., There were two $SI = 4$ sources with greater than 100 delay measurements that are not shown.
 There is good agreement between the mean aud median values sugeesting little or no dependence on outliers., There is good agreement between the mean and median values suggesting little or no dependence on outliers.
 The results show no sieuificant difference in the mean and median position uncertaiutfies from one structure iudex category to the next., The results show no significant difference in the mean and median position uncertainties from one structure index category to the next.
" Iu addition. we find the mean and mecian position uncertainties in à are roughly twice the uncertainties in ocosó for all three $7 categories,"," In addition, we find the mean and median position uncertainties in $\delta$ are roughly twice the uncertainties in $\alpha\cos\delta$ for all three $SI$ categories."
 Iu Fev&Charlot(2000).. it was shown that the niean and median X-band source position uncertainties in both àcosó and 9 increased regularly as a functiou of structure iudex frou Sf=1 to |.," In \cite{FC:00}, it was shown that the mean and median X-band source position uncertainties in both $\alpha\cos\delta$ and $\delta$ increased regularly as a function of structure index from $SI$ =1 to 4."
 In addition to the LOO eroup delay measurement restriction. Fey&Char- used the formal position uncertainties frou Mactal. (1998)... which were adjusted by the standard ICRF inflation factor described therein.," In addition to the 100 group delay measurement restriction, \cite{FC:00} used the formal position uncertainties from \cite{MA:98}, , which were adjusted by the standard ICRF inflation factor described therein."
 Iu order to accurately compare our R&-baud values. we applied. the," In order to accurately compare our K-band values, we applied the"
science. and when we are planning ground ancl space-based facilities to eather SN data.,"science, and when we are planning ground and space-based facilities to gather SN data."
" Now we will brielly review the effect of peculiar velocities on ἱνρο Ia SN data. wherein we measure SN redshifis z and humninositw distances D, to produce a “Hubble diagram."""," Now we will briefly review the effect of peculiar velocities on type Ia SN data, wherein we measure SN redshifts $z$ and luminosity distances $D_L$ to produce a “Hubble diagram."""
 To lowest order. peculiar velocities add an extra redshift.," To lowest order, peculiar velocities add an extra redshift."
" For an observer with a peculiar velocily v, and a source with a peculiar velocity ν.. an unperturbed redshift 2. and an unperturbed Inuiinosity distance D,. the final (perturbed) redshift is and the final Iluminosity. distance is where n is a unit vector along the line of sight. pointing [rom observer to source: these are equivalent to Eqs. ("," For an observer with a peculiar velocity ${\bf v}_o$ and a source with a peculiar velocity ${\bf v}_s$ , an unperturbed redshift $\tilde{z}$, and an unperturbed luminosity distance $\tilde{D}_L$, the final (perturbed) redshift is and the final luminosity distance is where ${\bf n}$ is a unit vector along the line of sight, pointing from observer to source; these are equivalent to Eqs. ("
11) and (13) of Li Greene (2006).,11) and (13) of Hui Greene (2006).
 Note that we have set the speed ol light e=1., Note that we have set the speed of light $c=1$.
 Although it is (vpically assumed that these corrections are negligible. they actually can become quite important lor verv nearby SNe. lor which z<(10—100)n/c. where e=[v|.," Although it is typically assumed that these corrections are negligible, they actually can become quite important for very nearby SNe, for which $z\lesssim (10-100)v/c$, where $v\equiv |{\bf v}|$."
 Having one end of the Hubble diagram with such errors will have more significant consequences (han one might naively expect when it comes time to fit the data to a moclel., Having one end of the Hubble diagram with such errors will have more significant consequences than one might naively expect when it comes time to fit the data to a model.
 A further complication arises because the peculiar velocities are correlated. and correlated errors will not decrease as [ast as YN. where V is the munber of SNe in the sample.," A further complication arises because the peculiar velocities are correlated, and correlated errors will not decrease as fast as $\sqrt{N}$, where $N$ is the number of SNe in the sample."
" From Cooray Caldwell (2006). in the limit oflarge NX. the final variance of some measurecl parameter will be where r? is the ratio of the average olf-diagonal covariance matrix element to the average diagonal covariance matrix element. aud both ση aud + depend on the masxinnuu survey redshift 24,4."," From Cooray Caldwell (2006), in the limit oflarge $N$, the final variance of some measured parameter will be where $r^2$ is the ratio of the average off-diagonal covariance matrix element to the average diagonal covariance matrix element, and both $\sigma_0$ and $r$ depend on the maximum survey redshift $z_{\rm max}$."
 Note that 0<9?<L. with r—0 correspondingto no correlation and r—1 corresponding to perfect correlation.," Note that $0\leq r^2\leq 1$, with $r\rightarrow 0$ correspondingto no correlation and $r\rightarrow 1$ corresponding to perfect correlation."
 Therefore. the first terii on the right haud. side of equation (3)) corresponds to the uncorrelated Poissonian part of the error. aud the second term corresponds (o the correlated. part.," Therefore, the first term on the right hand side of equation \ref{error}) ) corresponds to the uncorrelated Poissonian part of the error, and the second term corresponds to the correlated part."
 We also see that the error cannotbe arbitrarily reduced simply by having larger NV. as there is a limit of σ—apr lor N— ox.," We also see that the error cannotbe arbitrarily reduced simply by having larger $N$ , as there is a limit of $\sigma\rightarrow \sigma_0 r$ for $N\rightarrow\infty$ ."
the CTU integrator.,the CTU integrator.
 We use f(a.v) and ία.uw) to denote source terms [ον (he acceleration of particles ancl gas respectively. due to forces other than the drag force (e.g.. Coriolis force. tidal force and (he global pressure gradient).," We use ${\mb f}({\mb x},{\mb v})$ and ${\mb g}({\mb x},{\mb u})$ to denote source terms for the acceleration of particles and gas respectively, due to forces other than the drag force (e.g., Coriolis force, tidal force and the global pressure gradient)."
 The formalism in relssec:formalism ean be summarized as We do not distinguish between (u.v) and (a’.v’) here because it does not affect. our description of the numerical algorithms.," The formalism in \\ref{ssec:formalism} can be summarized as We do not distinguish between ${\mb u}, {\mb v}$ ) and ${\mb u}', {\mb v}'$ ) here because it does not affect our description of the numerical algorithms."
" Our predictor-corrector scheme. which integrates the coupled equations from time step / to 7 P, can be illustrated as In the above. (τα) and (το) ave generalizations of the predictor and corrector step of the MILD integrator. and particle feedback to gas is expressed as Ap? ο. [or the two steps respectively,"," Our predictor-corrector scheme, which integrates the coupled equations from time step $t^{(n)}$ to $t^{(n+1)}$ , can be illustrated as In the above, \ref{eq:scheme1}) ) and \ref{eq:scheme3}) ) are generalizations of the predictor and corrector step of the MHD integrator, and particle feedback to gas is expressed as $\Delta{\mb p}_i^{\rm pred}$ $\Delta{\mb p}_i^{\rm corr}$ for the two steps respectively."
 Their expressions are given in the following paragraphs., Their expressions are given in the following paragraphs.
 Wis the weight function for interpolation (see next paragraph). (vb)), $W$ is the weight function for interpolation (see next paragraph). \ref{eq:scheme2}) )
 represents (he particle integrator. which we will discuss in detail in refsecintegrator..," represents the particle integrator, which we will discuss in detail in \\ref{sec:integrator}. ."
 Note that in the bracket on the right hand side of this equation. particle quantities a; and v; can be combinations of step (2) aud step (2+1) quantities. depencine on the particle integrator.," Note that in the bracket on the right hand side of this equation, particle quantities ${\mb x}_i$ and ${\mb v}_i$ can be combinations of step $(n)$ and step $(n+1)$ quantities, depending on the particle integrator."
 The calculation of the drag force experienced by particles requires interpolation of grid quantities to the particle location on the eric., The calculation of the drag force experienced by particles requires interpolation of grid quantities to the particle location on the grid.
 The interpolation scheme is described by the weight function Wola—a5)., The interpolation scheme is described by the weight function $W({\mb x}-{\mb x}_i)$.
 For consistency. (he sne interpolation scheme is used to distribute the feedback [rom individual particles tothe eas exrid points. as in equation (7)).," For consistency, the same interpolation scheme is used to distribute the feedback from individual particles tothe gas grid points, as in equation \ref{eq:scheme}) )."
 In order avoid spurious numerical artifacts in the hvbrid scheme. the weight [function VW should satisfy certain constrains.," In order avoid spurious numerical artifacts in the hybrid scheme, the weight function $W$ should satisfy certain constrains."
 Ht should be continuous over the computational domain to avoid sharp transitions. and VW(Xa) should be non-negative for anv Aa to reduce noise (Youdin&Johansen2007).," It should be continuous over the computational domain to avoid sharp transitions, and $W(\Delta{\mb x})$ should be non-negative for any $\Delta{\mb x}$ to reduce noise \citep{YoudinJohansen07}."
. The interpolation should be accurate enough (to minimize errors., The interpolation should be accurate enough to minimize errors.
 In particular. interpolation error should not be much worse than the error from the spacial reconstruction of (he MIID integrator (we use the third order piecewise parabolic method).," In particular, interpolation error should not be much worse than the error from the spacial reconstruction of the MHD integrator (we use the third order piecewise parabolic method)."
 Finally. interpolation is time consuming. so the scheme should be as efficient as possible.," Finally, interpolation is time consuming, so the scheme should be as efficient as possible."
 We have comparedthree interpolation schemes Birdsall&Langdon 2005.. YJOT). namely. cloud-in-a-cell(CIC). tviangular-shaped cloud. (TSC) and quadratic polynomial (QP).," We have comparedthree interpolation schemes \citealp{BirdsallLangdon05}, , YJ07), namely, cloud-in-a-cell(CIC), triangular-shaped cloud (TSC) and quadratic polynomial (QP)."
 The, The
"that available from spin-down (whence the name ""anomalous"": 3).",that available from spin-down (whence the name “anomalous”; \citealt{mereghetti95}) ).
 SGRs were first noticed as hard-X/>-ray transients (2).. characterized by recurrent. short (<1 s) and relatively soft (peak photon energy —25—-30 keV) flashes with super-Eddington luminosity.," SGRs were first noticed as $\gamma$ -ray transients \citep{laros87}, characterized by recurrent, short $<$ 1 s) and relatively soft (peak photon energy $\sim$ 25–30 keV) flashes with super-Eddington luminosity."
 Although SGRs and AXPs have been discovered through very different channels. observations performed over the last few years highlighted several similarities among these two classes of objects and pointed towards a common magnetar nature (see e.g. 2)).," Although SGRs and AXPs have been discovered through very different channels, observations performed over the last few years highlighted several similarities among these two classes of objects and pointed towards a common magnetar nature (see e.g. \citealt{rea09}) )."
 In particular. short and hard X-ray bursts. originally considered as the detining characteristic of SGRs. have now been observed in several AXPs (see e.g. 2: 29). wwas discovered in 1998. when about one hundred bursts in six weeks were observed by CGRO//BATSE and other instruments (2)..," In particular, short and hard X-ray bursts, originally considered as the defining characteristic of SGRs, have now been observed in several AXPs (see e.g. \citealt*{gavriil02}; \citealt{mereghetti09}) was discovered in 1998, when about one hundred bursts in six weeks were observed by /BATSE and other instruments \citep{woods99}."
 Its soft X-ray counterpart was identitied with iin 1998 at a luminosity level of ~LO* citepwoods99.., Its soft X-ray counterpart was identified with in 1998 at a luminosity level of $\sim$$10^{35}$ \\citep{woods99}.
7 Subsequent observations carried out withBeppoSAX..ASCA..Chandra. and sshowed a spectral softening and a monotonic decrease in the luminosity. down to a level of ~10°? citepkouveliotouO3.mereghetti06.e1708..," Subsequent observations carried out with, and showed a spectral softening and a monotonic decrease in the luminosity, down to a level of $\sim$$10^{33}$ \\citep{kouveliotou03,mereghetti06,eiz08}."
 After nearly ten years of quiescence. rre-activated on 2008 May 14. when several bursts were detected by Swif/f//BAT and other hard X-ray instruments ¢?)..," After nearly ten years of quiescence, re-activated on 2008 May 14, when several bursts were detected by /BAT and other hard X-ray instruments \citep{eiz08}."
 The burst re-activation was associated with a large enhancement of the soft X-ray flux and a marked spectral Until very recently. wwas the only magnetar candidate with no pulsation period known.," The burst re-activation was associated with a large enhancement of the soft X-ray flux and a marked spectral Until very recently, was the only magnetar candidate with no pulsation period known."
 In order to search in depth for pulsations taking advantage of the high flux state. we asked for a long oobservation to be carried out during its outburst.," In order to search in depth for pulsations taking advantage of the high flux state, we asked for a long observation to be carried out during its outburst."
 The observation was performed on 2008 September 27—28 and we could detect a clear pulsation period of 5578(6) s (2)..., The observation was performed on 2008 September 27–28 and we could detect a clear pulsation period of 578(6) s \citep{esposito09}.
 However. no meaningful constraints on the period derivative could be derived from that Here we report on a new measurement of the period using data gathered shortly after the burst activation by theObservatory.," However, no meaningful constraints on the period derivative could be derived from that Here we report on a new measurement of the period using data gathered shortly after the burst activation by the."
.. This allows us to estimate for the first time the spin-down rate of aand to infer its magnetic field. characteristic age. and spin-down luminosity.," This allows us to estimate for the first time the spin-down rate of and to infer its magnetic field, characteristic age, and spin-down luminosity."
 Taking advantage of the new pieces of information about the timing properties of1627-41... we also searched for a pulsed signal in archival radio data collected at the Parkes observatory.," Taking advantage of the new pieces of information about the timing properties of, we also searched for a pulsed signal in archival radio data collected at the Parkes observatory."
 The (2) pointed its mirror towards oon 2008 June 3 (MID 54620) and observed the source for about 40 ks (observation identifier: 9126)., The \citep{weisskopf00} pointed its mirror towards on 2008 June 3 (MJD 54620) and observed the source for about 40 ks (observation identifier: 9126).
 The observation was carried out with the Advanced CCD Imaging Spectrometer (ACIS: ?)) instrument operated in the Continuous Clocking (CC) mode. which provides a time resolution of 2.85 ms and imaging along a single direction.," The observation was carried out with the Advanced CCD Imaging Spectrometer (ACIS; \citealt{garmire03}) ) instrument operated in the Continuous Clocking (CC) mode, which provides a time resolution of 2.85 ms and imaging along a single direction."
 The event telemetry was in Faint mode., The event telemetry was in Faint mode.
 The source was positioned in the back-illuminated ACIS-S3 chip. sensitive to photons in the 0.2—10 keV energy The data were processed using the Interactive Analysis of Observation software(CIAO.. version 4.1) and we employed the most updated calibration files available at the time the reduction was performed 4.1).," The source was positioned in the back-illuminated ACIS-S3 chip, sensitive to photons in the 0.2–10 keV energy The data were processed using the Interactive Analysis of Observation software, version 4.1) and we employed the most updated calibration files available at the time the reduction was performed 4.1)."
 Standard screening criteria were applied in the extraction of scientific No significant background flares affected the The source photons for the timing and spectral analyses were accumulated from a 5 pixels region centred on (tone ACIS-S pixel corresponds to 07402): the background events were extracted from source-free regions of the same chip as the source., Standard screening criteria were applied in the extraction of scientific No significant background flares affected the The source photons for the timing and spectral analyses were accumulated from a $5\times5$ pixels region centred on (one ACIS-S pixel corresponds to $0\farcs492$ ); the background events were extracted from source-free regions of the same chip as the source.
 A total of about 1120+40 counts above the background were collected from iin the 2-10 keV energy range., A total of about $1120\pm40$ counts above the background were collected from in the 2–10 keV energy range.
 The ancillary response file and the redistribution matrix for the spectral fitting were generated with the tasksASPHIST..MKART.. and MKACISRMP.. using the specitie bad-pixel file of this observation.," The ancillary response file and the redistribution matrix for the spectral fitting were generated with the tasks, and , using the specific bad-pixel file of this observation."
 The data were grouped with a minimum of 20 counts per energy bin and the spectrum was analysed with the version 12.4 analysis package (?).., The data were grouped with a minimum of 20 counts per energy bin and the spectrum was analysed with the version 12.4 analysis package \citep{arnaud96}.
 Given the paucity of counts. we fit a simplemodel to the data: a power law corrected for interstellar absorption.," Given the paucity of counts, we fit a simplemodel to the data: a power law corrected for interstellar absorption."
 We obtained the following best-tit parameters (47—1.18 for S1 degrees of freedom): absorption Ny=LO11077 ? and photon index there and in the following all errors are at lo confidence level)., We obtained the following best-fit parameters $\chi^2_{\rm{r}}=1.13$ for 51 degrees of freedom): absorption $N_{\rm H}=10^{+1}_{-2}\times10^{22}$ $^{-2}$ and photon index (here and in the following all errors are at $\sigma$ confidence level).
"5/25 The absorbed 2-10 keV flux was —1.310 +. corresponding to a luminosity of 3104ο,"," The absorbed 2–10 keV flux was $\sim$$1.3\times10^{-12}$ , corresponding to a luminosity of $\sim$$3\times10^{34}$."
 These results are consistent with those reported in «? and confirm the bright and hard state of the source following the 2008 May 28 burst activation (22)..," These results are consistent with those reported in \citet{woods08atel1564} and confirm the bright and hard state of the source following the 2008 May 28 burst activation \citep{eiz08,esposito09}."
 For the timing analysis. the photon arrival times were converted to the Solar System barycentre with the task using the source coordinates reported in ?..," For the timing analysis, the photon arrival times were converted to the Solar System barycentre with the task using the source coordinates reported in \citet{wachter04}."
" We searched for the presence of a periodic signal using a Z3 test (see 2)) over the period range 2.584 11—2.59460 s: this range was determined by extrapolating from the 3o lower limit on the value reported in ?.. conservatively assuming a period derivative of 0:""m10° ss +."," We searched for the presence of a periodic signal using a $Z_2^2$ test (see \citealt{esposito09}) ) over the period range $2.584\,71$ $2.594\,60$ s; this range was determined by extrapolating from the $\sigma$ lower limit on the value reported in \citet{esposito09}, conservatively assuming a period derivative of $0\leq\dot{P}\leq10^{-9}$ s $^{-1}$ ."
" The period search step size was ~S«10."" s. which is equivalent to oversampling the Fourier period resolution (P7ΕΤ μι) by a factor of 10."," The period search step size was $\sim$$8\times10^{-6}$ s, which is equivalent to oversampling the Fourier period resolution $\frac{1}{2}P^2/T_{\rm{obs}}$ ) by a factor of 10."
 A significant signal was found in the Z3;-periodogram at, A significant signal was found in the $Z_2^2$ -periodogram at
For the set of SAD area measurements. and for the set of SAD Παν estimates. we show the frequency distributions in Figures l(a) and 2(a).,"For the set of SAD area measurements, and for the set of SAD flux estimates, we show the frequency distributions in Figures 1(a) and 2(a)."
 As also mentioned in (2011).. the distributions show a greater number of smaller sizes/fhixes (han larger ones.," As also mentioned in \citet{SavageMcKenzie_11}, the distributions show a greater number of smaller sizes/fluxes than larger ones."
 The downturn of frequeney distribution lor the smallest size/flux bins is characteristic of a log-normal distribution., The downturn of frequency distribution for the smallest size/flux bins is characteristic of a log-normal distribution.
 Plots of the frequency. distributions for /n(area) ancl fi(lis) indicate normal-like distributions as well (and thus suggest log-normal distributions of size and flux). but are omitted here in the interest of space.," Plots of the frequency distributions for $ln($ $)$ and $ln($ $)$ indicate normal-like distributions as well (and thus suggest log-normal distributions of size and flux), but are omitted here in the interest of space."
 In. Figures 1(a) and 2(a). a distribution is overplotted [or comparison: Figure 2(a) also displavs an exponential curve for comparison.," In Figures 1(a) and 2(a), a log-normal distribution is overplotted for comparison; Figure 2(a) also displays an exponential curve for comparison."
 The shape of the log-normal curve is defined by the mean and standard deviation of the data. and (he exponential curve is defined fully by the mean of the data.," The shape of the log-normal curve is defined by the mean and standard deviation of the data, and the exponential curve is defined fully by the mean of the data."
 Therelore the curves in Figures l(a) and 2(a) should be considered fits only to the extent that they produce the same mean. standard deviation. and total number of SADs as the data.," Therefore the curves in Figures 1(a) and 2(a) should be considered fits only to the extent that they produce the same mean, standard deviation, and total number of SADs as the data."
 For a more quantitative diagnostic of the distributions we construct (he cumulative distribution of the data in Figures 1(b) and 2(b). which are then compared to the analytic cumulative distribution functions (CDFs) of four common statistical distributions: normal. log-normal. exponential. aud power-law.," For a more quantitative diagnostic of the distributions we construct the cumulative distribution of the data in Figures 1(b) and 2(b), which are then compared to the analytic cumulative distribution functions (CDFs) of four common statistical distributions: normal, log-normal, exponential, and power-law."
 In each figure. the cumulative distribution of the data sample is shown as diamond-shaped symbols.," In each figure, the cumulative distribution of the data sample is shown as diamond-shaped symbols."
 To test the goodness of fit for each of the proposed CDFEs. we emploved the Kuiper variant. of the IXolmogorov-Smirnov test.," To test the goodness of fit for each of the proposed CDFs, we employed the Kuiper variant of the Kolmogorov-Smirnov test."
 According to Pressetal.(1992).. the traditional ]xolmogorov-Sumürnov tends to be most sensitive to deviations in the middle ofa CDF's range. and least sensitive al (he extrema.," According to \citet{Press_EA}, the traditional Kolmogorov-Smirnov tends to be most sensitive to deviations in the middle of a CDF's range, and least sensitive at the extrema."
 We elected to use the Kuiper variant in order to preserve sensilivily (o deviations throughout the full range of the CDF., We elected to use the Kuiper variant in order to preserve sensitivity to deviations throughout the full range of the CDF.
 The Kuiper signilicances, The Kuiper significances
in direction of the linear polarization.,in direction of the linear polarization.
 To solve the equations of state. sole asunptious have been made.," To solve the equations of state, some assumptions have been made."
" The Zeeman frequency shift gQ. is assumed to be much ereater than the rate for stimulated emission 2. decay rate P and cross-velaxation rate D,."," The Zeeman frequency shift $g\Omega$, is assumed to be much greater than the rate for stimulated emission $R$, decay rate $\Gamma$ and cross-relaxation rate $\Gamma_\nu$."
 In this regime the offdiagonal clemeuts of the density matrix which describes he molecular states are negligible. which ereatly simplifics he calculations.," In this regime the off-diagonal elements of the density matrix which describes the molecular states are negligible, which greatly simplifies the calculations."
" The aaser is assumed to propagate rearly ouc-dimensionally,", The maser is assumed to propagate nearly one-dimensionally.
 Additionally. the pumping las a Maxwellian velocity dependence aud is the same for all naecucticsubstates.," Additionally, the pumping has a Maxwellian velocity dependence and is the same for all magneticsubstates."
 For expected magnetic fields of zz 100 mC the values of g@ for the stronger hvperfue transitions are about 1000 st.," For expected magnetic fields of $\approx$ 100 mG the values of $g\Omega$ for the stronger hyperfine transitions are about 1000 ${\rm
s}^{-1}$."
 The rate for stimmlated ocniissiou cau be estimated by: lere Ti is the brightness temperature. AQ the beamingsolid angle for the mascr radiation aud A the Einstein cocficient.," The rate for stimulated emission can be estimated by: Here $T_{\rm b}$ is the brightness temperature, $\Delta\Omega$ the beamingsolid angle for the maser radiation and $A$ the Einstein coefficient."
" For Ti,AQ.=10°. Rz100s1,"," For $T_{\rm b}\Delta\Omega~=~10^{12}$, $R\approx
100~{\rm s}^{-1}$."
 Thus gQ<>R. require or ignoring the off-diagonal elements of the density matrix. is satisfied for most of the relevaut brisbtuess regine. up to TAQ=10%.," Thus $g\Omega\gg R$, required for ignoring the off-diagonal elements of the density matrix, is satisfied for most of the relevant brightness regime, up to $T_{\rm b}\Delta\Omega =
10^{12}$."
 For lieher brighltuess temperatures the results for 0z07 lua be unreliable., For higher brightness temperatures the results for $\theta\neq 0^\circ$ may be unreliable.
 For 0=07 he off-diagonal elements are uot preseut. thus the results are reliable up to the highest values of TAQ.," For $\theta=0^\circ$ the off-diagonal elements are not present, thus the results are reliable up to the highest values of $T_{\rm b}\Delta\Omega $ ."
" Detailed calculations of he cross-relaxation rate (D, ). which is expected to be considerably larger than the decayrate (D). give D,=9ἩE at temperatures of LOO Is (Aucerson Watson. 1993)."," Detailed calculations of the cross-relaxation rate $\Gamma_\nu$ ), which is expected to be considerably larger than the decayrate $\Gamma$ ), give $\Gamma_\nu = 2~{\rm s}^{-1}$ at temperatures of 400 K (Anderson Watson, 1993)."
" So g0>D, [is satisfied as well", So $g\Omega\gg \Gamma_\nu \gg \Gamma$ is satisfied as well.
 The calculations here use (EiTj=1st. but NW have shown that the resulting iutensities scale with the decay rate and the cross-relaxation rate as παν|D].," The calculations here use $(\Gamma+\Gamma_\nu) =
1~{\rm s}^{-1}$, but NW have shown that the resulting intensities scale with the decay rate and the cross-relaxation rate as $[{\rm
flux}/(\Gamma+\Gamma_\nu)]$."
 To perform the umuerical calculations. we hac to chose the strength of the radiation iucident outo the masing region.," To perform the numerical calculations, we had to chose the strength of the radiation incident onto the masing region."
 The caleulatiouns preseuted here are based on a radiation of Πλ=0.1 Ik sr.," The calculations presented here are based on a radiation of $T_{\rm b}\Delta\Omega =
0.1$ K sr."
 This coutiunun radiation is taken to be unpolarized., This continuum radiation is taken to be unpolarized.
 It was verified iun NW that the results are inscusitive to the chosen value. and we have confirmed this result.," It was verified in NW that the results are insensitive to the chosen value, and we have confirmed this result."
 Iu contrast ο the LTE analysis preseuted above. the results from the non-LTE trausfer trcatineut are V-xpectra which are not auti-svuunetric.," In contrast to the LTE analysis presented above, the results from the non-LTE transfer treatment are V-spectra which are not anti-symmetric."
 This cau be seen comparing the nou-LTE spectra in Fig., This can be seen comparing the non-LTE spectra in Fig.
 3. to the svuthetic LTE spectra in Fig. l.., \ref{nwf} to the synthetic LTE spectra in Fig. \ref{vs}. .
 The spectra are not proportional to the derivative of the total power intensity profile. T. as used before. due to the bleudiug of Iperfine lines with different gQ.," The spectra are not proportional to the derivative of the total power intensity profile, I', as used before, due to the blending of hyperfine lines with different $g\Omega$."
 Fie., Fig.
" 3. also shows that for high 7,AQ. the total intensity spectra are increasingly less Gaussian in shape."," \ref{nwf} also shows that for high $T_{\rm b}\Delta\Omega$, the total intensity spectra are increasingly less Gaussian in shape."
" The line shape thus euables us to estimate the saturation leve of the Laser,", The line shape thus enables us to estimate the saturation level of the maser.
 The model with TAQ=10 corresponds to a coipletcly unsaturated maser., The model with $T_{\rm b}\Delta\Omega=10^8$ corresponds to a completely unsaturated maser.
" The models with T,AQ=10! and 1013 correspond to slightly aud fully saturated masers respectively."," The models with $T_{\rm b}\Delta\Omega =
10^{10}$ and $10^{11}$ correspond to slightly and fully saturated masers respectively."
 The mon-LTE analysis also xoducees. linear volarization for 0z0°., The non-LTE analysis also produces linear polarization for $\theta \ne 0^\circ$.
 Stokes Q is shown in Fig. L. ," Stokes $Q$ is shown in Fig. \ref{lin}, ,"
"which indicates that for (0— 15. linear polarization of up to ~1054 is observedfor Ti,AQ.~ 10H, "," which indicates that for $\theta=75^{\circ}$ , linear polarization of up to $\approx 10\%$ is observedfor $T_{\rm
b}\Delta\Omega \approx 10^{11}$ ."
NW show thatfor slightly saturated niasers. lincar polarization of a few percent should be observed when 02 157.," NW show thatfor slightly saturated masers, linear polarization of a few percent should be observed when $\theta > 15^{\circ}$ ."
reflects that mocel 1: shows the same velocity distribution as model 2 (Fig.,reflects that model 1 shows the same velocity distribution as model 2 (Fig.
 2). although to attain the same peak height at 300 kms I. f be a few factor larger and the selected range of/ be a few degree higher than the respective values in model 2. because of less number of debris particles near the Sun.," 2), although to attain the same peak height at $\sim 300$ km $^{-1}$, $f$ be a few factor larger and the selected range of $l$ be a few degree higher than the respective values in model 2, because of less number of debris particles near the Sun."
 This rule applies to other considerations below as well., This rule applies to other considerations below as well.
 The halo kinematics at the North Calactie Pole (NG) deserve special attention., The halo kinematics at the North Galactic Pole (NGP) deserve special attention.
 Alajewski (1992) suggested. that 1e outer halo at the NGP. shows a retrograde rotation C9 55kms 1 at 2l kpc., Majewski (1992) suggested that the outer halo at the NGP shows a retrograde rotation $\langle v_\phi \rangle \sim -55$ km $^{-1}$ at $z>4$ kpc.
 Also. dX)3 reported. [rom their analysis of RR Lyrac and blue horizontal branch stars that the halo at 2κοz<12 kpe shows a retrograde rotation abi)65 km |.," Also, K03 reported from their analysis of RR Lyrae and blue horizontal branch stars that the halo at $2<z<12$ kpc shows a retrograde rotation at $\langle v_\phi \rangle \sim -65$ km $^{-1}$."
 On the other hand. halo stars near the Sun show no significant retrograde rotation (CD).," On the other hand, halo stars near the Sun show no significant retrograde rotation (CB)."
 For the purpose of elucidating the effect of the debris stars on the NGDP kinematics. we select t10 debris of model 2 and randomly generated stars at b>TO” and 2<Deh kpe (resembling IxX03's selection).," For the purpose of elucidating the effect of the debris stars on the NGP kinematics, we select the debris of model 2 and randomly generated stars at $b>70^\circ$ and $2<D<5$ kpc (resembling K03's selection)."
 Since he observational determination of full space velocities invoves rather inaccurateDotted. information of proper motions compared to radial velocities. we convolve the velocity distribution ofstars with a Gaussian distribution for velocity errors. having 1:0 of a typical 30 km s| error.," Since the observational determination of full space velocities involves rather inaccurate information of proper motions compared to radial velocities, we convolve the velocity distribution of stars with a Gaussian distribution for velocity errors, having 1 $\sigma$ of a typical 30 km $^{-1}$ error."
 Figure 4 shows the velocity distributions at various values of f., Figure 4 shows the velocity distributions at various values of $f$.
 Ht follows that the debris stars provide a non-Gaussian feature in the velocity distribution., It follows that the debris stars provide a non-Gaussian feature in the velocity distribution.
" The me, distribution shows an extra peak at ~100 km s+. whereby the debris stars decrease eo) from that of a pure halo sample."," The $v_\phi$ distribution shows an extra peak at $\sim -100$ km $s^{-1}$, whereby the debris stars decrease $\langle v_\phi \rangle$ from that of a pure halo sample."
" Llowever. the change of £65) by the inclusion ofthe debris stars with f—5 amounts to only 19( 14) km | for g=0.55 (0.7). which are still insullicient. for explaining the reported £6,=35-~15 km +."," However, the change of $\langle v_\phi \rangle$ by the inclusion ofthe debris stars with $f=5$ amounts to only $-19$ $-14$ ) km $^{-1}$ for $q=0.55$ $0.7$ ), which are still insufficient for explaining the reported $\langle v_\phi \rangle = -35 \sim -75$ km $^{-1}$."
" For the ep and es distributions. their means at the cases of q=0.7 and f=5'X are slightly increased to £j)=7 km and fe.)=3 km respectively, whereas the velocity dispersions are decreased by the amounts of 6 km + and 5kms +. respectively. when the debris stars are considered."," For the $v_R$ and $v_z$ distributions, their means at the cases of $q=0.7$ and $f=5$ are slightly increased to $\langle v_R \rangle = 7$ km $^{-1}$ and $\langle v_z \rangle = 3$ km $^{-1}$, respectively, whereas the velocity dispersions are decreased by the amounts of 6 km $^{-1}$ and 5 km $^{-1}$, respectively, when the debris stars are considered."
 Note that if we extend the selection of the stars at higher > or instead. consider model 1. the changes of £6? become smaller than the above mentioned values. because there are no debris stars in our current model (Eig.," Note that if we extend the selection of the stars at higher $z$ or instead consider model 1, the changes of $\langle v_\phi \rangle$ become smaller than the above mentioned values, because there are no debris stars in our current model (Fig."
 1)., 1).
 Phus. it is sale to conclude that the debris stars contribute only in part to a reported retrograde motionat the NOGI.," Thus, it is safe to conclude that the debris stars contribute only in part to a reported retrograde motionat the NGP."
 We select the simulated stars at the evlindrical coordinates of 6.5«BRκ9.5 kpe and z«4 kpc and at the distance from the Sun of D«4 kpe (as was drawn by CB). convolve the velocities with a Gaussian error distribution of 1a=30 kim os and compare with the corresponding stars with Fels2 in Boo.," We select the simulated stars at the cylindrical coordinates of $6.5<R<9.5$ kpc and $z<4$ kpc and at the distance from the Sun of $D<4$ kpc (as was drawn by CB), convolve the velocities with a Gaussian error distribution of $1~\sigma = 30$ km $^{-1}$, and compare with the corresponding stars with $\le-2$ in B00."
 It follows that the non-Gaussian feature of the velocity distribution is much weaker than that at the NOGP: the change of D for f—5% is onlv 9 10) km in model 1 (model 2)., It follows that the non-Gaussian feature of the velocity distribution is much weaker than that at the NGP: the change of $\langle v_\phi \rangle$ for $f=5$ is only $-9$ $-10$ ) km $^{-1}$ in model 1 (model 2).
 This is due to the characteristic debris distribution. where the number density hear >=0 is smaller than at high |z| (Fig.," This is due to the characteristic debris distribution, where the number density near $z=0$ is smaller than at high $|z|$ (Fig."
 1)., 1).
 Our simple model of an orbiting dwarf galaxy that once contained w Cen predicts a sequence of tidal streams in retrograde rotation and. their existence can be imprinted in kinematies of nearby stars. especially in the direction against Galactic rotation (ΛΑ) and at the NGP (Ix03). while local halo kinematics remain unchanged.," Our simple model of an orbiting dwarf galaxy that once contained $\omega$ Cen predicts a sequence of tidal streams in retrograde rotation and their existence can be imprinted in kinematics of nearby stars, especially in the direction against Galactic rotation (GWN) and at the NGP (K03), while local halo kinematics remain unchanged."
 The simulated streams are mostly distributed. inside the solar circle. as sugeested from the current orbital motion of w Cen (ονX: Dinescu 2002).," The simulated streams are mostly distributed inside the solar circle, as suggested from the current orbital motion of $\omega$ Cen (DGvA; Dinescu 2002)."
 In contrast to Ser dwarf galaxy having polar orbit (Lhata ct al., In contrast to Sgr dwarf galaxy having polar orbit (Ibata et al.
 1997). the orbit of ω Cen's progenitor galaxy is largely allectecd by a non-spherical disk potential. where the orbital plane. exhibits precession with respect o the Galactic Pole. causing sell-crossing of tidal streams in the disk region (Fig.," 1997), the orbit of $\omega$ Cen's progenitor galaxy is largely affected by a non-spherical disk potential, where the orbital plane exhibits precession with respect to the Galactic Pole, causing self-crossing of tidal streams in the disk region (Fig."
 1)., 1).
 The projection of the orbit »erpendicular to the disk plane shows an XN-like feature. hereby leaving denser streams at high |z| than at low το] or a given radius.," The projection of the orbit perpendicular to the disk plane shows an 'X'-like feature, thereby leaving denser streams at high $|z|$ than at low $|z|$ for a given radius."
 These characteristic spatial distributions of the debris stars give rise to more significant effects. of he debris at the Αα than in the solar. neighborhood. as shown here. although the current simulation failed. to reproduce the reported Iargely retrograde rotation at NGL rom the w Cen debris alone: perhaps. other. vet unknown ido substructures must be considered. το reproduce. the observations.," These characteristic spatial distributions of the debris stars give rise to more significant effects of the debris at the NGP than in the solar neighborhood, as shown here, although the current simulation failed to reproduce the reported largely retrograde rotation at NGP from the $\omega$ Cen debris alone; perhaps, other, yet unknown halo substructures must be considered to reproduce the observations."
 Existing kinematic studies ofGalactic stars to search for a signature of c Con's progenitor galaxy are vet confined to nearby stars. where the significance of the debris streams is modest. as shown here.," Existing kinematic studies of Galactic stars to search for a signature of $\omega$ Cen's progenitor galaxy are yet confined to nearby stars, where the significance of the debris streams is modest, as shown here."
 Searches of stars inside the solar circle ave more encouraging (Fig., Searches of stars inside the solar circle are more encouraging (Fig.
" 1). in particular in the directions of/~320 and /—50 where we expect the presence of high-velocity streams ab íi,=200-—300 km s and 400—300 km s respectively."," 1), in particular in the directions of $l \sim 320^\circ$ and $l \sim 50^\circ$ , where we expect the presence of high-velocity streams at $v_{los} = 200 \sim 300$ km $^{-1}$ and $-400 \sim -300$ km $^{-1}$ , respectively."
 Future racial velocity surveys of these fields including the sami»le of the Sloan Digital Sky Survey or planned Iacdial Velocity, Future radial velocity surveys of these fields including the sample of the Sloan Digital Sky Survey or planned Radial Velocity
we solely use the membership probabilities of stars determined from the CCM considerations.,we solely use the membership probabilities of stars determined from the CCM considerations.
 Utilising the individual membership probabilities for all stars in each cluster we plotted J-K vs. K colour-magnitude (CMD) and H-K vs J-H colour-colour (CCD) diagrams for each FSR cluster candidate., Utilising the individual membership probabilities for all stars in each cluster we plotted J-K vs. K colour-magnitude (CMD) and H-K vs J-H colour-colour (CCD) diagrams for each FSR cluster candidate.
" In refexamplecmd0412 we show the diagrams, including the best fitting isochrone (see below) of the so far uninvestigated cluster 00412 33) as an example."," In \\ref{examplecmd0412} we show the diagrams, including the best fitting isochrone (see below) of the so far uninvestigated cluster 0412 3) as an example."
 One can nicely see that the cluster red giant stars are the most likely members (Peem>80 much less likely to be cluster members.," One can nicely see that the cluster red giant stars are the most likely members $P_{ccm} >
80$ much less likely to be cluster members."
 In refCMD we show the CMDs and CCDs for all clusters investigated in this paper., In \\ref{CMD} we show the CMDs and CCDs for all clusters investigated in this paper.
" We then inspected the 1788 CMDs and CCDs generated for the entire FSR catalogue, to decide if the high probability members are consistent with a sequence representing an old stellar cluster."," We then inspected the 1788 CMDs and CCDs generated for the entire FSR catalogue, to decide if the high probability members are consistent with a sequence representing an old stellar cluster."
" In other words, we manually selected all FSR objects that either showed a Red Giant Branch (RGB) or the top of the Main Sequence (MS) and a number of giant stars."," In other words, we manually selected all FSR objects that either showed a Red Giant Branch (RGB) or the top of the Main Sequence (MS) and a number of giant stars."
" Note that this selection has been performed 'blind', without the knowledge of which object is which cluster (known or unknown) in order to ensure an unbiased selection."," Note that this selection has been performed 'blind', without the knowledge of which object is which cluster (known or unknown) in order to ensure an unbiased selection."
 In total 269 of the 1788 objects were selected as candidates for old clusters and analysed in more detail for this paper., In total 269 of the 1788 objects were selected as candidates for old clusters and analysed in more detail for this paper.
 We cross-identified the list of 269 clusters with the database., We cross-identified the list of 269 clusters with the database.
" In total 63 known globular clusters are in the list, 174 known open clusters (including some already confirmed FSR objects) and 32 so far unclassified FSR cluster candidates."," In total 63 known globular clusters are in the list, 174 known open clusters (including some already confirmed FSR objects) and 32 so far unclassified FSR cluster candidates."
" Some obviously old clusters, in particular some of the known globular clusters (e.g. FSR00005 or 66569, 2260), are missing in our sample of old FSR clusters."," Some obviously old clusters, in particular some of the known globular clusters (e.g. 0005 or 6569, 260), are missing in our sample of old FSR clusters."
" This is mainly caused by the fact that they do not contain a large enough number of high probability cluster members, representing an old stellar sequence."," This is mainly caused by the fact that they do not contain a large enough number of high probability cluster members, representing an old stellar sequence."
" We obtained the distances, metallicities and reddening for the known globular clusters from the list of Harris (1996).."," We obtained the distances, metallicities and reddening for the known globular clusters from the list of Harris \cite{1996AJ....112.1487H}."
 The parameters for 00040 11) are obtained from Ivanov et al., The parameters for 0040 1) are obtained from Ivanov et al.
 (2000) and the values for 11735 are taken from Froebrich et al. (2008b).., \cite{2000A&A...362L...1I} and the values for 1735 are taken from Froebrich et al. \cite{2008MNRAS.390.1598F}.
" The cluster 11762 226, 771, 22) is listed as globular or cluster of stars in SIMBAD and we used its parameters from the list of Harris (1996).."," The cluster 1762 26, 71, 2) is listed as globular or cluster of stars in SIMBAD and we used its parameters from the list of Harris \cite{1996AJ....112.1487H}."
" The clusters 00190, 0584 and 1716 are also listed as globular or open cluster."," The clusters 0190, 0584 and 1716 are also listed as globular or open cluster."
" In those cases we used the literature data from Froebrich et al. (2008a),,"," In those cases we used the literature data from Froebrich et al. \cite{2008MNRAS.383L..45F},"
 Bica et al., Bica et al.
 (2007) and Froebrich et al., \cite{2007A&A...472..483B} and Froebrich et al.
" (2008b) and Bonatto Bica (2008), respectively."," \cite{2008MNRAS.390.1598F} and Bonatto Bica \cite{2008A&A...491..767B}, respectively."
 The open cluster parameters were obtained (as first choice) from the database for galactic open clusters., The open cluster parameters were obtained (as first choice) from the database for galactic open clusters.
 If no data was available for an open cluster we searched the literature., If no data was available for an open cluster we searched the literature.
 The main refproperties with the cluster parameters indicates the papers used in those cases., The main \\ref{properties} with the cluster parameters indicates the papers used in those cases.
 In total we obtained data for 147 of the known open clusters., In total we obtained data for 147 of the known open clusters.
" For 27 open clusters no data was available and their properties have hence been determined here, together with the parameters for the 32 so far unclassified FSR cluster candidates."," For 27 open clusters no data was available and their properties have hence been determined here, together with the parameters for the 32 so far unclassified FSR cluster candidates."
" From our analysis so far we only determined the cluster position and radius, as well as the BIC value."," From our analysis so far we only determined the cluster position and radius, as well as the BIC value."
" In order to determine the cluster parameters such as distance, reddening and age, we need to fit an appropriate isochrone to the CMD and CCD for each cluster."," In order to determine the cluster parameters such as distance, reddening and age, we need to fit an appropriate isochrone to the CMD and CCD for each cluster."
 We used the isochrone models from Girardi et al., We used the isochrone models from Girardi et al.
 (2002) for 2MASS data to perform this task., \cite{2002A&A...391..195G} for 2MASS data to perform this task.
 The Figures containing the CMDs and CCDs for all selected old FSR clusters in refCMD show in general two isochrones: One with the literature values for the cluster and our best fitting isochrone., The Figures containing the CMDs and CCDs for all selected old FSR clusters in \\ref{CMD} show in general two isochrones: One with the literature values for the cluster and our best fitting isochrone.
" The literature isochrone is shown as dashed blue line, the best fitting isochrone from this paper is shown as a solid black line."," The literature isochrone is shown as dashed blue line, the best fitting isochrone from this paper is shown as a solid black line."
 The parameters used for our best isochrone fit for all clusters are listed in refproperties.., The parameters used for our best isochrone fit for all clusters are listed in \\ref{properties}.
 The uncertainties of the determined parameters are discussed in refcomp.., The uncertainties of the determined parameters are discussed in \\ref{comp}.
 The reddening to each cluster used in our best fitting isochrone is given as the K-band extinction in refproperties.., The reddening to each cluster used in our best fitting isochrone is given as the K-band extinction in \\ref{properties}.
 To overplot the isochrones on the CMDs and CCDs we need to convert the K-band into the J and H-band extinction using Ay=C;k*Ax and Αη=Cpu k*Ay., To overplot the isochrones on the CMDs and CCDs we need to convert the K-band into the J and H-band extinction using $A_J = C_{JK} * A_K$ and $A_H = C_{HK} * A_K$ .
Weuse aconversion factor ουκ— 22.618 following Mathis (1990).., We use a conversion factor $C_{JK} =$ 2.618 following Mathis \cite{1990ARA&A..28...37M}.
" In order to fit the isochrone data in the CCD as well, in general the conversion factor Cj— 11.529 from Mathis (1990) seems too low."," In order to fit the isochrone data in the CCD as well, in general the conversion factor $C_{HK}
=$ 1.529 from Mathis \cite{1990ARA&A..28...37M} seems too low."
 For the majority of clusters we hence use C'yx= 11.67., For the majority of clusters we hence use $C_{HK} =$ 1.67.
" However, in some cases those valuesdo not provide a satisfying fit, and we hence adjusted the value for C for each cluster separately."," However, in some cases those valuesdo not provide a satisfying fit, and we hence adjusted the value for $C_{HK}$ for each cluster separately."
 The used values for each cluster are listed in refproperties.., The used values for each cluster are listed in \\ref{properties}. .
The presence of broad. permitted lines in the optical spectra of type | AGN. indicates the presence of dense (og.>105 ο). relatively low-ionisation gas close to the central engine (e.g. Peterson 1997. Krolik 1999).,"The presence of broad, permitted lines in the optical spectra of type 1 AGN, indicates the presence of dense $n_{\rm H}>10^{8}$ $^{-3}$ ), relatively low-ionisation gas close to the central engine (e.g. Peterson 1997, Krolik 1999)."
 The covering factor of the “broad line region’ tor BER) is estimated from line equivalent widths to be aroundc... while the strengths of low-ionisation and Balmer lines imply column densities Ny1077 > (see Peterson 1997 and Krolik 1999 for reviews).," The covering factor of the `broad line region' (or BLR) is estimated from line equivalent widths to be around, while the strengths of low-ionisation and Balmer lines imply column densities $N_{\rm
H}>10^{22}$ $^{-2}$ (see Peterson 1997 and Krolik 1999 for reviews)."
" ""Reverberation. mapping measurements of time delays in the response of optical lines to changes in the optical continuum indicate that the BLR lies within à few light-weeks of the continuum source (e.g. Peterson et al.", `Reverberation mapping' measurements of time delays in the response of optical lines to changes in the optical continuum indicate that the BLR lies within a few light-weeks of the continuum source (e.g. Peterson et al.
 1998. Kaspi et al.," 1998, Kaspi et al."
 2000)., 2000).
 It is perhaps surprising that clearcut evidence for the low-ionisation BLR clouds in type | AGN has not previously emerged in the X-ray band., It is perhaps surprising that clearcut evidence for the low-ionisation BLR clouds in type 1 AGN has not previously emerged in the X-ray band.
 The soft X-ray band (<2 keV) is particularly sensitive to absorption by gas along the line of sight to the central X-ray source., The soft X-ray band $<2$ keV) is particularly sensitive to absorption by gas along the line of sight to the central X-ray source.
" Numerous studies using missions sensitive to the soft X-ray band (e.g.ROSAT.ASCA.BeppoSAX and most recently the grating instruments on and XMM-Newton) have shown the presence of absorption due to more highly ionised gas (the ""warm absorber’) along the line of sight in many Seyfert Is. but the precise location of this gas is still fairly uncertain (e.g. ΝΤ Hardy et al."," Numerous studies using missions sensitive to the soft X-ray band (e.g., and most recently the grating instruments on and ) have shown the presence of absorption due to more highly ionised gas (the `warm absorber') along the line of sight in many Seyfert 1s, but the precise location of this gas is still fairly uncertain (e.g. $^{\rm c}$ Hardy et al."
 1995. George et al.," 1995, George et al."
 1998a. Netzer et al.," 1998a, Netzer et al."
 2002. Schurch Warwick 2002).," 2002, Schurch Warwick 2002)."
 Column density variations of cold X-ray absorbing gas have been reported on time-scales of months-years in. both type | and type 2 Seyferts on time-scales of months to years (Malizia et al., Column density variations of cold X-ray absorbing gas have been reported on time-scales of months-years in both type 1 and type 2 Seyferts on time-scales of months to years (Malizia et al.
 1997. Risaliti. Elvis Nicastro 2002).," 1997, Risaliti, Elvis Nicastro 2002)."
 Tf such variations are due to clouds crossing the line of sight with Keplerian velocities. the obscuring clouds may He within or not much beyond the BLR.," If such variations are due to clouds crossing the line of sight with Keplerian velocities, the obscuring clouds may lie within or not much beyond the BLR."
 Unfortunately. due to the sparse temporal sampling of X-ray spectra of AG available with most X-ray missions. it is difficult to put these apparent absorption changes into context. and assess if they really are caused by the motion of dense absorbing clouds across the line of sight to the X-ray source.," Unfortunately, due to the sparse temporal sampling of X-ray spectra of AGN available with most X-ray missions, it is difficult to put these apparent absorption changes into context, and assess if they really are caused by the motion of dense absorbing clouds across the line of sight to the X-ray source."
 In this letter. we present a study of the long-term X-ray spectral variability of the Seyfert 1.5 galaxy NGC 3227. using data from a monitoring campaign carried out by the (RXTE).," In this letter, we present a study of the long-term X-ray spectral variability of the Seyfert 1.5 galaxy NGC 3227, using data from a monitoring campaign carried out by the )."
 A previous study of spectral variability in NGC 3227 showed evidence of an order of magnitude increase in the cold/low-ionisation column (from ~107 ? to ~1077 =) between observations obtained in 1993 and 1995 (George et al., A previous study of spectral variability in NGC 3227 showed evidence of an order of magnitude increase in the cold/low-ionisation column (from $\sim10^{21}$ $^{-2}$ to $\sim10^{22}$ $^{-2}$ ) between observations obtained in 1993 and 1995 (George et al.
 1998b)., 1998b).
 Using data from our monitoring campaign. we show that in 2000/2001 NGC 3227 underwent an unusual event lasting 3 months. during which the spectrum became exceptionally hard.," Using data from our monitoring campaign, we show that in 2000/2001 NGC 3227 underwent an unusual event lasting $\sim3$ months, during which the spectrum became exceptionally hard."
 The symmetry of this event suggests it is due to absorption by a high column density cloud, The symmetry of this event suggests it is due to absorption by a high column density cloud
with the disc and the power-law component are shown in the lower panel of Fig.,with the disc and the power-law component are shown in the lower panel of Fig.
" 1 (2-15 keV), and in the middle and lower panels of Fig."," \ref{hid} (2-15 keV), and in the middle and lower panels of Fig."
 3 (2-6 keV and 6-15 keV)., \ref{rmsc} (2-6 keV and 6-15 keV).
 The following is noted by comparing these results with the hardness and rms evolution: Using the results from the spectral fits we computed the absolute count-rates associated with the disc and the power-law 15 keV)., The following is noted by comparing these results with the hardness and rms evolution: Using the results from the spectral fits we computed the absolute count-rates associated with the disc and the power-law (2--15 keV).
 We have over-plotted them in Fig. 5.., We have over-plotted them in Fig. \ref{lc}.
 Only during the HSS epochs (dark grey bands) the disc dominates the observed rate., Only during the HSS epochs (dark grey bands) the disc dominates the observed count-rate.
" As seen in other systems the disc is not observed within the XTE/PCU band at the beginning and at the end of the outburst (e.g., ?). We also note that all the wiggles present in the light-curve are observed in both components until the system reaches the HSS for the first time."," As seen in other systems the disc is not observed within the XTE/PCU band at the beginning and at the end of the outburst (e.g., \citealt{Motta2009}) We also note that all the wiggles present in the light-curve are observed in both components until the system reaches the HSS for the first time."
" From that point onwards (day ~ 21), the count- associated with the disc decreases monotonically, probably following the accretion rate, and the wiggles observed in the light- are solely caused by variations in the power-law count rate."," From that point onwards (day $\sim 21$ ), the count-rate associated with the disc decreases monotonically, probably following the accretion rate, and the wiggles observed in the light-curve are solely caused by variations in the power-law count rate."
To demonstrate the quality of (he background subtraction. Eshow in Figure 1 (right) the region around a background line at 1014 keV. This line. like the background line atkeV... is due to the prompt decay. of a short-livecl isomer created by cosmic-ray interactions in aluminum.,"To demonstrate the quality of the background subtraction, I show in Figure 1 (right) the region around a background line at 1014 keV. This line, like the background line at, is due to the prompt decay of a short-lived isomer created by cosmic-ray interactions in aluminum."
 Thus. iit subtracts well. one should be able to assume that the bbackground line does also.," Thus, if it subtracts well, one should be able to assume that the background line does also."
 The figure demonstrates subtraction better than the shown for comparison., The figure demonstrates subtraction better than the shown for comparison.
 There is a hint of a residual 1014 keV line which. when fit with a Gaussian. eives a [lux of (1.22:0.5) of the background line.," There is a hint of a residual 1014 keV line which, when fit with a Gaussian, gives a flux of $(1.2 \pm
0.5)$ of the background line."
 The averaged cosmic-ray count rate in the detectors over all the periods used for source pointings is hieher (han the same average over (he background periods., The averaged cosmic-ray count rate in the detectors over all the periods used for source pointings is higher than the same average over the background periods.
 This is consistent with the slight undersubtvaction hinted al in Figure 1 (right)., This is consistent with the slight undersubtraction hinted at in Figure 1 (right).
 I find that subtracting out an extra or of the bbackeround line has no significant effect on the Galactic line width. whether I use the natural form of the backerouncl spectrum. (which includes ihe 1811 keV line) or whether I substitute an artificial single Gaussian line al exactly 1808.65 keV with the instrumental resolution.," I find that subtracting out an extra or of the background line has no significant effect on the Galactic line width, whether I use the natural form of the background spectrum (which includes the 1811 keV line) or whether I substitute an artificial single Gaussian line at exactly 1808.65 keV with the instrumental resolution."
 Since the Galactic line flux. is of the average background. these extra subtractions would reduce its value by and9%... respectively.," Since the Galactic line flux is of the average background, these extra subtractions would reduce its value by and, respectively."
 To further demonstrate that the cosmic-rav-induced background line is well-subtractec. I divided the data set into two roughly equal parts bv the value of the cosmic-ray count rate during each oneaninute spectrum.," To further demonstrate that the cosmic-ray-induced background line is well-subtracted, I divided the data set into two roughly equal parts by the value of the cosmic-ray count rate during each one-minute spectrum."
 The rate averaged 158 counts | for the lower data set and 237 counts | for the higher data set. for a ratio of 1.50.," The rate averaged 158 counts $^{-1}$ for the lower data set and 237 counts $^{-1}$ for the higher data set, for a ratio of 1.50."
 The count rate in the total. unsubtracted lline had a similar ratio of 1.42. with aand ii (he two sets. respectively.," The count rate in the total, unsubtracted line had a similar ratio of 1.42, with and in the two sets, respectively."
 Once the backgrounds were subtracted. however. the values for the residual (Galactic) line were (1.1340.15) aand (1.2320.15)|... respectively. a ratio of only 1.09 and well within statistical agreement.," Once the backgrounds were subtracted, however, the values for the residual (Galactic) line were $(1.13 \pm 0.15)$ and $(1.23 \pm 0.15)$, respectively, a ratio of only 1.09 and well within statistical agreement."
 The derived Galactic signal (ius appears to be independent of the intensitv of the background line., The derived Galactic signal thus appears to be independent of the intensity of the background line.
 The conversion of the count rate in the Galactic line to a total Galactic [hix is strongly dependent on the assumed Galactic distribution., The conversion of the count rate in the Galactic line to a total Galactic flux is strongly dependent on the assumed Galactic distribution.
 The effective area of the eight rear segments used. calculated at. uusineg the distribution of angles of incidence over (he observation period assuming the source is concentrated at the Galactic center. is 20.5 eni.," The effective area of the eight rear segments used, calculated at using the distribution of angles of incidence over the observation period assuming the source is concentrated at the Galactic center, is 20.5 $^{2}$ ."
 The incident [lux is then (5.71£0.54)x {for the artificial case of a point source.," The incident flux is then $(5.71 \pm
0.54)$ for the artificial case of a point source."
 Since the effective area of the instrument is nearly, Since the effective area of the instrument is nearly
systematic changes that the secondaries may produce iu the power spectra need to be considered.,systematic changes that the secondaries may produce in the power spectra need to be considered.
" The contribution to the power spectrum from patchy relohization is one to two orders of magnitude smaller than the primordial CMD anisotropies on the relevant scales, but owing to the exquisite sensitivity of these experiments it biases parameter estimates."," The contribution to the power spectrum from patchy reionization is one to two orders of magnitude smaller than the primordial CMB anisotropies on the relevant scales, but owing to the exquisite sensitivity of these experiments it biases parameter estimates."
 For the analytic models of patchy reionization suggested by Knox aud Santosetal.(2003) this parameter bias was estimated., For the analytic models of patchy reionization suggested by \citet{Knox:1998fp} and \citet{Santos:2003jb} this parameter bias was estimated.
 Iu these models the mean bubble size is «λαο than iu our computation. and the signal peaks at higher nultipoles.," In these models the mean bubble size is smaller than in our computation, and the signal peaks at higher multipoles."
ab ο=OTS.,at $z = 0.78$.
 A future study will perform a more detailed analvsis of these results., A future study will perform a more detailed analysis of these results.
" The fitted values of the pairwise velocity dispersion in each redshift slice are a,=(35441.294431.21645s)h km s5 (marginalizing over f and 5)."," The fitted values of the pairwise velocity dispersion in each redshift slice are $\sigma_v = (354 \pm 41, 294 \pm 31, 216 \pm 58) \, h$ km $^{-1}$ (marginalizing over $f$ and $b$ )."
 We lind. evidence that the pairwise small-scale velocity dispersion of WieeleZ ealaxies systematically decreases with increasing recdshift., We find evidence that the pairwise small-scale velocity dispersion of WiggleZ galaxies systematically decreases with increasing redshift.
 The measured. bias factors for cach redshilt slice are b=(0.93+0.03.1.08=1.200.06) (marginalizing over f and 7).," The measured bias factors for each redshift slice are $b = (0.93 \pm 0.03, 1.08 \pm
0.03, 1.20 \pm 0.06)$ (marginalizing over $f$ and $\sigma_v$ )."
 We can compare these galaxy. bias measurements to those deduced. from the WigeleZ survey small-scale correlation function measurements: for three redshift slices similar to those analyzed here. Blake et ((2009) obtained b=(1.01.1.27.1.27) (although assuming a higher value of a— 0.9).," We can compare these galaxy bias measurements to those deduced from the WiggleZ survey small-scale correlation function measurements: for three redshift slices similar to those analyzed here, Blake et (2009) obtained $b = (1.01, 1.27, 1.27)$ (although assuming a higher value of $\sigma_8 = 0.9$ )."
 The main cause of this dilference is the superior determination. of ο in the current analysis., The main cause of this difference is the superior determination of $\beta$ in the current analysis.
 Other issues wth this comparison include: (i) galaxy bias is à scale-dependent function. (ii) small-scale pairwise velocities were not been modellec in the Blake et ((2009) analysis. (iii) the power-law correlation function modcl assumed in Blake et ((2009) breaks down at large scales.," Other issues wth this comparison include: (i) galaxy bias is a scale-dependent function, (ii) small-scale pairwise velocities were not been modelled in the Blake et (2009) analysis, (iii) the power-law correlation function model assumed in Blake et (2009) breaks down at large scales."
 Using these model fits we can combine the nine LD power spectrum measurements in the different regions and recshilt slices into a single. “stacked” survey LD power spectrum using inverse-variance weighting., Using these model fits we can combine the nine 1D power spectrum measurements in the different regions and redshift slices into a single “stacked” survey 1D power spectrum using inverse-variance weighting.
 The dillicultv with this step is that the power spectrum amplitude in cach region is modulated by a dillerent. level of convolution with the selection function. as illustrated by Figure 15..," The difficulty with this step is that the power spectrum amplitude in each region is modulated by a different level of convolution with the selection function, as illustrated by Figure \ref{figpkreg}."
" In addition. the shape of the power spectrum varies. with. redshift in accordance with the dilfering redshift-space. distortion parameters ancl galaxy bias factors,"," In addition, the shape of the power spectrum varies with redshift in accordance with the differing redshift-space distortion parameters and galaxy bias factors."
" Therefore. before combining the results in the cdilferent regions and redshift slices. we performed. an approximate ""de-convolution of amplitude by multiplving the power spectra by a correction factor equal to the scale-dependent ratio of the convolved ancl unconvolved model power spectra. tthe ratio of the solid. ancl dashed: curves plotted. in Figure 15.. ("," Therefore, before combining the results in the different regions and redshift slices, we performed an approximate “de-convolution” of amplitude by multiplying the power spectra by a correction factor equal to the scale-dependent ratio of the convolved and unconvolved model power spectra, the ratio of the solid and dashed curves plotted in Figure \ref{figpkreg}. ("
"In detail we did not use the model power spectra to generate these corrections but a ""reference"" power spectrum in which the barvon oscillation features have been smoothed out. tthe 7no-wigeles"" power spectrum of Eisenstein Llu (1998).","In detail we did not use the model power spectra to generate these corrections but a “reference” power spectrum in which the baryon oscillation features have been smoothed out, the “no-wiggles” power spectrum of Eisenstein Hu (1998)."
 We preferred. to correct. the amplitude using a wigele-[ree power spectrum {ο avoid spuriouslv introducing apparent barvon oscillations into the combined power spectrum)., We preferred to correct the amplitude using a wiggle-free power spectrum to avoid spuriously introducing apparent baryon oscillations into the combined power spectrum).
 We additionally corrected. the measurement in each Fourier bin by the angle-averaged ratio of the redshift-space galaxy power spectrum. (using the best-fitting values of 3 and o for each redshift slice) to the real-space matter power spectrum at redshift 2=0.6., We additionally corrected the measurement in each Fourier bin by the angle-averaged ratio of the redshift-space galaxy power spectrum (using the best-fitting values of $\beta$ and $\sigma_v$ for each redshift slice) to the real-space matter power spectrum at redshift $z=0.6$.
 Following these corrections. the nine power spectra “line up? with consistent shape and amplitude. and can be combined.," Following these corrections, the nine power spectra “line up” with consistent shape and amplitude, and can be combined."
 In Figure 19. we show separate combinations of power spectra across suürvev regions in each redshift slice. and across redshift slices in each survey region.," In Figure \ref{figpkstack} we show separate combinations of power spectra across survey regions in each redshift slice, and across redshift slices in each survey region."
 Phe combination of all nine power spectra is presented in Figure 20: the lower panel indicates the fractional accuracy of the measurement. which approaches 5% in Fourier bins of width As=0.01P +.," The combination of all nine power spectra is presented in Figure \ref{figpkcomb}; the lower panel indicates the fractional accuracy of the measurement, which approaches $5\%$ in Fourier bins of width $\Delta k = 0.01 \, h$ $^{-1}$."
 Phe scale dependence of the fractional accuracy. is determined by a balance between the increasing number of Fourier modes contributing to each successive bin (tending to decrease the error). and the increasing importance with A of shot noise relative to cosmic variance (tending to increase the error).," The scale dependence of the fractional accuracy is determined by a balance between the increasing number of Fourier modes contributing to each successive bin (tending to decrease the error), and the increasing importance with $k$ of shot noise relative to cosmic variance (tending to increase the error)."
 Finally. in Figure 21. we display the 2D. power spectra for cach redshift slice. combining cdilferent regions in the manner described above.," Finally, in Figure \ref{figpk2red} we display the 2D power spectra for each redshift slice, combining different regions in the manner described above."
" As a final exercise we fitted the measured. power spectra for the cosmological matter ancl barvon densities (parameterized by ,, and fi;=O,/034,).", As a final exercise we fitted the measured power spectra for the cosmological matter and baryon densities (parameterized by $\Omega_{\rm m}$ and $f_{\rm b} = \Omega_{\rm b}/\Omega_{\rm m}$ ).
". We tried. three different initial approaches to this analysis. with increasing degrees of sophistication: Figure 22 displavs the probability contours in the 2D space of Oy and fi= QO,/O0,,. mareinalizing over"," We tried three different initial approaches to this analysis, with increasing degrees of sophistication: Figure \ref{figomfbprob} displays the probability contours in the 2D space of $\Omega_{\rm m}$ and $f_{\rm b} = \Omega_{\rm b}/\Omega_{\rm
 m}$ , marginalizing over"
∙∙ ο... uportant (Jappsenctal.2007:tGlover&JappsenSuuithMetweal.B2008.Q02009:oJappΒ(ontTMH€. 2009a.1)).. (IauuholzCuedinetal.2009).," \citep{Jap07, Glo07, Smi08, Smi09, Jap09a, Jap09b}. \citep{Kru05, Rob08, Gne09}."
. ⋅⋅ and iu uuncerical simulations (e.g. 2005)., and in numerical simulations \citep[e.g.][]{Spr05}.
. Such a recipe is based on the Ορσα]. correlations observed im local 8galaxies. ∐⋜⋯∐∖↕⋅↖↽↑↕∐∖↕↘⊽↸∖∐↕∐↸⊳∏↑≓≋↸⊳∐∐∐≼∐↕⋜↧↖↖↽⋖↕↘⊽↸∖∐∐↕↸⊳↿⇈ 1998).," Such a recipe is based on the empirical correlations observed in local galaxies, namely the Kennicut-Schmidt law \citep{Ken98}."
. These correlations have oulv been studied relatively well for nearby massive or star bursting ealaxios., These correlations have only been studied relatively well for nearby massive or star bursting galaxies.
 However. for galaxies with low surface bishtuess and/or low-metallicity. this οΊσα] relation may not be valid.," However, for galaxies with low surface brightness and/or low-metallicity, this empirical relation may not be valid."
 Indeed. both nearby metal-poor galaxies (Bigicletal.2008) aud high-redshiftwp ealaxics. (Wolfe-.&Chen2006) provide. a variety of clues sugeesting that eas conversion iuto stars i low-mass. low-uctallicity galaxies is very mefficient.," Indeed, both nearby metal-poor galaxies \citep{Big08} and high-redshift galaxies \citep{Wol06} provide a variety of clues suggesting that gas conversion into stars in low-mass, low-metallicity galaxies is very inefficient."
 The star formation efficiency may depend onu ability to couvert a fraction of gas mass into uolecular form., The star formation efficiency may depend on ability to convert a fraction of gas mass into molecular form.
 Molecular hwdrogenu is produced x chemical reactious iu gas phase in first ealaxy ialos., Molecular hydrogen is produced by chemical reactions in gas phase in first galaxy halos.
 Iu the cra. reionizationIT» molecule dissociation i the Lyiuzui- ultraviolet (UV) backerouud retween 11.2 and 13.6 eV. is important inthe lower uass Ilo cooling halos.," In the reionization era, ${\rm H}_{2}$ molecule dissociation by the Lyman-Werner ultraviolet (UV) background between 11.2 and 13.6 eV is important in the lower mass ${\rm H}_{2}$ cooling halos."
 Cas coudensation in the ower nass [lo cooling halos cau be delaved by, Gas condensation in the lower mass ${\rm H}_{2}$ cooling halos can be delayed by
OI huuinositios where our survey is complete.,[OII] luminosities where our survey is complete.
" This sugeests that the majority of our detections are simply ficld galaxies innediatelv in frout and behind the cluster or Which [OTL], alls into our on-baud and the density of star-forming ealaxies bound to MS1512|3617 is indistinguishable from he field.", This suggests that the majority of our detections are simply field galaxies immediately in front and behind the cluster for which [OII] falls into our on-band and the density of star-forming galaxies bound to MS1512+3647 is indistinguishable from the field.
 Ou the other hand. Abell 851 Iuuinositv fiction shows au excess of [OTL ciission-line galaxies 3-1 times he deusity of the field [OT] galaxies at τί=0.1 (Paper 1) and MS1512.013617 sample.," On the other hand, Abell 851 luminosity function shows an excess of [OII] emission-line galaxies 3-4 times the density of the field [OII] galaxies at $z=0.4$ (Paper 1) and MS1512.4+3647 sample."
 We find that the MS1512.113617 eunission-liue objects are not strongly clustered. towards the central cluster ealaxy (filled square. top of Figure 8).," We find that the MS1512.4+3647 emission-line objects are not strongly clustered towards the central cluster galaxy (filled square, top of Figure 8)."
 This is in coutrast to the galaxies with elliptical-Hke colors (gy9/>2.0. open squares). which are more likely to be found around the central cluster galaxw at projected radi « Royy. ( Που.," This is in contrast to the galaxies with elliptical-like colors $g-i > 2.0$, open squares), which are more likely to be found around the central cluster galaxy at projected radii $<$ $_{200}$. ( $_{200}$,"
 the radius at which the mean inner density of the cluster is 200 times the critical deusity of the wniverse.  1.2 \Ipe for MS1512.113617 assuuiug cluster velocity dispersion σ — 575 lau 1.)," the radius at which the mean inner density of the cluster is 200 times the critical density of the universe, $\sim$ 1.2 Mpc for MS1512.4+3647 assuming cluster velocity dispersion $\sigma$ = 575 km $^{-1}$.)"
 At -0.37. our field of view is ~ L Mpc * 1 Apc aud will include most of the cluster.," At $z=0.37$, our field of view is $\sim$ 4 Mpc $\times$ 4 Mpc and will include most of the cluster."
 The surface density of ΟΠ cutters is consistent with the field [OT] cluission-line population (IIoge et al., The surface density of [OII] emitters is consistent with the field [OII] emission-line population (Hogg et al.
 L998)., 1998).
 Except for the inner 100 ((~770 kpe) Abell 851 star-forming ealaxies are also weakly clustered relative to the red ealaxics (bottom of figure 8) out to 1.5 Rogo. even though the surface density of star-forming galaxies observed iu the Abell 851 field is well above that expected for field [OTT] eumditters.," Except for the inner 100 $\sim 770$ kpc), Abell 851 star-forming galaxies are also weakly clustered relative to the red galaxies (bottom of figure 8) out to 1.5 $_{200}$, even though the surface density of star-forming galaxies observed in the Abell 851 field is well above that expected for field [OII] emitters."
 Civeu that the MS1512.113617. Iununositv. function shows no over-density of |OII| cmitters aud the surface density of star-foriiiung galaxies is likely to be dominated bv field galaxies at all cluster radii it seocns likely that most of our MS1512.113617. sample are field ealaxics suroundiue M$1512.112617. which are not bound to the cluster potential.," Given that the MS1512.4+3647 luminosity function shows no over-density of [OII] emitters and the surface density of star-forming galaxies is likely to be dominated by field galaxies at all cluster radii, it seems likely that most of our MS1512.4+3647 sample are field galaxies surrounding MS1512.4+3647 which are not bound to the cluster potential."
 MS1512.1123617 does possess some ealaxies which have had receut star-formation the CNOCL survev found that ~ 20 of spectroscopically-confirmed cluster members brighter than AL.=19.0 in the core of MS1512.113617 ave bluer than yoo’= 425. like other clusters observed by CNOCT at. similar redshifts (Ellinegsou ct al.," MS1512.4+3647 does possess some galaxies which have had recent star-formation $-$ the CNOC1 survey found that $\sim$ 20 of spectroscopically-confirmed cluster members brighter than $_{r'} = -19.0$ in the core of MS1512.4+3647 are bluer than $g'-r' = 0.25$ , like other clusters observed by CNOC1 at similar redshifts (Ellingson et al."
 2001)., 2001).
 Tf MS1512.1]3617. is a typical z:~OL cluster. then most clusters at i—1 do not have hieh densities of star-forming ealaxics. nmt are instead slowing swallowing up the field galaxv x»pulation.," If MS1512.4+3647 is a typical $z \sim 0.4$ cluster, then most clusters at $z \sim 0.4$ do not have high densities of star-forming galaxies, but are instead slowing swallowing up the field galaxy population."
 Assuniug accreted ealaxies eventually cease star-production aud havedetectable |OIT| euissiou for ~ 1 Gar (Balogh et al., Assuming accreted galaxies eventually cease star-production and havedetectable [OII] emission for $\sim$ 1 Gyr (Balogh et al.
 2000). then a average z 0.1 cluster as assenbled most of its mass at redshifts 2 0.5.," 2000), then a average $z \sim$ 0.4 cluster has assembled most of its mass at redshifts $\geq$ 0.5."
 Abcll 851. ou the other haud. is clearly au uuusual cluster iu teris of its mass. N-rav Iuninositv. aud deusitv of star-forming galaxies.," Abell 851, on the other hand, is clearly an unusual cluster in terms of its mass, X-ray luminosity, and density of star-forming galaxies."
 Its virial mass is approximately 10 times that of MS1512.113617 aud its bolometric N-ray Dhuunositv is over twice that of AISTS12.1)3617 (16.08 10H oe toys. 7.62 S10H cre 5; Wir et al., Its virial mass is approximately 10 times that of MS1512.4+3647 and its bolometric X-ray luminosity is over twice that of MS1512.4+3647 (16.08 $\times 10^{-44}$ erg $^{-1}$ vs. 7.62 $\times 10^{-44}$ erg $^{-1}$; Wu et al.
 1999)., 1999).
 This cluster has significant sub-structure in its X-rav enudsson (Schindler Waibseanss 1996) aud galaxy distribution (INodama et al., This cluster has significant sub-structure in its X-ray emission (Schindler Wambsganss 1996) and galaxy distribution (Kodama et al.
 2001)., 2001).
 It appears to be a cluster in formation. aud has most likely acquired its large ΠΠΡΟ of star-forming galaxies from a collapsing svsteum of groups and filamcuts as opposed to eradual accretion of the surrounding field population.," It appears to be a cluster in formation, and has most likely acquired its large number of star-forming galaxies from a collapsing system of groups and filaments as opposed to gradual accretion of the surrounding field population."
 The vast difference between the MS1512.113617. aud Abell 851 [OTI] cmiissiou-line galaxy densities iniplies that the density of star-forming galaxies in a cluster relative to the field may be au stroug tracer of the recent assenibly history of the cluster., The vast difference between the MS1512.4+3647 and Abell 851 [OII] emission-line galaxy densities implies that the density of star-forming galaxies in a cluster relative to the field may be an strong tracer of the recent assembly history of the cluster.
 Balogh ct al. (, Balogh et al. (
2002) reached a simular conchision when they found a significantly higher density of Πα cutting galaxies in the :=0.18 cluster Abell 1689 than in the more relaxed but more distaut cluster AC 111 at 2=0.31.,2002) reached a similar conclusion when they found a significantly higher density of $\alpha$ emitting galaxies in the $z=0.18$ cluster Abell 1689 than in the more relaxed but more distant cluster AC 114 at $z=0.31$.
 Normalizing each of our cluster’s deusities of [OIL] cmitters bv their bolometric N-rav luminosities and correcting for selection effects; we find that the normalized deusitv of star-formune galaxies above the MS1512.113617 detections Bits is 0.0058 c 0.0005 ? νι lott ere s1) + for Abell 851 aud 0.0031. 0 0.0001 Ὁ Ly( 102 cre s1) |.," Normalizing each of our cluster's densities of [OII] emitters by their bolometric X-ray luminosities and correcting for selection effects, we find that the normalized density of star-forming galaxies above the MS1512.4+3647 detections limits is 0.0058 $\pm$ 0.0005 $^{-3}$ $_X$ ( $^{44}$ erg $^{-1}$ $^{-1}$ for Abell 851 and 0.0031 $\pm$ 0.0004 $^{-3}$ $_X$ ( $^{44}$ erg $^{-1}$ $^{-1}$."
 These values are a lower limit for Abell 551 as our field of view chcompassed only the iuner half of the cluster (Paper 1). anda upper liuüt for MS1512.113617 due to the significant field contamination.," These values are a lower limit for Abell 851 as our field of view encompassed only the inner half of the cluster (Paper 1), and a upper limit for MS1512.4+3647 due to the significant field contamination."
 Therefore Abell 551 has at least twice (and possibly ten times) as many star-forming galaxies per nuit vohune aud X-ray huninosity than the more typical cluster AMIST512.113617., Therefore Abell 851 has at least twice (and possibly ten times) as many star-forming galaxies per unit volume and X-ray luminosity than the more typical cluster MS1512.4+3647.
 Iu this section. we use the [OT] cmissiou-lineequivalent widths and broad-band colors of the ALST512.1013617 OU] candidates to coustrain their recent. star-formation.," In this section, we use the [OII] emission-lineequivalent widths and broad-band colors of the MS1512.4+3647 [OII] candidates to constrain their recent star-formation."
 We then compare the derived star-formation histories of he MS1512.113617 field-dominated aud the Abell 851 cluster-dominated [OT] cinissiou-line galaxy samples for clues to the origin of the disparity iu the deusitv of star- ealaxies between the two clusters., We then compare the derived star-formation histories of the MS1512.4+3647 field-dominated and the Abell 851 cluster-dominated [OII] emission-line galaxy samples for clues to the origin of the disparity in the density of star-forming galaxies between the two clusters.
 Finally. we discuss the iuplications for dwarf galaxy evolution in the Bold aud clusters.," Finally, we discuss the implications for dwarf galaxy evolution in the field and clusters."
 The dependence of |OII| luminosity onu the star-orlation rate has been curpirically calibrated using voth Wa aud. IL? cunission (Ikeuuicutt. 1992: Gallagher. Dushouse Unuter 1989).," The dependence of [OII] luminosity on the star-formation rate has been empirically calibrated using both $\alpha$ and $\beta$ emission (Kennicutt 1992; Gallagher, Bushouse Hunter 1989)."
 We adopt the observed. [OT] 3727 to IL} relation. = 3.2 Fy derived. for local star-forming galaxies F[OII](Gallagher et al., We adopt the observed [OII] 3727 to $\beta$ relation F[OII] = 3.2 $_{H\beta}$ derived for local star-forming galaxies (Gallagher et al.
 1989)., 1989).
 To convert he observed (aud dust-extincted) flux to a star orluation rate. we assume a dust-correctiou[OT] for the observed 11.) fiux. derive the intrinsic ratio of IT./ to Πα Hux. and assume an intrinsic Πα to star formation rate relation.," To convert the observed (and dust-extincted) [OII] flux to a star formation rate, we assume a dust-correction for the observed $\beta$ flux, derive the intrinsic ratio of $\beta$ to $\alpha$ flux, and assume an intrinsic $\alpha$ to star formation rate relation."
 We adopt Ap=1.0 extinction correction. typical of nearby star-forming divurfs aud nregular ealaxics (IIuuter Toffinan 1999).," We adopt $A_B = 1.0$ extinction correction, typical of nearby star-forming dwarfs and irregular galaxies (Hunter Hoffman 1999)."
" Asstmineg nebular temperature = 10!) Case B recombination. and Ay, = (0.59 for Ap= 10. we derive extinctiou-corrected ffm fluxes. 2.0 times larger than the measured. uncorrected fluxes."," Assuming nebular temperature $=10^4$ , Case B recombination, and $A_{H\alpha}$ = 0.59 for $A_B = 1.0$ , we derive extinction-corrected $H\alpha$ fluxes 2.0 times larger than the measured, uncorrected [OII] fluxes."
" Finally, we adopt INemuicutt. Tamblyn. [OIT| Congdous (1991) intrinsic Πα ΕΤ calibration. assume the E83 initial mass function (I&enuicutt 1983) from 0.1 to LOO AL. By choosing au extinction correction appropriate for"," Finally, we adopt Kennicutt, Tamblyn, Congdon's (1994) intrinsic $\alpha$ -SFR calibration, assuming the K83 initial mass function (Kennicutt 1983) from 0.1 to 100 $\Msun$ : By choosing an extinction correction appropriate for"
 .2....).,"(here $k = 1, 2,\dots$ )."
 Theterm /j is now given by One can specify the parameters b and « of the transition so that the second integral in Eq. (26)), Theterm $h_1$ is now given by One can specify the parameters $b$ and $\alpha$ of the transition so that the second integral in Eq. \ref{bd}) )
 can be neglected. at least for thin disks.," can be neglected, at least for thin disks."
 The next expansion terms /s (A= 2.3....) are given by We can use estimate (23)) in order to obtain the inequality The elliptic function E(275.2) 1s integrable on any finite disk.," The next expansion terms $h_k$ 's $k = 2, 3,\dots$ ) are given by We can use estimate \ref{ay}) ) in order to obtain the inequality The elliptic function $E \left( r, r_k, z \right)$ is integrable on any finite disk."
 The inequality (27)) means that the series expansion is convergent for sufficiently small values of the product It suffices that the mass current constant Fo is small enough. which means—notice the conservation law (17))—that stationary disks cannot have arbitrarily large luminosity.," The inequality \ref{bf}) ) means that the series expansion is convergent for sufficiently small values of the product It suffices that the mass current constant $F$ is small enough, which means—notice the conservation law \ref{ap}) )—that stationary disks cannot have arbitrarily large luminosity."
 The mass accretion rate influences the disk geometry. as seen from the following discussion.," The mass accretion rate influences the disk geometry, as seen from the following discussion."
" At the boundary we have fig+i)=0: thus (keeping only the leading term of /7,) we have forr> band for r€b.", At the boundary we have $h_0 + h_1 \approx 0$; thus (keeping only the leading term of $h_1$ ) we have for$r>b$ and for $r\le b$.
 Assuming that the outer part of the disk extends up to row. one obtains the value of F where One can check that for small zo.," Assuming that the outer part of the disk extends up to $r_\mathrm{out}$, one obtains the value of $F$ where One can check that for small $z_0$."
 Here y(rij/rau) 18 a coefficient. with values depending on the ratio 75/4. ranging between 0.01 and 1 for Fal'a=007.....I.," Here $\gamma(r_\mathrm{in}/r_\mathrm{out})$ is a coefficient, with values depending on the ratio $r_\mathrm{in}/r_\mathrm{out}$, ranging between 0.01 and 1 for $r_\mathrm{in}/r_\mathrm{out} = 10^{-9}, \dots, 1$."
 It is found numerically as the largest coefficient ensuring that the inequality isPout satisfied., It is found numerically as the largest coefficient ensuring that the inequality is satisfied.
 Inequality (31)) combinedFinPout with Eq. (30)), Inequality \ref{inequality_i}) ) combined with Eq. \ref{bj}) )
" yields Obviouslyn, for thin disks the right hand side is much smaller than one: that implies the convergence of our approximation scheme.", yields Obviously for thin disks the right hand side is much smaller than one; that implies the convergence of our approximation scheme.
 The consistency condition F<[dzor?p. discussed earlier. can be checked only aposteriori. after solving all equations.," The consistency condition $F\ll \int dz \omega r^2 \rho$, discussed earlier, can be checked only aposteriori, after solving all equations."
 Eq. (29)), Eq. \ref{bi}) )
 allows. putting r27j. to specify the parameter c that appears in the rotation curve in the transient zone (7.b).," allows, putting $r = r_\mathrm{in}$, to specify the parameter $\alpha$ that appears in the rotation curve in the transient zone $(r_\mathrm{in}, b)$."
 By a proper choice of 5. ri. row and zo one ean always achieve a<I: that gives the total luminosity close to the value corresponding to the Keplerian rotation curve.," By a proper choice of $b$, $r_\mathrm{in}$, $r_\mathrm{out}$ and $z_0$ one can always achieve $\alpha \ll 1$; that gives the total luminosity close to the value corresponding to the Keplerian rotation curve."
 Formula (17)) ylelds now Other quantities. including the gas density. can be found from the Ewler equations and the radiation transport equations.," Formula \ref{ap}) ) yields now Other quantities, including the gas density, can be found from the Euler equations and the radiation transport equations."
 Solutions corresponding to heavy selfgravitating disks can be obtained numerically by solving Eqs. (6)). (11))," Solutions corresponding to heavy selfgravitating disks can be obtained numerically by solving Eqs. \ref{ac}) ), \ref{aj}) )"
 and (13))., and \ref{al}) ).
 In the following we shall specialize to the polytropic equation of state p=Kp!. so that h=(KE.—109p!1.," In the following we shall specialize to the polytropic equation of state $p = K \rho^\Gamma$, so that $h = (K \Gamma / (\Gamma - 1)) \rho^{\Gamma - 1}$."
" As before the rotation law @=w"") is fixed. and we restrict the discussion to «-const. v-const and j-const rotation laws."," As before the rotation law $\omega = \omega(r)$ is fixed, and we restrict the discussion to $\omega$ -const, $v$ -const and $j$ -const rotation laws."
 The system of Eqs. (6)), The system of Eqs. \ref{ac}) )
 and {1 D) with Y—0. i.e. without radiation. corresponds to a simple model of a rotating star or a toroid.," and \ref{aj}) ) with $\hat \Psi = 0$, i.e., without radiation, corresponds to a simple model of a rotating star or a toroid."
 There is a long tradition in the numerical analysis of these equations (seee.g.Stoeckly.1965:Ostriker&Mark.1968:Eriguchi.1978:Eriguchi&Müller. 1985).," There is a long tradition in the numerical analysis of these equations \citep[see e.g.][]{stoeckly_1965, ostriker_mark_1968, eriguchi_1978, eriguchi_muller_1985}."
. In particular. it is known that they can be solved iteratively starting with some initial guess of the density distribution.," In particular, it is known that they can be solved iteratively starting with some initial guess of the density distribution."
 A very fruitful iterative scheme of Ostriker&Mark(1968) based on the Green function expression for the gravitational potential is known as the Self-Consistent Field method., A very fruitful iterative scheme of \citet{ostriker_mark_1968} based on the Green function expression for the gravitational potential is known as the Self-Consistent Field method.
 It has been used successfully by many authors and 1n many variants. including computation of general-relativistic solutions (cf.Clement.1974:Blinnikov. 1992)..," It has been used successfully by many authors and in many variants, including computation of general-relativistic solutions \citep[cf.][]{clement_1974, blinnikov_1975, komatsu_eriguchi_hachisu_1989, nishida_eriguchi_lanza_1992}. ."
 An analytic expansion scheme has been also proposed by Odrzywolek (2003)., An analytic expansion scheme has been also proposed by \citet{Odrzywolek}. .
. Since in our case Eq. (13)), Since in our case Eq. \ref{al}) )
 for the radiation potential is also Poisson-like. the numerical method of this paper follows the Self-Consitent Field pattern.," for the radiation potential is also Poisson-like, the numerical method of this paper follows the Self-Consitent Field pattern."
 Knowing the density distribution. one can compute the gravitational potential @® from (14)).," Knowing the density distribution, one can compute the gravitational potential $\Phi$ from \ref{am}) )."
 Eq. (14)), Eq. \ref{am}) )
 is clearly, is clearly
The high equivalent width absorption systems tha comprise our sample are extremely rare in the local Universe bu an understanding of the origins of the few that do exist may revea the physical mechanism responsible for strong absorption.,The high equivalent width absorption systems that comprise our sample are extremely rare in the local Universe but an understanding of the origins of the few that do exist may reveal the physical mechanism responsible for strong absorption.
 Spectroscopy of a small number of luminous galaxies associatec with low-redshift absorbers has been undertaken by Zych et al. (, Spectroscopy of a small number of luminous galaxies associated with low-redshift absorbers has been undertaken by Zych et al. (
2007).,2007).
 The galaxies. predominantly spirals. possess high metallicities and exhibit substantial star formation rates.," The galaxies, predominantly spirals, possess high metallicities and exhibit substantial star formation rates."
 Further progress with such investigations would greatly aid in our interpretation of results a higher redshift., Further progress with such investigations would greatly aid in our interpretation of results at higher redshift.
 We would like to thank Emma Ryan-Weber. Chris Thom. Martin Zwaan and Alan MeConnachie for valuable discussions. and the anonymous referee for useful comments.," We would like to thank Emma Ryan-Weber, Chris Thom, Martin Zwaan and Alan McConnachie for valuable discussions, and the anonymous referee for useful comments."
 VW is supported by the MAGPOP Marie Curie EU Research and Training Network., VW is supported by the MAGPOP Marie Curie EU Research and Training Network.
 The United Kingdom Infrared Telescope is operated by the Joint Astronomy Centre on behalf of the U.K. Particle Physics and Astronomy Research Council., The United Kingdom Infrared Telescope is operated by the Joint Astronomy Centre on behalf of the U.K. Particle Physics and Astronomy Research Council.
 An anonymous referee provided a careful reading of the original manuscript that resulted in a number of improvements to the paper., An anonymous referee provided a careful reading of the original manuscript that resulted in a number of improvements to the paper.
 Funding for the Sloan Digital Sky Survey (SDSS) has been wovided by the Alfred P. Sloan Foundation. the Participating Institutions. the National Aeronautics and Space Administration. 1ο National Science Foundation. the U.S. Department of Energy. 1$. Japanese Monbukagakusho. and the Max Planck Society.," Funding for the Sloan Digital Sky Survey (SDSS) has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society."
 The SDSS Web site is httpz//www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for qe Participating Institutions., The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions.
" The Participating Institutions are The University of Chicago. Fermilab. the Institute for Advanced Study. 1ο Japan Participation Group. The Johns Hopkins University. Los Alamos National Laboratory. the Max-Planck-Institute for Astronomy (ΜΡΙΑ). the Max-Planck-Institute for Astrophysics (MPA). New Mexico State University. University of Pittsburgh. Princeton University. the United States Naval Observatory. and the University of Washington,"," The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, Princeton University, the United States Naval Observatory, and the University of Washington."
Observations of precession of neutron stars. probe the manner in which the stellar crust is coupled to the liquid interior.,Observations of precession of neutron stars probe the manner in which the stellar crust is coupled to the liquid interior.
 Stairs. Lyne Shemar (2000) recently presented strong evidence for recession of an isolated neutron star at a period of 1000 d. 500 d or 250 d. with correlated variations in the pulse duration.," Stairs, Lyne Shemar (2000) recently presented strong evidence for precession of an isolated neutron star at a period of $\simeq 1000$ d, 500 d or 250 d, with correlated variations in the pulse duration."
 The wobble angle of the precession is inferred to » c3 (Link Epstein 2001)., The wobble angle of the precession is inferred to be $\simeq 3^\circ$ (Link Epstein 2001).
 Less compelling evidence or precession is seen [from other neutron stars., Less compelling evidence for precession is seen from other neutron stars.
 »eriodic timing residuals are exhibited. by PSR. DI642-)3 (Shabanova. Lyne Urama 2001). in association with roughly evclical changes in pulse duration. (Cordes. 1993).," Quasi-periodic timing residuals are exhibited by PSR B1642-03 (Shabanova, Lyne Urama 2001), in association with roughly cyclical changes in pulse duration (Cordes 1993)."
 Quasi-periodic timing residuals are seen in the Crab (Lyne. ritehard Smith LOSS: Caadez 22001) and Vela pulsars (Deshpande AleCulloch 1996). hough associated. changes in pulse duration are not seen.," Quasi-periodic timing residuals are seen in the Crab (Lyne, Pritchard Smith 1988; Čaadež 2001) and Vela pulsars (Deshpande McCulloch 1996), though associated changes in pulse duration are not seen."
 The 35-cl periodicitv seen in the acercting svstem Ller X-1 (Tannanbaum. 11972) has been interpreted as precession bx many authors(c.g... Brecher 1972: Trümmper 11986: Caadez.. Galieiié Calvani. 1997: Shakura. Postnov Prokhorov 1998).," The 35-d periodicity seen in the accreting system Her X-1 (Tannanbaum 1972) has been interpreted as precession by many authors, Brecher 1972; Trümmper 1986; Čaadež,, Galičiič Calvani, 1997; Shakura, Postnov Prokhorov 1998)."
 The fluid. of the neutron star inner crust is expected to form à neutron superlluid threaded by vortices., The fluid of the neutron star inner crust is expected to form a neutron superfluid threaded by vortices.
 Above a Iluid density of ~1017 & . an attractive vortex-nucleus interaction could. pin vortices to the lattice.," Above a fluid density of $\sim 10^{13}$ g $^{-3}$, an attractive vortex-nucleus interaction could pin vortices to the lattice."
 Vortex pinning in the crust has been a key ingredient in models of the spin jumps.glifehes. observed in many radio pulsars(e.g... Lyne. Shemar Smith 2000).," Vortex pinning in the crust has been a key ingredient in models of the spin jumps, observed in many radio pulsars, Lyne, Shemar Smith 2000)."
 In all candidate precessing neutron stars. the putative precession is of long period. months to vears. which is in dramatic conllict with the notion of vortex pinning in the neutron star's inner crust.," In all candidate precessing neutron stars, the putative precession is of long period, months to years, which is in dramatic conflict with the notion of vortex pinning in the neutron star's inner crust."
" As demonstrate bv Shaham (1977). vortex pinning exerts a large torque on the crust that causes the star to precess with a perioc GfL,)p. where 4, is the moment of inertia of the pinne superlluid. p is the spin period and ἐν is the moment of inertia of the solid crust and. any component coupled to i over a timescale «p."," As demonstrated by Shaham (1977), vortex pinning exerts a large torque on the crust that causes the star to precess with a period $(I_c/I_p)p$, where $I_p$ is the moment of inertia of the pinned superfluid, $p$ is the spin period and $I_c$ is the moment of inertia of the solid crust and any component coupled to it over a timescale $\ll p$."
" LW pinning occurs through most. of the inner crust (as assumed in many models of glitches). £,, constitutes about of the entire star."," If pinning occurs through most of the inner crust (as assumed in many models of glitches), $I_p$ constitutes about of the entire star."
 Though the coupling of the solid to the core is not well-known. Z. cannot exceee the stars total moment of inertia. so the precession pericc ismost ~100 spin periods.," Though the coupling of the solid to the core is not well-known, $I_c$ cannot exceed the star's total moment of inertia, so the precession period is $\sim 100$ spin periods."
 Hence. if the long-perioc periodic behavior seen in the precession candidates: really represents precession. In this paper we present a resolution to this puzzle.," Hence, if the long-period periodic behavior seen in the precession candidates really represents precession, In this paper we present a resolution to this puzzle."
 We show that vortices initially pinned to the inner crust would probably be unpinnec by the forces exerted. on them. by a crust set into precession., We show that vortices initially pinned to the inner crust would probably be unpinned by the forces exerted on them by a crust set into precession.
 In the absence of precession. vortices could still pin to the inner crust with sullicient strength to account for giant pulsar glitches.," In the absence of precession, vortices could still pin to the inner crust with sufficient strength to account for giant pulsar glitches."
 The outline of the paper is as follows., The outline of the paper is as follows.
 In Section 2 we review the dvnamies of precession with pinning., In Section 2 we review the dynamics of precession with pinning.
 In Section 3 we calculate the Magnus forces on a pinnecl vortex in a precessing neutron star. ancl show that the Magnus force per unit length. is ~1055 dyvne + throughout most. of the crust of PSR. DBIS28-11. nearly two orders of magnitude largerὃν than the minimum force on pinned vortices in Vela just prior to a ὃνgiant. oelitch.," In Section 3 we calculate the Magnus forces on a pinned vortex in a precessing neutron star, and show that the Magnus force per unit length is $\sim 10^{17}$ dyne $^{-1}$ throughout most of the crust of PSR B1828-11, nearly two orders of magnitude larger than the minimum force on pinned vortices in Vela just prior to a giant glitch."
" Thus. if we assume that the force/length f, required. to unpin a supertluiel vortex. is"," Thus, if we assume that the force/length $f_p$ required to unpin a superfluid vortex is"
0.08—10 keVband*.. The intrinsic energy resolution of the HRC being a channel plate detector is marginal.,$0.08-10$ keV. The intrinsic energy resolution of the HRC being a channel plate detector is marginal.
 Rutledge et al. (, Rutledge et al. (
2004) used the 2002 data together with a series of archival XTE data to re-investigate the pulsars temporal X-ray emission properties.,2004) used the 2002 data together with a series of archival XTE data to re-investigate the pulsars temporal X-ray emission properties.
 With respect to their analysis we included the HRC-S observation taken in 2006 which almost doubles the number of photons available for the Chandra timing analysis of PSR J1824-2452A. This allowed us to measure the pulse arrival time. fraction of pulsed photons. the width of the two X-ray pulses and the pulse phase separation of the two peaks by using the Chandra data alone.," With respect to their analysis we included the HRC-S observation taken in 2006 which almost doubles the number of photons available for the Chandra timing analysis of PSR J1824-2452A. This allowed us to measure the pulse arrival time, fraction of pulsed photons, the width of the two X-ray pulses and the pulse phase separation of the two peaks by using the Chandra data alone."
 As Chandra is an imaging instrument it allows to measure the pulse properties by its better signal-to-noise ratio with much higher accuracy than using XTE data only., As Chandra is an imaging instrument it allows to measure the pulse properties by its better signal-to-noise ratio with much higher accuracy than using XTE data only.
 Selecting all events from within a circle of 1.5 aresee radius centered on the pulsar position gave us a total of 773 counts to construct à pulse profile by period folding (Buccheri De Jager 1989)., Selecting all events from within a circle of 1.5 arcsec radius centered on the pulsar position gave us a total of 773 counts to construct a pulse profile by period folding (Buccheri De Jager 1989).
 The background contribution is estimated to be 45+7 counts., The background contribution is estimated to be $45 \pm 7$ counts.
" The pulsar ephemeris which were used to fold the arrival times with the pulsar's rotation period P=3.0543151 ms, predicted for the epoch JD=2451468.5, arc summarized in Table 7.."," The pulsar ephemeris which were used to fold the arrival times with the pulsar's rotation period P=3.0543151 ms, predicted for the epoch JD=2451468.5, are summarized in Table \ref{t:ephemeris}."
 The X-ray pulse profile relative to the radio profile taken at 800 MHz by Backer Sallmen (1997) is shown in Figure 11.., The X-ray pulse profile relative to the radio profile taken at 800 MHz by Backer Sallmen (1997) is shown in Figure \ref{figure11}.
" Unlike the radio profile, which is observed to show three peaks of which the second is observed to vary in intensity on time scales of weeks to month (Backer Sallmen 1997). only two narrow pulse peaks are observed in the X-ray band."," Unlike the radio profile, which is observed to show three peaks of which the second is observed to vary in intensity on time scales of weeks to month (Backer Sallmen 1997), only two narrow pulse peaks are observed in the X-ray band."
 Their phase separation obtained from fitting the pulse peaks by Gaussian functions is found to be 0.449+0.0009., Their phase separation obtained from fitting the pulse peaks by Gaussian functions is found to be $0.449 \pm 0.0009$.
" The FWHM of the phase width of the first and second peaks are fitted to be 0.0273+0.0009 and 0.053+0.002, corresponding to 9.8£03 and 19.3+0.7 degrees."," The FWHM of the phase width of the first and second peaks are fitted to be $0.0273\pm 0.0009$ and $0.053 \pm 0.002$, corresponding to $9.8\pm 0.3$ and $19.3\pm 0.7$ degrees."
 The three radio pulse peaks have a phase separation of and RP3—RP2z0.193+0.003., The three radio pulse peaks have a phase separation of $\mbox{RP2}-\mbox{RP1}= 0.295 \pm 0.001$ and $\mbox{RP3}-\mbox{RP2}= 0.193 \pm 0.003$.
" The FWHM phase width of the radio pulse peaks are fitted to be 0.0452+0.0013, 0.037£0.002 and 0.16£0.01 for the main, second and third radio pulse."," The FWHM phase width of the radio pulse peaks are fitted to be $0.0452 \pm 0.0013$, $0.037 \pm 0.002$ and $0.16 \pm 0.01$ for the main, second and third radio pulse."
 The X-ray pulsed traction is determined to be 85+4% by using a bootstrap method (cf., The X-ray pulsed fraction is determined to be $85\pm 4\%$ by using a bootstrap method (cf.
 Becker Triimmper 1999; Swanepoel et al., Becker Trümmper 1999; Swanepoel et al.
 1996)., 1996).
 The error represents the 10 confidence range., The error represents the $1\sigma$ confidence range.
" For the phase difference between the radio and X-ray peak it can be seen from Figure 11. that the main radio pulse leads the main X-ray pulse by 0.0243+0.0004 in phase, corresponding to 74.2+1.2 pus."," For the phase difference between the radio and X-ray peak it can be seen from Figure \ref{figure11} that the main radio pulse leads the main X-ray pulse by $0.0243\pm0.0004$ in phase, corresponding to $74.2 \pm 1.2\, \mu\mbox{s}$ ."
 Rots (2006) has recently estimated the accuracy of Chandra’s absolute time stamps to be 44-4yis.," Rots (2006) has recently estimated the accuracy of Chandra's absolute time stamps to be $4\pm 4\,\mu\mbox{s}$."
 A 30 clock uncertainty of 16:5 together with the HRC’s intrinsic temporal resolution thus results in a total uncertainty of 32yis for the absolute phase assigned to an X-ray photon.," A $3\sigma$ clock uncertainty of $16\,\mu\mbox{s}$ together with the HRC's intrinsic temporal resolution thus results in a total uncertainty of $32\,\mu\mbox{s}$ for the absolute phase assigned to an X-ray photon."
 Using 79 phase bins to construct the X-ray profile one bin corresponds to ~38/s of the pulsar's rotation period.," Using 79 phase bins to construct the X-ray profile one bin corresponds to $\sim 38\,\mu\mbox{s}$ of the pulsar's rotation period."
 The uncertainty of the relative phase between the radio and X-ray profiles plotted in Figure 11 thus corresponds to +1 phase bin in the X-ray profile., The uncertainty of the relative phase between the radio and X-ray profiles plotted in Figure \ref{figure11} thus corresponds to $\pm 1$ phase bin in the X-ray profile.
 The only other globular clustermillisecond pulsars for which pulsed X-ray emission is detected, The only other globular clustermillisecond pulsars for which pulsed X-ray emission is detected
overlap is given in Table L.,overlap is given in Table \ref{tab:nw-thisworkcompare}.
 Because of the large amounts of enerev imposed iu the region by those authors. and because the temperature profile imposed implies that the detonation would normally begin where the teiiperature drops to that of the ambicut medium. the results are actually quite similar. with only the one point at 75=2 cifferine markedly.," Because of the large amounts of energy imposed in the region by those authors, and because the temperature profile imposed implies that the detonation would normally `begin' where the temperature drops to that of the ambient medium, the results are actually quite similar, with only the one point at $T_9 = 2$ differing markedly."
 Auv currently feasible mechanism for the explosion of a Type Ia supernova involves propagating a burning frout iu a carbon-oxvgen white dwarf., Any currently feasible mechanism for the explosion of a Type Ia supernova involves propagating a burning front in a carbon-oxygen white dwarf.
 Correctly modeling the process which leads to ignition is crucial to understanding the resulting explosion: ouce a thermonuclear burning frout beeins propagating it is very difficult to extiuguish (77) aud differing locations. numbers and sizes of the ignition poiuts can siguificautly change the large-scale character of the explosion (6.9...2?).," Correctly modeling the process which leads to ignition is crucial to understanding the resulting explosion; once a thermonuclear burning front begins propagating it is very difficult to extinguish \citep{zingaleflamevortex,niemeyerddt} and differing locations, numbers and sizes of the ignition points can significantly change the large-scale character of the explosion \citep[\eg{},."
 Iu this paper. we have exanuned ignition at a single poiut by calculating aud fitting ignition times over aranee of thermodvunamic conditions and abundances relevant for almost amv iiechiauisui of ignition for a Type Ia supernova.," In this paper, we have examined ignition at a single point by calculating and fitting ignition times over a range of thermodynamic conditions and abundances relevant for almost any mechanism of ignition for a Type Ia supernova."
 We have also cousidered the iguition of spherical detonatious. determining sizes necessary for a detonation successfully ignite. and the enerey required for a Sedov blast wave to lead to a shock-ignited detonation.," We have also considered the ignition of spherical detonations, determining sizes necessary for a detonation successfully ignite, and the energy required for a Sedov blast wave to lead to a shock-ignited detonation."
 Ciireutly the favored model of SNIa ignition is for the central deusitv aud temperature to iucrease as a carbon-oxveen white chwarf grows by accretion from a madn-sequence conipanion m a binary svsteni., Currently the favored model of SNIa ignition is for the central density and temperature to increase as a carbon-oxygen white dwarf grows by accretion from a main-sequence companion in a binary system.
 When the encrey deposited by carbon burning exceeds neutrino losses. the white dwarf cuters a simuucrine. convective stage that lasts 500-1000 vears with convective velocities of order 20100 (ey...22).," When the energy deposited by carbon burning exceeds neutrino losses, the white dwarf enters a simmering, convective stage that lasts 500-1000 years with convective velocities of order 20–100 \citep[\eg{},."
 Owing to the convection. the eutropy of the core is almost constant.," Owing to the convection, the entropy of the core is almost constant."
 As the temperature continues to rise. thermonuclear flames are born at poiuts with the highest temperatures at or near the center of the white dwarf.," As the temperature continues to rise, thermonuclear flames are born at points with the highest temperatures at or near the center of the white dwarf."
 Tot. Ravleigh-Tavlor uustable bubbles beein to rise through the convective interior.," Hot, Rayleigh-Taylor unstable bubbles begin to rise through the convective interior."
 Iu this turbulent convective picture of SNIa ignition.Oo the first poiuts to runaway will be rare events at ↑↕∐∖↕∐∶↴∙⊾∐≓↑↸∖⋯↴⋉∖↥⋅⋜↧⊓∐⋅↸∖⋜↧∐∪↕⋟↑↕∐∖↑↿∐⋅↴⋝∏↸∖∐↑≼∐↴∖↴⊓⋅," In this turbulent convective picture of SNIa ignition, the first points to runaway will be rare events at the high-temperature tail of the turbulent distribution."
∏⋝∏⊓∪∐∙↽∕∏∐↴∖↴∙↕↑↕↴∖↴↕∐∏⋯↥⋅↑⋜⋯↑↑∪⋜↧↸⊳↸⊳⋯⋅⋜↧↑↸∖↕⋅↖↽≺∣∏⋜⋯↑↕↕⋟⋅↖↽↕∶↴∙," Thus, it is important to accurately quantify ignition conditions."
⊾↕∐↑↕∪∐ ↸⊳∪∐≼∐↑↕∪∐↴∖↴∙↻↿∐⋅∐↖↽↸∖⊣≻⋜∐⋅⋜∐⊔↸∖↑↸∖↥⋅∐↑↑↕∐∶↴∙⊾≯∪↥⋅∐⋯↕⋜∥∖≺↸∖≺∣∏⋜↧↑↕∪∐↴∖↴⊇⋜⋯≼↧∶≩⊔↥⋅↸∖↻↥⋅∪≼⊔∐⊳↸∖⋯∐⋅↸⊳∪∐∏⋯↑↸∖≼↧↕∶↴∙⊾∐↕↑↕∪∐≼∐∖↕⋜↧⋅↖⇁ ↑↕⋯↸∖↴∖↴↖⇁↸∖↥⋅⋅↖⇁↖↖↽↸∖↕∪↖↽↸∖↥⋅↽⋅↱⊐∪↥⋅≼∐∖↥⋅↴∖↴∪↕≯⋯⋜↧∶↴∙⊾∐↕↑⋯∐∖∙↸⊳∪↖↽↸∖↥⋅↕∐∶↴⋁∐⋯↴∖↴↑↑∐↸∖↥⋅⋯≺⋉↧⋅↖↽∐⋜⋯∏↸⊳↸⊳∪∐≼∐↑↕∪∐↴∖↴⋜⋯≼↧↸⊳∪∐∏⋯↴∖↴↕↑↕∪∐↴∖↴ ↥⋅↸∖↕↸∖↖↽⋜⋯↑," Our five-parameter fitting formulae (equations \ref{eq:cpfit} and \ref{eq:cvfit}) ) reproduce our computed ignition delay times very well over 15 orders of magnitude, covering most thermodynamic conditions and compositions relevant for ignition in a carbon-oxygen white dwarf."
↕≯∪↥⋅↕∶↴∙⊾∐↕↑↕∪∐↕∐⋜↧↸⊳⋜∐⋅↴⋝∪∐⊣≻↘⋅↖↽∶↴∙⊾↸∖⊔↖↽∐↕↑↸∖≼↧↖↖↽⋜∐⋅↕≯∙↕↕∪≻⋜∐⋅↑↕↸⊳∏↕⋜∐⋅∙↖↖⇁↸∖∐⋜↧↖↽↸∖↕⋟∪∏∐⊔∐⋜↧↑↕∐↸⊳↥⋅↸∖⋜↕↴∖↴↸∖↴∖↴↕∐↑∐↸∖↖↖↽↕∐↑↸∖ ≼↧↖↖⇁⋜∐⋅↕⋯↸∖↑⋜↧∐↸⊳↕⋅↖⇁∙⋯∪≺↸∖↕↸∖≺∏⋝⋅↖⇁↕∐↸⊳↥⋅↸∖⋜↧↴∖↴↸∖↴∖↴∐↓↑∐↸∖−∪⋀∖↸∖⋜⋔∏∐≼↧⋜⋯∩∖∙↸⊳⋜⋯↴∖↴↻↸∖↸∖≼↧∏↻↑∐↸∖↕∶↴∙⊾↕∐⊓∪∐≼∐∖↕⋜↧⋅↖↽↑∐⊔↸∖↴⋝∙↖⇁∿ ∶≩∩↖⋰⋰⊓⊲∶↙↕↕⋡↑∐↸∖∐∖∪⊔⊳∪⋯↸∖↴∖↴↕⋜∐⋅∶↴∙⊾↸∖↕⋅↖⇁," In particular, we have found that increases in the white dwarf metallicity, modeled by increases in the } abundance, can speed up the ignition delay time by $\sim$ if the neon comes largely from oxygen, or decrease the ignition delay time by a similar amount if it comes equally from carbon and oxygen."
↕≯↥⋅∪⊔∪⊼⋅↖⇁∶↴⋁↸∖∐∙∪↥⋅≺∐∖↸⊳↥⋅↸∖⋜↕↴∖↴↸∖↑∐↸∖↕∶↴∙⊾∐↕↑↕∪↕⊔∐∖↕⋜↧⋅↖↽↑↕⊔↸∖↴⋝∙↖⇁⋜↧↴∖↴↕∐↓∐⋜∐⋅⋜⊔⊔∪∏∐↑↕↕≯↕↑ ↸⊳∪↕⊔↸∖↴∖↴↸∖≺∣∏⋜↧↕↖↽≯↥⋅∪∐⊔⊳⋜∐⋅↴⋝∪∐⋜⋯≼↧∪⊼⋅↖⇁∶↴⋁↸∖∐∙↕∐↑↕∐∖⋞↥⋅⋜∐⋅↸∖↸∖↖↽↸∖∐↑⋅↻↕↸⊳⊓∐⋅↸∖∙↕↕≯⋜↧∐↸∖↕↴∖↴↸∖↕↴∖↴↸∖≺∣∏⋜↕↕∙↑↕∐↴∖↴↴∖↴∏∶↴⋁∶↴⋁↸∖↴∖↴↑↴∖↴↑∐⋜↧↑ ↑↕∐∖∱∐⋅↴∖↴↑↕∶↴∙⊾∐↕↑↕∪∐↻∪↕∐↴∖↴∐↓⋜↧⋅↖↽∐⋜∏∏⋉∖∐⋜↧↑↴∖↴↕∶↴∙⊾∐↕∱∎⊔⊳⋜⋯↑↕⋅↖↽≼∐↕−↥∎↸∖↥⋅↸∖∐↑↸⊳∪∐≼∐↑↕∪∐↴∖↴↕∐∐∐∖↑⋜↧↕≓↻∪," In the `rare event' picture, if all else is equal, this suggests that the first ignition points may happen at significantly different conditions in metal-poor white dwarfs than in metal-rich progenitors – either the first ignition points could occur when the mean core temperature is somewhat lower, or more points could ignite."
∪↥⋅↖↖↽↕∐↑↸∖≼↧↖↖↽⋜∐⋅↕↸∖↴↑∐⋜⋯ ↕∐⋯↸," To quantify this effect, Fig."
∖↑⋜↧↕≓∏↸⊳↕↻↥⋅∪∶↴∙⊾↸∖↕∏↑∪↥⋅↴∖↴↸∖↕↑↕∐∖↥⋅↕∐∖∱∎∐⋅↴∖↴↑↕∶↴∙⊾↕∐↑↕∪∐↴⋯↕∐↑↴∖↴⋯∏∐∪↸⊳↸⊳↿∐⋅↖↖↽∐↸∖∐↑∐∖∐∐∖⋜⋯↸⊳∪↥⋅↸∖↑↸∖∐∏⋉∖↥⋅⋜↧⊓∐⋅↸∖↕↴, \ref{fig:probabilities} shows the increase in the probability of a point igniting due to a reduction in ignition time.
∖↴ ↴∖↴∪⋯↸∖↖↖↽∐⋜↧↑↕∪↖↖⇁↸∖↥⋅∙∪↥⋅⋯∪↥⋅↸∖↻∪↕∐↑↴∖↴↸⊳∪∏↕≼⊔∶↴⋁∐↕↑↸∖∙ ⊺↴∪≺∣∏⋜⊔↑↕↕⋟⋅↖↽↑↕∐↴∖↴↸∖↕−∐∖↸⊳↑∙∏∶↴∙⊾∙↕↴∖↴∐∪↖↖⇁↴∖↴↑∐↸∖↕↕⊔⊳↥⋅↸∖⋜↧↴∖↴↸∖↕↕↕↑∐↸∖↻↥⋅∪↴⋝⋜∏⋝↕∐↑⋅↖↽∪↕⋟⋜↧≻∪↕∐↑↕∶↴∙⊾∐↕↑↕∐∶↴⋁≼⊔∐∖↑∪⋜↧∶≩∩↖⋰⋰⊒∶↙ ↥⋅↸∖≼⊔∐⊳↑↕∪∐↕∐↕∶↴∙⊾∐↕↑↕∪∐," \citet{kuhlenwoosleyglatzmaier05} suggest that the distribution of temperature fluctuations during the simmering, convective phase is Gaussian, particularly at the positive-fluctuation end."
↑↕∐∐∖∙∎∙↗↴∖↴∏∶↴∙⊾∶↴∙⊾↸∖↴∖↴↑↑∐⋜↧↑↑∐↸∖≼∐↴∖↴∏⋅∏⋝∏↑↕∪∐∪↕⋟↑↸∖∐∏⋉∖↥⋅⋜↕⊓∐⋅↸∖∏⋯⊳↑∏⋜↧↑↕∪∐↴∖↴≼⊔∐⋅↕∐∶↴∙⊾↑∐↸∖ ↴∖↴↕∐∐⊔↸∖↥⋅↕∐∶↴⋁∙↸⊳∪∐↖↽↸∖↸⊳↑↕↖↽↸∖↻∐⋜↕↴∖↴↸∖↕↴∖↴≼∶⋜⋯↴∖↴↴∖↴↕⋜⋯∙↻⋜∐⋅↑↕↸⊳↿∏⋜∐⋅↕⋅↖⇁⋜↧↑↑∐↸∖↻≺≻↴∖↴↕↑↕↖↽↸∖≓∏⋯⊳↑∏⋜↧↑↕≺≻∐↸∖∐≺↧∙⊀≚↴∖↴↴∖↴⋯⊔↕∐∶↴⋁↑∐↕↴∖↴≼∐∖↴⊓⋅∏⋝∏↑↕∪∐ ⋜⋯≼⊔⋜∐↘↽↕∐∶↴∏⋝⊺↓⊰↼∖↓↔⋜↕↴∖↴⋜↧↕⋡↥⋅↸∖↸∖↻⋜∐⋅⋜↧⋯↸∖↑↸∖↥⋅↑∐⋜↧↑⋯↸∖⋜↧↴∖↴↿∐⋅↸∖↴∖↴↑↕∐∖↴∖↴⊓⋅↸∖∐∶↴∙⊾↑∐∪↕⋟⊓∐⋅↴∏∏↸∖⋯⊳↸∖⋅∪∐↸∖∐∐≼↧↴∖↴↑∐⋜↧↑↕↕⋟↕∶↴∙⊾∐↕↑↕∪∐↕↴∖↴ ↸∖⊼⊓⋅↸∖⋯↸∖↕⋅↖↽↥⋅⋜⋯∖∙⋜↧∶≩∩↖⋰∣⋰⊲∶↙↥⋅↸∖≼⊔∐⊳↑↕∪∐↕∐↕∶↴∙⊾∐↕↑↕∪∐↑↕⋯↸∖↸⊳∪∏↕≼⊔∐⋅∪≼⊔∐⊳↸∖⋜↧↴∖↴∏↴⋝↴∖↴↑⋜⋯↑↕⋜↧↕↕∐↸⊳↥⋅↸∖⋜↧↴∖↴↸∖↕∐↕⋯∐∐⋝↸∖↥⋅↕∐↑↕∐∖≺↴∖↴↑↕∐ paro) events.," Assuming this distribution and taking $\delta T_{\mathrm{RMS}}$ as a free parameter that measures the strength of turbulence, one finds that if ignition is extremely rare, a reduction in ignition time could produce a substantial increase in number in the (still rare) events."
We use the iethods developed by PSK to study eas dvnaiics on sub-parsec- and parsec-scales in ACiNs.,We use the methods developed by PSK to study gas dynamics on sub-parsec- and parsec-scales in AGNs.
 We consider an axisvunuetric TID fiw acercting outo a supermassive BIT., We consider an axisymmetric HD flow accreting onto a supermassive BH.
 The flow is uou-spherical because it is iradiated bv an accretion disk aud spherical corona., The flow is non-spherical because it is irradiated by an accretion disk and spherical corona.
 The disk radiation flux is the highest along the disk rotational axis and is eradually decreasing with iucreasmg polar auele. 0 as cos0.," The disk radiation flux is the highest along the disk rotational axis and is gradually decreasing with increasing polar angle, $\theta$ as $\cos{\theta}$."
 The corona radiation is isotropic., The corona radiation is isotropic.
 We take into account the radiation heating aud cooling. radiation pressure due to the electron scattering aud spectral lines.," We take into account the radiation heating and cooling, radiation pressure due to the electron scattering and spectral lines."
 We adopt a simplified treatineut of photoionization. and radiative cooling and heating that allow us to compute selt-cousisteutlv the ionization state. and therefore the line force. in the flow.," We adopt a simplified treatment of photoionization, and radiative cooling and heating that allow us to compute self-consistently the ionization state, and therefore the line force, in the flow."
 We conceutrate on assessing what fractio iof the inflow from large radi reaches the vicinity of a BIT aud what fraction ds firaed iuto an outflow., We concentrate on assessing what fraction of the inflow from large radii reaches the vicinity of a BH and what fraction is turned into an outflow.
 We aso assess the iupact of thequal expansion and radiatiol pressure oli diivius the outflow and on the outflow properties such as the two-dimensional structure. thermal aud kinetic power and temporal behavior.," We also assess the impact of thermal expansion and radiation pressure on driving the outflow and on the outflow properties such as the two-dimensional structure, thermal and kinetic power and temporal behavior."
 We describe our calculation in Section 2., We describe our calculation in Section 2.
 We preseut our results in Section 3., We present our results in Section 3.
 The paper ends. im section L with discussion aud our conclusions.," The paper ends, in section 4, with discussion and our conclusions."
 To compute the structure and evolution. of a flow irradiated by an AGN. we solve the equations of livclrodvuaics where p ds the mass desity. DP ds the eas pressure. vods the velocity. € is the internal cnerey density. £ is the net cooling rate. g is he gravitational acceleration of the central object. FM is the total radiation force per unit mass.," To compute the structure and evolution of a flow irradiated by an AGN, we solve the equations of hydrodynamics where $\rho$ is the mass density, $P$ is the gas pressure, ${\bf v}$ is the velocity, $e$ is the internal energy density, $\cal{L}$ is the net cooling rate, ${\bf g}$ is the gravitational acceleration of the central object, ${\bf F}^{\rm rad}$ is the total radiation force per unit mass."
 We adopt au adiabatic equation of state P=(l)e. and consider models with the adiabatic index. 5=4/3.," We adopt an adiabatic equation of state $P~=~(\gamma-1)e$, and consider models with the adiabatic index, $\gamma=5/3$."
 To solve eqs., To solve eqs.
 1-3.? we use the ZEUS-2D code (Stone Norman 1992) extended by PSI.," 1-3, we use the ZEUS-2D code (Stone Norman 1992) extended by PSK."
 Wo perform our calculations in spherical polar coordinates (57.60.60) assunidue axial sviunietrv about the rotational axis of the accretion disk (0= 0°).," We perform our calculations in spherical polar coordinates $(r,\theta,\phi)$ assuming axial symmetry about the rotational axis of the accretion disk $\theta=0^o$ )."
" Our standard computational domain is defined to occupy the angular range 0""x0<90"" and the radial paneer,=90800.Seo,25«X1057. where ru= is the iner radius of the disk around a Sclavarzsclild BU with a ass. Mp aud radius ry=20Afpyy/e?."," Our standard computational domain is defined to occupy the angular range $0^o \leq \theta \leq 90^o$ and the radial range $r_{\rm i}~=~500~r_\ast \leq r \leq \ r_{\rm o}~=~ 2.5~\times~10^5~r_\ast$, where $r_\ast=3 r_{\rm S}$ is the inner radius of the disk around a Schwarzschild BH with a mass, $M_{\rm BH}$ and radius $r_{\rm S}=2GM_{\rm BH}/c^2$."
 The r0 domain is discretized iuto zones., The $r-\theta$ domain is discretized into zones.
" For r,=2.5«10x aud 1&109ον our παπιΊσα. resolution in the + direction consists of 10 and 180 zones. respectively,"," For $r_{\rm o}= 2.5~\times~10^5~r_\ast$ and $1~\times~10^6~r_\ast$, our numerical resolution in the $r$ direction consists of 140 and 180 zones, respectively."
 We fix the zone size ratio. driyafdry=LOL (i... the zone spacing Is Jucreasing outward).," We fix the zone size ratio, $dr_{k+1}/dr_{k}=1.04$ (i.e., the zone spacing is increasing outward)."
 Gridding i this niauner ensures good spatial resolution close to the imer boundary at ry., Gridding in this manner ensures good spatial resolution close to the inner boundary at $r_{\rm i}$.
 Iu the 0 direction. our standard iuuerical resolution consists of 50 but we also performed simulations with LOO zones.," In the $\theta$ direction, our standard numerical resolution consists of 50 but we also performed simulations with 100 zones."
" Zone size ratio is always dj/d0;4=1.0 ἄνοι, grid points are equally spaced)."," Zone size ratio is always $d\theta_{l}/d\theta_{l+1} =1.0$ (i.e., grid points are equally spaced)."
 For the initial condition. we typically απλο spherical svuuuetrv set alb ΠΟ variables to constant values everywhere in the computational domain. ic. por)=py ο0)=ey. er0)=py0. ορ.0)=coy0. and ο@)=eo0.," For the initial condition, we typically assume spherical symmetry set all HD variables to constant values everywhere in the computational domain, i.e., $\rho(r,\theta)=\rho_{\rm 0}$ $e(r,\theta)=e_{\rm 0}$, $v_r(r,\theta)=v_{r,0}=0$, $v_\theta(r,\theta)=v_{\theta,0}=0$, and $v_\phi(r,\theta)=v_{\phi,0}=0$."
 For comparison. we performed siuulatious where we initially set IID variables to values which resulted from one-dimensional simulations without radiation pressure.," For comparison, we performed simulations where we initially set HD variables to values which resulted from one-dimensional simulations without radiation pressure."
 We spectfv the boundary conditions in the following wav., We specify the boundary conditions in the following way.
 At the pole (e. 0=07). we apply an axis-of-sviunietry boundary condition while for 0=907. we apply reflecting boundary conditions.," At the pole (i.e., $\theta = 0^\circ$ ), we apply an axis-of-symmetry boundary condition while for $\theta=90^\circ$, we apply reflecting boundary conditions."
" For the iuuner aud outer radial bouudaries, we apply au outflow boundary condition (1.0.. to extrapolate the flow bevond the boundary. we set values of viriades in the ghost zones equal to the values iu the correspo1cine active zones. see Stone Norman 1992 for more details)."," For the inner and outer radial boundaries, we apply an outflow boundary condition (i.e., to extrapolate the flow beyond the boundary, we set values of variables in the ghost zones equal to the values in the corresponding active zones, see Stone Norman 1992 for more details)."
" To represent steady conditions at the outer radial boundary. during the evolution of cach mocel we continue to apply the coustraints that in the last zone in the radial direction. co(r,.0)=Ὁο0)0. and the density aud internal euergv are fixed at coustaut values at all times."," To represent steady conditions at the outer radial boundary, during the evolution of each model we continue to apply the constraints that in the last zone in the radial direction, $v_\theta(r_{\rm o},\theta) =v_\phi(r_{\rm o},\theta) =0$, and the density and internal energy are fixed at constant values at all times."
" We allow e, to float.", We allow $v_r$ to float.
 We lave found that this technique produces a solution that relaxes to a steady state solution for both spherically svuunetriic accretion aud non spherical accretion with au outflow (see also Proga Beechnan 200343)., We have found that this technique produces a solution that relaxes to a steady state solution for both spherically symmetric accretion and non spherical accretion with an outflow (see also Proga Begelman 2003a).
 Our approach then is to mimic the situation where there is always eas available for accretion., Our approach then is to mimic the situation where there is always gas available for accretion.
 The geometry anc assunptious needed to compute the radiation field from the disk aud ceutral object are stuular to those cousidered bv PSIX but here we make some simplifications to the earlier model., The geometry and assumptions needed to compute the radiation field from the disk and central object are similar to those considered by PSK but here we make some simplifications to the earlier model.
 The disk is flat. Neplerian. ecometrically-thin and optically-thick.," The disk is flat, Keplerian, geometrically-thin and optically-thick."
 The disk photosphere is coiucident with the 0=90° axis., The disk photosphere is coincident with the $\theta=90^o$ axis.
 We specifv the radiation field of the disk by asstuine that the temperature follows the radial profile of the optically thick accretion disk (Shakura Suuvaev 1973). and therefore depends ou the mass accretion rate in the disk. Mp. the mass of the BIL. Mp aud the inner edge of the disk. +. Iu particuku. the total accretion hpuninosity. L—2GAlpAyfirs. where 4 is the rest mass conversion efficiency.," We specify the radiation field of the disk by assuming that the temperature follows the radial profile of the optically thick accretion disk (Shakura Sunyaev 1973), and therefore depends on the mass accretion rate in the disk, $\dot{M}_{\rm D}$, the mass of the BH, $M_{\rm BH}$ and the inner edge of the disk, $r_\ast$, In particular, the total accretion luminosity, $L=2 \eta G M_{\rm BH} \MDOT_{\rm a}/r_{\rm S}$, where $\eta$ is the rest mass conversion efficiency."
 The geometry of the central eugiue in ACUNS is poorly known., The geometry of the central engine in AGNs is poorly known.
 As in PSK. we consider the central cugine as the most inner part of the accretion disk plus an extended corona.," As in PSK, we consider the central engine as the most inner part of the accretion disk plus an extended corona."
 We refer to the corona as the ceutral object., We refer to the corona as the central object.
 The inner radius of the computational domain is large compared to the radius of the central object., The inner radius of the computational domain is large compared to the radius of the central object.
 Therefore the central object can be approximated as a point source located at ¢=0., Therefore the central object can be approximated as a point source located at $r=0$.
 We express the disk luminosity. £j and the ceutral object Iuniuositv. £. iu units of the total accretion luminosity. Le.. Lp=fol aud L.=f.L(1. fp)L.," We express the disk luminosity, $L_{\rm D}$ and the central object luminosity, $L_\ast$ in units of the total accretion luminosity, i.e., $L_{\rm D}=f_{\rm D} L$ and $L_\ast=f_\ast L=(1-f_{\rm D}) L$ ."
 For simplicity. we assiune that the disk euütts oulv iu the UV. whereas the ceutral object enütts ouly the N-rays.," For simplicity, we assume that the disk emitts only in the UV, whereas the central object emitts only the X-rays."
 Lo. the system UV luminosity. Loy=fiLLp aud the svsteii N-rav luuinosity. Lx=ἐνL. (in other words fry=fp and fx f.)," i.e., the system UV luminosity, $L_{\rm UV}=f_{\rm UV} L=L_{\rm D}$ and the system X-ray luminosity, $L_{\rm X}=f_{\rm X} L=L_\ast$ (in other words $f_{\rm UV}=f_{\rm D}$ and $f_{\rm X}=f_\ast$ )."
 With the above simplifications. oulv the central object radiation is responsible for ioniziug the flow to a very high," With the above simplifications, only the central object radiation is responsible for ionizing the flow to a very high"
The [ist combined spectrum was extracted considering the PDS data resulting bv the automatic selection operated by the SANDAS package7.,The first combined spectrum was extracted considering the PDS data resulting by the automatic selection operated by the SAXDAS package.
. The confidence level of the excess. in (he range 20-80 keV and for an average gas temperature of 8.11 keV. is ~ 2.90 (observed count rate = 0.1717250.0146. .. model predicted rate = 0.1295 )) takine into account only the uncontaminated -OFF position.," The confidence level of the excess, in the range 20-80 keV and for an average gas temperature of 8.11 keV, is $\sim$ $\sigma$ (observed count rate = $\pm$ 0.0146, model predicted rate = 0.1295 ) taking into account only the uncontaminated -OFF position."
 The effective exposure time is 42.8 ks in ODS1 and 119.3 ks in ODS2 for a total exposure time of 162.1 ks., The effective exposure time is 42.8 ks in OBS1 and 119.3 ks in OBS2 for a total exposure time of 162.1 ks.
 To resolve the discrepancy between these results and those obtained by FFO4 with a NAS analysis (see previous section). a new combined spectrum was extracted considering the time windows used in the NAS analvsis.," To resolve the discrepancy between these results and those obtained by FF04 with a XAS analysis (see previous section), a new combined spectrum was extracted considering the time windows used in the XAS analysis."
 These (ime windows are different. from those used by RAIO4 in their SANDAS analvsis., These time windows are different from those used by RM04 in their SAXDAS analysis.
 The reason is in the dilferent criterion for eliminating the spurious spikes produced by the charged particles that interact with the PDS detectors: a semi-autonmalted procedure (i.e. an automated procedure followed by a visual check) for NAS and a completely automated procedure for SANDAS (Guainazzi Matteuzzi 1997)., The reason is in the different criterion for eliminating the spurious spikes produced by the charged particles that interact with the PDS detectors: a semi-automated procedure (i.e. an automated procedure followed by a visual check) for XAS and a completely automated procedure for SAXDAS (Guainazzi Matteuzzi 1997).
 With ihe same time windows used by NAS. the c.l.," With the same time windows used by XAS, the c.l."
 of the excess in the SANDAS spectrum raises al c 4.20 (observed count rate = 0.1902+0.0148 1... model predicted rate = 0.1280 )). while the total exposure time reduces to 160.9 ks Git was 162.1 ks).," of the excess in the SAXDAS spectrum raises at $\sim$ $\sigma$ (observed count rate = $\pm$ 0.0148, model predicted rate = 0.1280 ), while the total exposure time reduces to 160.9 ks (it was 162.1 ks)."
 The (wo packages. starting [from the same (nme windows. produce a difference in the total effective exposure time of 5.8 ks (yay = 166.7 ks. /sixpas = 160.9) essentially due to: a) the different earth angle above which data are selected (the earth angle is defined as the angle between the earth limb and the pointing direction).," The two packages, starting from the same time windows, produce a difference in the total effective exposure time of 5.8 ks $t_{XAS}$ = 166.7 ks, $t_{SAXDAS}$ = 160.9) essentially due to: a) the different earth angle above which data are selected (the earth angle is defined as the angle between the earth limb and the pointing direction)."
 The earth angle is 5° for NAS and 107 for SANDAS: b) the removal of observational time alter anv South Atlantic Geomagnetic Anomaly (SAGA) passage., The earth angle is $^{\circ}$ for XAS and $^{\circ}$ for SAXDAS; b) the removal of observational time after any South Atlantic Geomagnetic Anomaly (SAGA) passage.
 The SANDAS package removes 5 minutes aller anv passage. while XÀS eliminates the time necessary to reach the correct voltage of ihe instruments after their shut-down diuring the SAGA passage.," The SAXDAS package removes 5 minutes after any passage, while XAS eliminates the time necessary to reach the correct voltage of the instruments after their shut-down during the SAGA passage."
 In conclusion. we have a lower exposure time lor the SANDAS analysis which may imply a lower c.l.," In conclusion, we have a lower exposure time for the SAXDAS analysis which may imply a lower c.l."
 of the excess., of the excess.
 To quantily this difference we have extracted a further combined spectrum using the same time windows selected in the NAS analvsis but imposing an earth angle of 5° in the SANDAS package., To quantify this difference we have extracted a further combined spectrum using the same time windows selected in the XAS analysis but imposing an earth angle of $^{\circ}$ in the SAXDAS package.
 The total effective time exposure of the two observations is now /s4xpas = 169.1 ks instead of 160.9 ks., The total effective time exposure of the two observations is now $t_{SAXDAS}$ = 169.1 ks instead of 160.9 ks.
 The excess results to be at the c.l., The excess results to be at the c.l.
 of e 4.60 (observed count rate = 0.19442-0.0144.—.. model predicted rate = 0.1280. )).," of $\sim$ $\sigma$ (observed count rate = $\pm$ 0.0144, model predicted rate = 0.1280 )."
 This ILXR spectrum is reported in Fig., This HXR spectrum is reported in Fig.
 2., 2.
 The difference in the initial energv of ihe SANDAS and XAS spectra (SANDAS spectrum starts at 12 keV. while NAS al 15 keV) gives insignificant. variations in the c.l.," The difference in the initial energy of the SAXDAS and XAS spectra (SAXDAS spectrum starts at 12 keV, while XAS at 15 keV) gives insignificant variations in the c.l."
 values of the excess., values of the excess.
 Les us turn our attention to mature plauctary svstenis., Les us turn our attention to mature planetary systems.
 As of this writing. there are 38 exoplanets that are in a system with at least 2 stellar coumpoucuts (sine LOOAAT as the upper limit for binary separation). includingLB 5 systems with a stellar companions within 5AAU (Muerauer&Neuhauscr2009.andreferences rere)..," As of this writing, there are 38 exoplanets that are in a system with at least 2 stellar components (using AU as the upper limit for binary separation), including 5 systems with a stellar companions within AU \citep[][and references therein]{mugrauer09}."
. Most of these plauet-beariug stars are of solar ype., Most of these planet-bearing stars are of solar type.
 The overall detection rates of gas giant planets im ΗΝ svstenis and in sinele stars are uudistiuguishable (Bonavita&Desidera20073., The overall detection rates of gas giant planets in binary systems and in single stars are undistinguishable \citep{bonavita07}.
. There is mareiual evideuce at planets in binaries tighter than 100 AAT inav be somewhat less frequent than one would assume based ou ie frequency of planets in wider binaries (by6.042.7%.Eeecubergeretal. 2008).," There is marginal evidence that planets in binaries tighter than $\sim100$ AU may be somewhat less frequent than one would assume based on the frequency of planets in wider binaries \citep[by 6.0$\pm$2.7\%,][]{eggenberger08}."
. Dowever. the all sample size. adverse selection biases and iucoupleteness of current uultiplicity surveys are such that it is premature to reach definitive couclisious.," However, the small sample size, adverse selection biases and incompleteness of current multiplicity surveys are such that it is premature to reach definitive conclusions."
 Iu aux case. we can use this sample ο test whether the separation of the stellar binary has any influcuce ou planet properties.," In any case, we can use this sample to test whether the separation of the stellar binary has any influence on planet properties."
 Despite an earlier claim for a distinct period-nmiass distribution (Zucker&.Mazeh2002).. Donavita&Desidera(2007) have shown that there is esseutially no difference in the properties of planetary svstenis around single stars and in binary svsteimis.," Despite an earlier claim for a distinct period-mass distribution \citep{zucker02}, \cite{bonavita07} have shown that there is essentially no difference in the properties of planetary systems around single stars and in binary systems."
" However. a previously ""recognized trend is evident in refüe:planets.."," However, a previously unrecognized trend is evident in \\ref{fig:planets}."
 While planets covering two orders of magnitude m mass can be found iu wide binaries (as around sinele stars). svstenus tighter than 100 AAU appear to host onlv high-mass. M2Mj. planets.," While planets covering two orders of magnitude in mass can be found in wide binaries (as around single stars), systems tighter than $\sim100$ AU appear to host only high-mass, $M \gtrsim M_{J}$, planets."
 To quautifv this effect. E used the two-sided Fischer Exact test to determine whether close aud wide binaries (with the usual sliding threshold) have different proportion of lieh- aud low-mass plancts.," To quantify this effect, I used the two-sided Fischer Exact test to determine whether close and wide binaries (with the usual sliding threshold) have different proportion of high- and low-mass planets."
 I used. 1.63. the median for all planets known todate?.. to separate low- frou Ilüeh-uass planets.," I used $M_J$, the median for all planets known to, to separate low- from high-mass planets."
 refüe:proba confirms that This conclusion is siguificant at the 30 level., \\ref{fig:proba} confirms that This conclusion is significant at the $\sigma$ level.
 It is unuportaut to test whether this trend is uot a uere consequence of a selection bias. as a close stellar conrpauion can alter the detectability of a planet-ziuduced radial velocity signal.," It is important to test whether this trend is not a mere consequence of a selection bias, as a close stellar companion can alter the detectability of a planet-induced radial velocity signal."
 To evaluate this possibility. I mill ou the “uniform detectability’ sample defied w Fischer&Valenti(2005) which coutains all stars or Which close-in plancts as low mass as 0.247; (well low the apparent cut-off in mass for planets in tight ynarics). as well as LAL; planets on a lyr orbit. could be detected.," To evaluate this possibility, I build on the “uniform detectability” sample defined by \cite{fischer05} which contains all stars for which close-in planets as low mass as $M_J$ (well below the apparent cut-off in mass for planets in tight binaries), as well as $M_J$ planets on a 4yr orbit, could be detected."
 Iu the current sample of binary auet hosts. the proportions of stars that belong to he uniform detectability sample among binarics tighter and wider than AAT are indistinguishable (5/9 aud 21/10. respectively).," In the current sample of binary planet hosts, the proportions of stars that belong to the uniform detectability sample among binaries tighter and wider than AU are indistinguishable (5/9 and 24/40, respectively)."
 IE therefore conclude that the trend discussed above is unlikely to be the consequence of a selection bias or of observational Buitations., I therefore conclude that the trend discussed above is unlikely to be the consequence of a selection bias or of observational limitations.
 An indirect signpost of planet formation is the debris disk plenomenon., An indirect signpost of planet formation is the debris disk phenomenon.
 In these svstenis. sinall dust grains are produced via the collisions of large solid bodies (Zuckerusn2001).," In these systems, small dust grains are produced via the collisions of large solid bodies \citep{zuckerman01}."
 Tulliusetal.(2007)| observed 69 A- and F-tvpe kuowu binaries withSpfzer and found debris disks in svstenis spanning 6 decades in separation., \cite{trilling07} observed 69 A- and F-type known binaries with and found debris disks in systems spanning 6 decades in separation.
 They further suggested that intermediate separation AAT) binaries are substantially less likely to host a debris disks than either tighter or wider svstenis. although the formal siguificance of this difference is mareinal at best.," They further suggested that intermediate separation AU) binaries are substantially less likely to host a debris disks than either tighter or wider systems, although the formal significance of this difference is marginal at best."
 No such trend was found by Plavchanctal.(2009)... who included 21 A- through N-tvpe binarics in their ownS$pifzer survey.," No such trend was found by \cite{plavchan09}, who included 24 A- through M-type binaries in their own survey."
 This latter survey focused onu targets that are more simula iu mass to exoplanet hosts and the PAIS population discussed in the previous section., This latter survey focused on targets that are more similar in mass to exoplanet hosts and the PMS population discussed in the previous section.
 I used the two-sided Fischer test to determine whether the occurrence of debris disks is indeed ditfereut iu tight and wide binaries. using the same sliding threshold as above (see refüe:proba)).," I used the two-sided Fischer test to determine whether the occurrence of debris disks is indeed different in tight and wide binaries, using the same sliding threshold as above (see \\ref{fig:proba}) )."
 There is no significant difference for aly value of the threshold iu the sample from Trillingctal.(2007).. nor in a combined sample that also iucludes systems from Plavehaetal.(2009).," There is no significant difference for any value of the threshold in the sample from \cite{trilling07}, nor in a combined sample that also includes systems from \cite{plavchan09}."
. The combined sample coutains 52 binaries in the AAU rane. with a inedian separation of 5OAAU. an increase of 15 sources from the sole sample of Trilineetal...," The combined sample contains 52 binaries in the AU range, with a median separation of AU, an increase of 15 sources from the sole sample of \citeauthor{trilling07}."
 In addition. the occurrence rates of debris disks i binary systenas and single stars are very similar (Trilling2007).," In addition, the occurrence rates of debris disks in binary systems and single stars are very similar \citep{trilling07}."
. In other words.stage.," In other words,."
 This analvsis has revealed a clear dichotoniv between it and wide bimaries., This analysis has revealed a clear dichotomy between tight and wide binaries.
 Systems with separation = LOOAAT are indistinenishable frou sinele stars as far as the initial conditions aud cud product of planet formation are concerned., Systems with separation $\gtrsim 100$ AU are indistinguishable from single stars as far as the initial conditions and end product of planet formation are concerned.
 The only caveat to this statement is the possibility of wild disk truncation in AAU systems. but most disks iu these svsteis retain a lass reservoir that is sufficient to build up gas ejut plaucts.," The only caveat to this statement is the possibility of mild disk truncation in AU systems, but most disks in these systems retain a mass reservoir that is sufficient to build up gas giant planets."
 Ou the other laud. planet formation iu binaries with separations =100 AAT is characterized by aanuch shorter clearing timescale for the protoplanetary disks aud a strong bias towards high-mass plaucts.," On the other hand, planet formation in binaries with separations $\lesssim
100$ AU is characterized by a much shorter clearing timescale for the protoplanetary disks and a strong bias towards high-mass planets."
 Despite these differences. plauetesinals and mature planetary systems appear to form at roughly the same frequency as around other stars.," Despite these differences, planetesimals and mature planetary systems appear to form at roughly the same frequency as around other stars."
 Furthermore. while protoplanetary disks are more compact in tight svstenis because of truncation. a sienificant fraction of them possess Luge mass reservoirs (at least several times Aj).," Furthermore, while protoplanetary disks are more compact in tight systems because of truncation, a significant fraction of them possess large mass reservoirs (at least several times $M_J$ )."
 Taken together. The shorter disk lifetime in tight binarics makes it extremely difficult to foxu gas giant planets through the core accretion model. especially if the final plaucts are particularly massive.," Taken together, The shorter disk lifetime in tight binaries makes it extremely difficult to form gas giant planets through the core accretion model, especially if the final planets are particularly massive."
 Rather. this combination of observed trends supports an abrupt process to form planets in tight binaries. such as the disk fragmentation model.," Rather, this combination of observed trends supports an abrupt process to form planets in tight binaries, such as the disk fragmentation model."
 Dudeed. this mechanism can be extremely efficicut," Indeed, this mechanism can be extremely efficient"
Glitches. and post-eliteli relaxations. are widely believed. to be effects caused by (the superfiuid conrponeut in) the crust of ieutron stars (see.,"Glitches, and post-glitch relaxations, are widely believed to be effects caused by (the superfluid component in) the crust of neutron stars (see, eg.,"
 ce. Lyne Craham-Suuth 1995: INrawezvk et., \markcite{LGS8} Lyne Graham-Smith 1998; \markcite{KLGJ03} Krawczyk et.
 al., al.
 Ww103)., 2003).
 There exist. however. observatioual data ou elitches that could no be possibly due to 1e role of the stellar crust.," There exist, however, observational data on glitches that could not be possibly due to the role of the stellar crust."
" The data have been oeviouxlv. explained (Αρα, Pines ποιο —990: hereafter APC) in Cris of a sugeested PAxu-up of (a part of) the crustal superfiuid bv 16 spinming down crust (""the contaiuncr) over a iue much lager than the associated relaxation iniescaloe."," The data have been previously explained \markcite{APC} (Alpar, Pines Cheng 1990; hereafter APC) in terms of a suggested spin-up of (a part of) the crustal superfluid by the spinning down crust (“the container”) over a time much larger than the associated relaxation timescale."
 Ilowever. a closer look at the relative rotation of the superfluid aud its vortices reveals iat the sueeestedOO mechanisi faiIs quautitativelv X. at cast. more than one order of magnitude.," However, a closer look at the relative rotation of the superfluid and its vortices reveals that the suggested mechanism fails quantitatively by, at least, more than one order of magnitude."
 Iu addition. the suggested spin-up process is also argued to be in contradiction witi the well-known requirenieuts for a superfluid spiup.," In addition, the suggested spin-up process is also argued to be in contradiction with the well-known requirements for a superfluid spin-up."
 Hence. the (pinned) superfluid in the crust is uot the primary cause of the post-elitch relaxatiou.," Hence, the (pinned) superfluid in the crust is not the primary cause of the post-glitch relaxation."
 On the other hand. the pinning of he superfluid vortices iu the crust. aud also in the core. o fa neutron star has recently been objected by some authors on the account of the possible observatioas of long period precession iu isolated pulsars (Jones Anderson 2001: Linς 2003: Buckley. Metitshi Zhituitsky 2001).," On the other hand, the pinning of the superfluid vortices in the crust, and also in the core, of a neutron star has recently been objected by some authors on the account of the possible observations of long period precession in isolated pulsars (Jones Anderson 2001; Link 2003; Buckley, Metlitski Zhitnitsky 2004)."
 Thus the post-elitch relaxation must be driven by mechanisms) other han that due oulv o the enst superfluidity. whicher the pinning is realized or not.," Thus the post-glitch relaxation must be driven by mechanism(s) other than that due only to the crust superfluidity, whether the pinning is realized or not."
 In section 2. the general role of an assumed superfiuid component in (the crust or in he core o )aneutron star out 16 observable post-oelitch )ehiavior of the star is briefly described.," In section 2, the general role of an assumed superfluid component in (the crust or in the core of) a neutron star on the observable post-glitch behavior of the star is briefly described."
 In section 3. the relevant observatioua data aud the xoblenm raised bv these observations against anv nodel of post-glitch relaxation based ou the effects of the crust alone are highlighted.," In section 3, the relevant observational data and the problem raised by these observations against any model of post-glitch relaxation based on the effects of the crust alone are highlighted."
 The earlier sugeeested resolution (APC) of the problem is hen stated., The earlier suggested resolution \markcite{APC} (APC) of the problem is then stated.
 In section Loa quantitative evaluation of the suegeestedOO mechiauisui is eiven. indicating a arge disaereciuent with the data.," In section 4, a quantitative evaluation of the suggested mechanism is given, indicating a large disagreement with the data."
 The subsection l.l preseuts a more doetailec discussion of the rotaion of the different commponcuts in the crust. waving particular attention to he vortex lines. aud arrives at the same conclusion as already deduced. in the section l1.," The subsection 4.1 presents a more detailed discussion of the rotation of the different components in the crust, paying particular attention to the vortex lines, and arrives at the same conclusion as already deduced, in the section 4."
 Iu. section 5.Γ he feasibility. of he sugeested process. of spinning up of a piuned superfluid component in the crust during the spiuniug down of the crust iself. is questioned. altogether.," In section 5, the feasibility of the suggested process, of spinning up of a pinned superfluid component in the crust during the spinning down of the crust itself, is questioned, altogether."
 The possibility of such a process is argued to be ruled out. on a general dyuiuuical eround. aud also according to he vortex creep foriuulatkn.," The possibility of such a process is argued to be ruled out, on a general dynamical ground, and also according to the vortex creep formulation."
 We conclude iu section 6. with a," We conclude in section 6, with a"
Yonezhong Xu. and RyanSeranton?.,"Yongzhong Xu, and Ryan."
. It uses the natural SDSS stripe geometry to divide the skv into pixels aligned with the SDSS survey coordinates. cta/lambda.," It uses the natural SDSS stripe geometry to divide the sky into pixels aligned with the SDSS survey coordinates, eta/lambda."
 Pixels at a particular resolution have a constant width in eta. and ao variable width. in lambda to μαμα the equal area requirement.," Pixels at a particular resolution have a constant width in eta, and a variable width in lambda to satisfy the equal area requirement."
 While SDSSPix is useful because of the alignment of pixels with survey boundaries which makes seeing and reddening in pixels easier to quantify. the elongation of pixels away [rom the survey center interfered with the convergence properties of our algorithm. described below.," While SDSSPix is useful because of the alignment of pixels with survey boundaries which makes seeing and reddening in pixels easier to quantify, the elongation of pixels away from the survey center interfered with the convergence properties of our algorithm described below."
 This is because elongated. pixels smooth density variations preferentially in the direction of elongation while retaining that information in the perpendicular direction., This is because elongated pixels smooth density variations preferentially in the direction of elongation while retaining that information in the perpendicular direction.
 This increases the covariance between the smaller scale niocdes and drives increasing oscillation in high { bandpowers with each iteration., This increases the covariance between the smaller scale modes and drives increasing oscillation in high $\ell$ bandpowers with each iteration.
 IIZALDPix is also a hierarchical. equal area pixelization scheme (Ciórskietal.2005)... created for CMD experiments such as WALAP anc Planck.," HEALPix is also a hierarchical, equal area pixelization scheme \citep{gorski05}, created for CMB experiments such as WMAP and Planck."
 [t divides the sphere into 12 pixels at the base resolution. ancl higher resolutions recursively quarter these large pixels.," It divides the sphere into 12 pixels at the base resolution, and higher resolutions recursively quarter these large pixels."
 The benefit of using IHIZALDPix is that while pixel boundaries have no relation to our observational data. the pixels are not elongated as they are with SDSSPix.," The benefit of using HEALPix is that while pixel boundaries have no relation to our observational data, the pixels are not elongated as they are with SDSSPix."
 Due to the stability of the quadratic estimation method using LEALPix. we have opted. to pixelize our data with LUEALPix for our calculation.," Due to the stability of the quadratic estimation method using HEALPix, we have opted to pixelize our data with HEALPix for our calculation."
 Alasking with LIIZALDPix is more complicated. than with SDSSPix since pixels may overlap the survey boundaries., Masking with HEALPix is more complicated than with SDSSPix since pixels may overlap the survey boundaries.
 For unbiased results. any pixel that. overlaps a boundary must not be considered in the calculation since it may have an unphysical overdensity.," For unbiased results, any pixel that overlaps a boundary must not be considered in the calculation since it may have an unphysical overdensity."
 Phus many pixels on stripe edges are masked., Thus many pixels on stripe edges are masked.
 We also eliminate pixels that are not contiguous with the primary SDSS observing footprint., We also eliminate pixels that are not contiguous with the primary SDSS observing footprint.
 A random. sample of 100.000 of the pixels not. used. due to the boundary. are shown in the top panel of Figure 4.. we have plotted. only a sample to prevent obscuration of the coordinate lines.," A random sample of 100,000 of the pixels not used due to the boundary are shown in the top panel of Figure \ref{masks}, we have plotted only a sample to prevent obscuration of the coordinate lines."
 Furthermore. we must mask pixels due to areas with poor image quality. these pixels are also shown in the bottom of Figure 4..," Furthermore, we must mask pixels due to areas with poor image quality, these pixels are also shown in the bottom of Figure \ref{masks}."
 Adclitionally. we remove pixels where the mean secing is more than 1.5 areseconds. and pixels where the mean reddening is greater than 0.2. shown in the top and bottom panels of Figure 5.. respectively.," Additionally, we remove pixels where the mean seeing is more than 1.5 arcseconds, and pixels where the mean reddening is greater than 0.2, shown in the top and bottom panels of Figure \ref{seeing}, respectively."
 The first step in our approach is to select the initial fine bandpowers., The first step in our approach is to select the initial fine bandpowers.
 Multipole resolution is limited by ACm180 fo. where ὁ is the analyzed area's smallest. angular dimension (Peebles1980).," Multipole resolution is limited by $\Delta \ell \approx 
180^{\circ} / \phi$ , where $\phi$ is the analyzed area's smallest angular dimension \citep{peebles80}."
. For this reason. we want the broadest survey possible.," For this reason, we want the broadest survey possible."
 Aside from. being restricted. to choosing bandpowers wider than this limit. the choice of the starting. ending. initial value. and widths of each bandpower is unrestrained. although some choices of initial values may cause non-convergence or singular matrices.," Aside from being restricted to choosing bandpowers wider than this limit, the choice of the starting, ending, initial value, and widths of each bandpower is unrestrained, although some choices of initial values may cause non-convergence or singular matrices."
 We chose initial bancdpowers of equal widths. each 5£ wide for the full sample and 204 wide for the individual stripes.," We chose initial bandpowers of equal widths, each $5 \ell$ wide for the full sample and $20 \ell$ wide for the individual stripes."
 We use initial values based on a prior angular power spectrum: however. since the quacratic estimation method uses iteration. the final result is fairly insensitive to the input angular power spectrum.," We use initial values based on a prior angular power spectrum; however, since the quadratic estimation method uses iteration, the final result is fairly insensitive to the input angular power spectrum."
" We assume all C; within a band to be constant (Llutereretal. 2001):: where μι=1 while £€b and zero otherwise. and we define ο, according to standard convention (Bond 2000)."," We assume all $\mathcal{C}_{\ell}$ within a band to be constant \citep{huterer01}: where $\chi_{b(\ell)} = 1$ while $\ell \in b$ and zero otherwise, and we define $\mathcal{C}_\ell$ according to standard convention \citep{bond00}."
. We start with an initial fine binning. to determine where the power is inside the larger bandpowers that we later use.," We start with an initial fine binning, to determine where the power is inside the larger bandpowers that we later use."
 The Fisher information matrix (defined. in. Equation, The Fisher information matrix (defined in Equation
galaxies.,galaxies.
 We note that these numbers are indeed much lower than the numbers of stars found in the optical photometric catalogs alone (see Sect. 2.1))., We note that these numbers are indeed much lower than the numbers of stars found in the optical photometric catalogs alone (see Sect. \ref{dataopt}) ).
" This is partly due to the fact that the ISAAC field of view is slightly smaller than the ACS one, and partly due to the higher resolution and photometric depth of ACS."," This is partly due to the fact that the ISAAC field of view is slightly smaller than the ACS one, and partly due to the higher resolution and photometric depth of ACS."
" Unfortunately, this results in a loss of information in the process of cross-correlation, since there could be some mismatches in the cases where more than one optical source is found in the vicinity of a NIR source."," Unfortunately, this results in a loss of information in the process of cross-correlation, since there could be some mismatches in the cases where more than one optical source is found in the vicinity of a NIR source."
" This is particularly true for SGC1319.1-4216 and ESO269-066, where the stellar density is higher, and from Fig."," This is particularly true for SGC1319.1-4216 and ESO269-066, where the stellar density is higher, and from Fig."
 8 and 9 we see that the NIR foreground sequences are poorly populated because of such mismatches., \ref{cmdcomb2} and \ref{cmdcomb3} we see that the NIR foreground sequences are poorly populated because of such mismatches.
" To avoid a loss of information for the part of the CMD in which we are most interested, we check visually the positions of the stars that are found within our selection boxes (see below) in both the NIR and optical catalogs, and add in this way a few more matches to our combined catalogs."," To avoid a loss of information for the part of the CMD in which we are most interested, we check visually the positions of the stars that are found within our selection boxes (see below) in both the NIR and optical catalogs, and add in this way a few more matches to our combined catalogs."
" On the same CMDs, we also overplot the boxes used in both optical and NIR to select candidate AGB stars."," On the same CMDs, we also overplot the boxes used in both optical and NIR to select candidate AGB stars."
" For the optical, the box extends from a magnitude of lo,rgGp—σι, where σι is the observational error at that magnitude (in order not to select RGB stars with erroneously higher magnitudes because of photometric errors), up until M;~—5.5."," For the optical, the box extends from a magnitude of $I_{0,TRGB}-\sigma_I$, where $\sigma_I$ is the observational error at that magnitude (in order not to select RGB stars with erroneously higher magnitudes because of photometric errors), up until $M_I\sim-5.5$."
 The color range goes from the bluest edge of the TRGB to Vo—Jp~4 (there are no stars redder than this value)., The color range goes from the bluest edge of the TRGB to $V_0-I_0\sim4$ (there are no stars redder than this value).
" This should be the magnitude range that luminous AGB stars with the average metallicity of the target galaxies cover (see?,andreferences therein)..", This should be the magnitude range that luminous AGB stars with the average metallicity of the target galaxies cover \citep[see][ and references therein]{rejkuba06}.
" For SGC1319.1-4216 and ESO269-066, we choose to extend the optical selection box based on a few stars with colors Vo—Ioz2.5 that have magnitudes below that of the TRGB derived from the median metallicity."," For SGC1319.1-4216 and ESO269-066, we choose to extend the optical selection box based on a few stars with colors $V_0-I_0\gtrsim2.5$ that have magnitudes below that of the TRGB derived from the median metallicity."
" These stars could belong to the metal-rich population, as the TRGB has in fact slightly fainter magnitudes at increasing metallicities (see, e.g., Fig. 1))."," These stars could belong to the metal-rich population, as the TRGB has in fact slightly fainter magnitudes at increasing metallicities (see, e.g., Fig. \ref{cmdopt}) )."
" For the NIR, the selection box contains all the stars that are found above the TRGB in these bands, and redwards of the reddest foreground stars of the vertical plume."," For the NIR, the selection box contains all the stars that are found above the TRGB in these bands, and redwards of the reddest foreground stars of the vertical plume."
" Our final “AGB candidates” are those stars that are simultaneously found in the optical and the NIR selection boxes, and are plotted in red on these CMDs."," Our final “AGB candidates” are those stars that are simultaneously found in the optical and the NIR selection boxes, and are plotted in red on these CMDs."
" We also overplot the 50% completeness limits to the NIR CMDs, in order to point out that we mightbe missing the detection of a few luminous AGB stars with colors Jo—Koz1.0-- 1.5."," We also overplot the $50\%$ completeness limits to the NIR CMDs, in order to point out that we mightbe missing the detection of a few luminous AGB stars with colors $J_0-K_0\gtrsim1.0-1.5$ ."
 This is true in particular for, This is true in particular for
"more mixed than the s, configuration - and therefore a transition δι5a is permitted bv the mixing theorem (Tremaine.Hénon&Lynden-Bell=1986) - we have calculated.the AZ(VY) functions of 5; and sy.",more mixed than the $s_1$ configuration - and therefore a transition $s_1\to s_3$ is permitted by the mixing theorem \citep{ref:Tre86} - we have calculatedthe $M(V)$ functions of $s_1$ and $s_3$.
 The ΔΙ} function is defined in the following way: we first define Al(+7) and V(4) as the cumulative mass and. phase-space volumes above the phase-space density. 4. with Z/(:) being the Lleavisicle step function.," The $M(V)$ function is defined in the following way: we first define $M(\eta)$ and $V(\eta)$ as the cumulative mass and phase-space volumes above the phase-space density $\eta$, with $H(\cdot)$ being the Heaviside step function."
 As V(η) is à monotonically decreasing function. we can invert it and express p in terms of the cumulative volume V.," As $V(\eta)$ is a monotonically decreasing function, we can invert it and express $\eta$ in terms of the cumulative volume $V$."
 Plugging this into ALG) we get the AZ(V) function., Plugging this into $M(\eta)$ we get the $M(V)$ function.
" According to the mixing theorem. the distribution s; is more mixed than the distribution s, if and only if AMa(V)xAV) for every V as is shown in3."," According to the mixing theorem, the distribution $s_3$ is more mixed than the distribution $s_1$ if and only if $M_3(V) \le M_1(V)$ for every $V$, as is shown in."
. Let us now turn our attention to the s» configuration., Let us now turn our attention to the $s_2$ configuration.
" Seemingly. we need to calculate the Tip) function of the 5, configuration. and together with an energv of &|AL. solve the equations The function g»(c) needs to be cdeulated from using the gravitational potentia qat). which has to be recovered from. fo(e) using the IXjsson equation (12))."," Seemingly, we need to calculate the $\tau_1(\eta)$ function of the $s_1$ configuration, and together with an energy of $E+\Delta E$, solve the equations The function $g_2(\epsilon)$ needs to be calculated from using the gravitational potential $\Phi_2(r)$, which has to be recovered from $f_2(\epsilon)$ using the Poisson equation \ref{eq:LB2-possion}) )."
 Finally. the resultant f»(c) would be compared to fe) to see if the two configurations are equal.," Finally, the resultant $f_2(\epsilon)$ would be compared to $f_3(\epsilon)$ to see if the two configurations are equal."
 There is. however. a much simple Εναν [o see if (ο) fatc).," There is, however, a much simpler way to see if $f_2(\epsilon)=f_3(\epsilon)$ ."
 Let us assume that. indeed his is the case. and that consequently also P(r)=Αι)and gole)= gast).," Let us assume that indeed this is the case, and that consequently also $\Phi_2(r)=\Phi_3(r)$and $g_2(\epsilon)=g_3(\epsilon)$ ."
 In such case it is possible to recov vohe full expression AleJo3789 pn terms of the known functions. fa(c) and.7 gat)," In such case it is possible to recover the full expression $\frac{1}{\Delta\eta}A(\epsilon)e^{-\beta_2
 \eta_0 (\epsilon-\mu_\eta)}$ in terms of the known functions $f_3(\epsilon)$ and $g_3(\epsilon)$."
 We start by replacing fs(c)-⋅in and qe(c)©gale) I5qs. (20--22))., We start by replacing $f_2(\epsilon)\leftrightarrow f_3(\epsilon)$ and $g_2(\epsilon)\leftrightarrow g_3(\epsilon)$ in Eqs. \ref{eq:LB3-f}- \ref{eq:LB3-vol})).
" Dilferentiating Iq. with respect to « and substituting f5(c) from (20).. we obtain which vields llere «d, is an unknown integration constant."," Differentiating with respect to $\epsilon$ and substituting $f_3(\epsilon)$ from , we obtain which yields Here $a_0$ is an unknown integration constant."
 The integral in 2lo(c) can be easily done analvtically if we recall the definition of fó(c) which is given in (17).. vieldingHaving found zA(e). we use to find the Lagrange," The integral in $A_0(\epsilon)$ can be easily done analytically if we recall the definition of $f_3(\epsilon)$ which is given in , yieldingHaving found $A(\epsilon)$ , we use to find the Lagrange"
al a distance of 7.5 kpe Irom the Galactic center and in the equatorial plane ol the Galactic disk (Moskalenkoetal.2006)..,at a distance of $7.5$ kpc from the Galactic center and in the equatorial plane of the Galactic disk \citep{2006ApJ...640L.155M}.
 Our results are not sensitive to details of the ISRF., Our results are not sensitive to details of the ISRF.
 Thermal X-ray eniission mostly depends on the densitv of the shocked interstellarmedium (19M) rj and the temperature of backeround electrons 7..., Thermal X-ray emission mostly depends on the density of the shocked interstellarmedium (ISM) $n_{\rm ISM}$ and the temperature of background electrons $T_e$.
 Depending on the effect of accelerated particles on the shock structure. the density is a factor of a few higher (han the densitv in the un-shocked upstream region (Berezhko&Ellison1999:Warren 2005)..," Depending on the effect of accelerated particles on the shock structure, the density is a factor of a few higher than the density in the un-shocked upstream region \citep{1999ApJ...526..385B, 
2005ApJ...634..376W}."
 The electron temperature due to Coulomb collisional energy exchange with ions is estimated by Πάροςetal.(2000):Fanοἱ(20102) where 7; is the temperature of background ions.," The electron temperature due to Coulomb collisional energy exchange with ions is estimated by \citet{2000ApJ...543L..61H,2010MNRAS.406.1337F}
 where $T_i$ is the temperature of background ions."
 7; is estimated to be higher than e1.3x105 K if the background is heated by the shock (Fanetal.2010a).., $T_i$ is estimated to be higher than $\sim 1.3\times 10^8$ K if the background is heated by the shock \citep{2010MNRAS.406.1337F}.
" For nga,220.02 . T? should be higher than 4x105 IK. Druryοἱal.(2009). alternatively proposed that the post-shock region temperature could be reduced sienilicantlv in the case of large Mach number of the shock anc effective particle acceleration."," For $n_{\rm ISM}\approx 0.02$ $^{-3}$, $T_e$ should be higher than $4\times 10^6$ K. \cite{2009A&A...496....1D} alternatively proposed that the post-shock region temperature could be reduced significantly in the case of large Mach number of the shock and effective particle acceleration."
 If (his is the case. as we will show below. the constraint on the density and (therefore (he relativistic proton energy in the hacdronic and hybrid models will be less strict.," If this is the case, as we will show below, the constraint on the density and therefore the relativistic proton energy in the hadronic and hybrid models will be less strict."
 However. there are still significant uncertainties in the plasma heating downstream (Ghavamianetal.2007;Gabici2008).. and it was also argued (hat suchan extreme condition was nol easy (o meet and (the post-shock plasma should be heated more strongly (Ellisonetal. 2010).. ," However, there are still significant uncertainties in the plasma heating downstream \citep{2007ApJ...654L..69G, 
Gabici2008}, and it was also argued that suchan extreme condition was not easy to meet and the post-shock plasma should be heated more strongly \citep{2010ApJ...712..287E}. ."
"Since there is no direct constraint on T, due to the lack of thermal emission. instead of including 7; in the MCMC fit. we take some tvpical values of T;."," Since there is no direct constraint on $T_e$ due to the lack of thermal emission, instead of including $T_e$ in the MCMC fit, we take some typical values of $T_e$."
 For the sake of simplicity. we assume that the background electrons are in ionization equilibrium with the background ions and use the Ravimonc-Sinith plasma code to ealeulate the thermal emission for given rg. 7) and the metalicitv (Ravmond&Smith 1911)..," For the sake of simplicity, we assume that the background electrons are in ionization equilibrium with the background ions and use the Raymond-Smith plasma code to calculate the thermal emission for given $n_{\rm ISM}$, $T_e$ and the metalicity \citep{1977ApJS...35..419R}."
 The emission includes (he recombination. bremnmstrahlung. (wo photon process. aud line emissions.," The emission includes the recombination, bremmstrahlung, two photon process, and line emissions."
 The chemical abundance of the ISM is taken from Allen(1973).., The chemical abundance of the ISM is taken from \cite{1973asqu.book.....A}.
 For emission lines ling in the energy range of N-ray data (0.5—33 keV). we convolve the model spectrum wilh a Gaussian energy spread function. whose width is adopted as the characteristic energv resolution of Suzaku (Ixovamaetal.2007)..," For emission lines lying in the energy range of X-ray data $0.5-33$ keV), we convolve the model spectrum with a Gaussian energy spread function, whose width is adopted as the characteristic energy resolution of ${\it Suzaku}$ \citep{2007PASJ...59S..23K}."
 In total there are 6 [ree parameters. a.EL.VW.ὃν.D. and my in the lepton model.," In total there are 6 free parameters, $\alpha_e,\,
E_c^e,\,W_e,\,\delta_e,\,B,$ and $n_{\rm ISM}$ in the lepton model."
 The I-dimensional (1-D) probability distributions and 2-dimensional (2-D) confidence regions (at lo and 2o confidence levels) of the model parameters. ancl (he best-fit spectral energy distribution (SED) of the source are shown in Fig. l..," The 1-dimensional (1-D) probability distributions and 2-dimensional (2-D) confidence regions (at $1\sigma$ and $2\sigma$ confidence levels) of the model parameters, and the best-fit spectral energy distribution (SED) of the source are shown in Fig. \ref{fig:lepton}. ."
 The best fit model parameters correspond to the peak ofthe 1-D probability. distributions., The best fit model parameters correspond to the peak ofthe 1-D probability distributions.
 The spectral parameters in the leptonic scenario are well constrained except [or mig. whose 26 upper limit is well," The spectral parameters in the leptonic scenario are well constrained except for $n_{\rm ISM}$ , whose $2\sigma$ upper limit is well"
 (Bennettetal.2003b:Tinshaw2008a.b)..," \citep{wmapmap,wmapsystematics,wmappw}. \citep{wmapfg}."
 ACDAL Walton2003:Efstathiou2003).. (I&o1iatsuetal.2003:Cliane," $\Lambda$ \citep{toh,oliveira,efstathiou}, \citep{wmapng,tacng,park,ndv03,ndv04,eriksenA,eriksenB,hansen}."
 C; Teemark.," $\Cl$ \citep{bbks,be}."
deOliveira-Costa&Tamilton(2003) Naselskvetal.(2003)..," \citep{dust} \citet{toh} \citet{pcm}, \citet{eriksenB}, \citep{te96,bouchet,hobson,stolyarov,delabrouille,toh,patanchon,barreiro,gonzalez},"
preceded by a “Wer.,preceded by a “We”.
 However. Walker did not use au extension of Wesseliuk's πρπας scheme for the new variables that he discovered.," However, Walker did not use an extension of Wesselink's numbering scheme for the new variables that he discovered."
 Instead. he denoted the new variables by their nuuber in his photometry Table 3.," Instead, he denoted the new variables by their number in his photometry Table 3."
 Tt is. however. convenient to have an identification svsteni that refers only to the known variable stars in NGC 1166.," It is, however, convenient to have an identification system that refers only to the known variable stars in NGC 1466."
 Therefore we have exteuded Wesselink uuuberug system. adding the additional variables thats are not included iu Wesselink(1971). to the end of Wessclink’s orignal list of variables.," Therefore we have extended Wesselink's numbering system, adding the additional variables that are not included in \citet{we71} to the end of Wesselink's orignal list of variables."
 All variables are named in the forma of Vxx. with stars up through 12 being ones that were originally found by Wesseliuk.," All variables are named in the form of Vxx, with stars up through $42$ being ones that were originally found by Wesselink."
 A cross identification of the original Walker numbers aud our variable star uunbers dis meluded in Table L.., A cross identification of the original Walker numbers and our variable star numbers is included in Table \ref{vartable}. .
 Figures 6 and 7 show the locatious of all of the variable stars listed in the table., Figures \ref{findout} and \ref{findin} show the locations of all of the variable stars listed in the table.
 We found [1 of Walkers (1992) 12 RR Lyrac stars along with 6 new RRab stars. 1 new RRe. aud 2 new RRd stars.," We found $41$ of Walker's (1992) $42$ RR Lyrae stars along with $6$ new RRab stars, $1$ new RRc, and $2$ new RRd stars."
 Six of the previously ideutified RRLyrac, Six of the previously identified RRLyrae
Over the past IO years the number of known high-mass X-ray binaries (HMXBs) located in the Small Magellanic Cloud (SMC) has been steadily increasing.,Over the past 10 years the number of known high-mass X-ray binaries (HMXBs) located in the Small Magellanic Cloud (SMC) has been steadily increasing.
 There are now approximately 50 such systems known in the SMC (Coeetal.2005)., There are now approximately 50 such systems known in the SMC \citep{coe05}.
.. Until recently the majority of X-ray observations byChandra.Newton andRXTE have concentrated on the Bar. since the large fraction of HMXBs are located in this region.," Until recently the majority of X-ray observations by, and have concentrated on the Bar, since the large fraction of HMXBs are located in this region."
 Coeetal.(2005) analysed the locations of the known X-ray pulsars and believed there to be a relationship between the HI intensity distribution and the distribution of the pulsars., \citet{coe05} analysed the locations of the known X-ray pulsars and believed there to be a relationship between the HI intensity distribution and the distribution of the pulsars.
 This prompted a large survey of the wing of the SMC usingChandra., This prompted a large survey of the wing of the SMC using.
 A total of 20 individua pointings were made of approximately kks each., A total of 20 individual pointings were made of approximately ks each.
 The survey was successful in finding two new pulsars (SXP65.8 and SXP700) and detecting two previously known pulsars (SXPIOL and SXP348)., The survey was successful in finding two new pulsars (SXP65.8 and SXP700) and detecting two previously known pulsars (SXP101 and SXP348).
 Due to high spatial resolution the counterparts to al four sources were identified (SXP348's being previously known)., Due to high spatial resolution the counterparts to all four sources were identified (SXP348's being previously known).
 Table | shows the positions and V band magnitudes of the counterparts to the detected pulsars., Table \ref{tasources} shows the positions and V band magnitudes of the counterparts to the detected pulsars.
 A more detailed description of the survey can be found in McGowanetal.(2007)., A more detailed description of the survey can be found in \citet{mcg07}.
. In order to evaluate where these new pulsars lie in relation to the Galactic spectral distribution of Be/X-ray binaries we need to classify the counterparts., In order to evaluate where these new pulsars lie in relation to the Galactic spectral distribution of Be/X-ray binaries we need to classify the counterparts.
 This paper reports the follow-up optical observations of these systems., This paper reports the follow-up optical observations of these systems.
 Since the observations were completed in March 2006 a number of telescopes have been used for the optical follow-up., Since the observations were completed in March 2006 a number of telescopes have been used for the optical follow-up.
 Table 2 presents a list of the data collected for each of the sources., Table 2 presents a list of the data collected for each of the sources.
 The telescope contigurations and reduction processes used are as follows:, The telescope configurations and reduction processes used are as follows:
"is that the high SMG densities trace only the central starburst region, and exclude more extended fainter envelopes of pre-merger stars.","is that the high SMG densities trace only the central starburst region, and exclude more extended fainter envelopes of pre-merger stars."
" At lower redshifts these stars would become visible and be of greater relative importance as the starburst fades, giving rise to larger half-light radii and smaller inferred densities (cf."," At lower redshifts these stars would become visible and be of greater relative importance as the starburst fades, giving rise to larger half-light radii and smaller inferred densities (cf."
 simulations by Hopkinsetal. (2008b)))., simulations by \citet{HopkinsP_08a}) ).
 We have constructed new halo merger trees from the MMillennium Simulation., We have constructed new halo merger trees from the Millennium Simulation.
" Our trees account for merger durations, and we use them to identify halos that are undergoing mergers and to extract dark matter accretion rates."," Our trees account for merger durations, and we use them to identify halos that are undergoing mergers and to extract dark matter accretion rates."
 We show that the high star formation rates observed in rotating disks at z=2 are plausibly consistent with the dark matter accretion rates expected for halos not undergoing major mergers., We show that the high star formation rates observed in rotating disks at $z\approx2$ are plausibly consistent with the dark matter accretion rates expected for halos not undergoing major mergers.
" Given the measured star formation rates of SMGs, and the supported assumption that they are undergoingobservationally major mergers, we infer their likely halo masses."," Given the measured star formation rates of SMGs, and the observationally supported assumption that they are undergoing major mergers, we infer their likely halo masses."
" Major mergers can neither lead to the complete transformation of the z~2 disks to z=0 ellipticals, nor to the disappearance of the very high density SMGs from z£22 to z20."," Major mergers can neither lead to the complete transformation of the $z\approx2$ disks to $z=0$ ellipticals, nor to the disappearance of the very high density SMGs from $z\approx2$ to $z=0$."
" Therefore, secular/internal processes are likely important in the evolution of these high-redshift populations to present time."," Therefore, secular/internal processes are likely important in the evolution of these high-redshift populations to present time."
" We thank Gabriella De Lucia, Mike Boylan-Kolchin and Volker Springel for useful discussions, and the anonymous referee for valuable comments."," We thank Gabriella De Lucia, Mike Boylan-Kolchin and Volker Springel for useful discussions, and the anonymous referee for valuable comments."
 The Millennium Simulation databases used in this paper and the web application providing online access to them were constructed as part of the activities of the German Astrophysical Virtual Observatory., The Millennium Simulation databases used in this paper and the web application providing online access to them were constructed as part of the activities of the German Astrophysical Virtual Observatory.
 We are grateful to Gerard Lemson who devotedly helped us to use the databases., We are grateful to Gerard Lemson who devotedly helped us to use the public databases.
" SG the PhD of the publicInternational Max Planckacknowledges Research School fellowshipin Astrophysics, and the support received from a Marie Curie Host Fellowship for Early Stage Research Training."," SG acknowledges the PhD fellowship of the International Max Planck Research School in Astrophysics, and the support received from a Marie Curie Host Fellowship for Early Stage Research Training."
The ISM in our model is made up of three components namely molecular (lls). neutral (LE 1) aid. ionized (1I. 11) hydrogen - all following the spatial distribution given by (see also Paper D.,"The ISM in our model is made up of three components - namely molecular $_2$ ), neutral (H ) and ionized (H ) hydrogen - all following the spatial distribution given by \citet{wolf03} (see also Paper I)."
 “Phe ISM is initially set in rotational equilibrium in the Galactic gravitational potential due to the summation of the dark matter halo. the bulge and. the disk contributions. as described by ?.. 2... and by a Hattence Wing profile (2).. respectively.," The ISM is initially set in rotational equilibrium in the Galactic gravitational potential due to the summation of the dark matter halo, the bulge and the disk contributions, as described by \citet{nfw96}, \citet{her90}, , and by a flattened King profile \citep{brma96}, respectively."
 A hot isothermal eas halo in hyerostatic equilibrium with the Galactic potential well is also added., A hot isothermal gas halo in hydrostatic equilibrium with the Galactic potential well is also added.
" This halo has a central density pow10* ecm anda temperature Z4—710"" Ix. lt is known that the great majority of the massive stars form in clusters (c.g.2.andreferencestherein).."," This halo has a central density $\rho_{\rm
 0,h}=2.17\times 10^{-27}$ g $^{-3}$ and a temperature $T_{\rm
 h}=7\times 10^6$ K. It is known that the great majority of the massive stars form in clusters \citep[e.g.][and references therein]{watho02}."
 In Paper ]. we defined a “single fountain” as a fountain powered by the SNe LL present in a singleelustert.," In Paper I, we defined a “single fountain” as a fountain powered by the SNe II present in a single."
. The OL association driving the fountain was assumed to be totally housed inside a single zone of the highest resolution level of our adaptive evicl (see section 2.3))., The OB association driving the fountain was assumed to be totally housed inside a single zone of the highest resolution level of our adaptive grid (see section \ref{subsec:nummet}) ).
 The SNe LE do not explode all at the same time because of the dilferent mass oftheir progenitors., The SNe II do not explode all at the same time because of the different mass of their progenitors.
 Thus the energy and the mass delivered by all the explosions are released over a time interval of Af=30 Myr (the lifetime oan S M. star. which is the least massive SN LE progenitor).," Thus the energy and the mass delivered by all the explosions are released over a time interval of $\Delta t$ =30 Myr (the lifetime of an 8 $M_{\odot}$ star, which is the least massive SN II progenitor)."
 The stellar explosions inject mass and energy at the rates AL-RAL: and Ly=RES respectively.," The stellar explosions inject mass and energy at the rates $\dot M ={\cal R}M_{\rm ej}$ and $L_{\rm w}={\cal R}E_0$, respectively."
 Here AL;=16 M. and fy=1075 erg are the mean mass ancl energy. released by a single explosion. respectively: Ro—Nex/At is the SN IL rate. and. Nsw is the total number of SN LL explosions occurring in the association.," Here $M_{\rm ej}=16$ $M_{\odot}$ and $E_0=10^{51}$ erg are the mean mass and energy released by a single explosion, respectively; ${\cal R}=N_{\rm SN}/\Delta t$ is the SN II rate, and $N_{\rm SN}$ is the total number of SN II explosions occurring in the association."
 Ly represents the mechanical luminosity of the wind driven by the SNe Lb ane inflating a superbubble., $L_{\rm w}$ represents the mechanical luminosity of the wind driven by the SNe II and inflating a superbubble.
 H£ the luminosity is larger than a critical value Loy. the superbubble breaks out of the disk forming a chimney in the ISM and gives rise to the GE (c£.," If the luminosity is larger than a critical value $L_{\rm cr}$, the superbubble breaks out of the disk forming a chimney in the ISM and gives rise to the GF (cf."
 Paper I and references therein)., Paper I and references therein).
 In section 2.3.2 we describe as Ly is implemented into the numerical erid., In section \ref{subsec:nummet} we describe as $L_{\rm w}$ is implemented into the numerical grid.
 At the observed rate (see below). several SGEs may occur sulliciently close to each other in time and space to mutually interact.," At the observed rate (see below), several SGFs may occur sufficiently close to each other in time and space to mutually interact."
 This interaction obviously modifies the general dynamics of the SN IL ejecta. of cach single fountain., This interaction obviously modifies the general dynamics of the SN II ejecta of each single fountain.
 Following with an adequate spatial resolution all the SN 1L explosions occurring in the whole disk is bevond our current computational capabilities., Following with an adequate spatial resolution all the SN II explosions occurring in the whole disk is beyond our current computational capabilities.
 Thus. throughout. the simulations of multiple fountains. we focus in particular on a circular area (hereafter referred to as the “active area) of the Galactic disk of 8 kpc which is resolved up to the maximum level of grid. refinement (this finest. grid. extends vertically up to z=3.2 kpe).," Thus, throughout the simulations of multiple fountains, we focus in particular on a circular area (hereafter referred to as the “active area”) of the Galactic disk of 8 $^2$ which is resolved up to the maximum level of grid refinement (this finest grid extends vertically up to $z=3.2$ kpc)."
 We allow the SNe LL to occur only in this area over a period. ZY=200 Myr., We allow the SNe II to occur only in this area over a period $T=200$ Myr.
 Le must be emphasized that the star formation rate (and the associated SN rate) is not. computed:self-consistentIiv. with the gas evolution., It must be emphasized that the star formation rate (and the associated SN rate) is not computedself-consistently with the gas evolution.
 Instead. we assume a mean SN rate adequately scaled [rom the rate 1.4107 + relative to the whole Galaxy. (2)..," Instead, we assume a mean SN rate adequately scaled from the rate $1.4\times 10^{-2}$ $^{-1}$ relative to the whole Galaxy \citep{cap97}."
" lt turns out that during the time ZY of our simulations Ni,24.2.10¢ SNe Lb are expected to explode in the active area of the Galactic disk (sec. however. the end of this section)"," It turns out that during the time $T$ of our simulations $N_{\rm tot}=4.2\times 10^4$ SNe II are expected to explode in the active area of the Galactic disk (see, however, the end of this section)."
 Let us assume fUNsx)Jd to be the number of stellar clusters with a number Nexof supernova progenitors between Nay and Nexτανκ., Let us assume $f(N_{\rm SN})dN_{\rm SN}$ to be the number of stellar clusters with a number of supernova progenitors between $N_{\rm SN}$ and $N_{\rm SN}+dN_{\rm SN}$.
 (κ) follows a power law distribution (?).. We normalize f(Nsx) in order to ect This normalization can be done once Aquis ane Nines have been chosen (see below in this section)," $f(N_{\rm SN})$ follows a power law distribution \citep{hili05}, , We normalize $f(N_{\rm SN})$ in order to get This normalization can be done once $N_{\rm min}$ and $N_{\rm max}$ have been chosen (see below in this section)."
 We choose bins in Nox such that we then assume that such a cluster contains 0. SNe Η.," We choose bins in $N_{\rm SN}$ such that we then assume that such a cluster contains $0.5(N^i_{\rm
SN}+N^{i+1}_{\rm SN})$ SNe II."
 Clearly. for £=1 we have Noy=Nus.," Clearly, for $i=1$ we have $N^1_{\rm
SN}=N_{\rm min}$."
 Once obtained the number anc the richness of the clusters. we place them within the active area.," Once obtained the number and the richness of the clusters, we place them within the active area."
 Vhis is made associating randomly to each th cluster à position {0 within the active area and a time /; in the range 0«/; T., This is made associating randomly to each $i$ -th cluster a position $P_j$ within the active area and a time $t_j$ in the range $0<t_j<T$ .
 As the time proceeds. the supernovae belonging to the 7-th cluster start to explode at Z2; at the time /; (and. continue toexplode for 30 Myr. as outlined. in section 2.2.1)).," As the time proceeds, the supernovae belonging to the $i$-th cluster start to explode at $P_j$ at the time $t_j$ (and continue toexplode for 30 Myr, as outlined in section \ref{subsubsec:sngas}) )."
 The, The
The images reveal a compact flat-spectrum radio component having 7j>2.1x105 I. which we identifv as the actual location of the active galactic nucleus and its 12-million solar mass black hole: this component is at the location inferred by Mundell et al. (,"The images reveal a compact flat-spectrum radio component having $T_{\rm B} > 2.1\times 10^8$ K, which we identify as the actual location of the active galactic nucleus and its 12-million solar mass black hole; this component is at the location inferred by Mundell et al. ("
1995. 2003).,"1995, 2003)."
 The radio flux density of ~3 4 mJy corresponds (ο a monochromatic power of ~LO eres st al 515 Gllz: comparison to the X-ray luminosity indicates (hat NGC 4151 is a racdio-quiet object. in contrast to a munber of other low huninositv active galaxies.," The radio flux density of $\sim$ 3–4 mJy corresponds to a monochromatic power of $\sim 10^{37}$ ergs $^{-1}$ at 5–15 GHz; comparison to the X-ray luminosity indicates that NGC 4151 is a radio-quiet object, in contrast to a number of other low luminosity active galaxies."
 A weak. (wo-sided beeinning to the larger scale radio jet is seen to exist well within the inner parsec of (he AGN.," A weak, two-sided beginning to the larger scale radio jet is seen to exist well within the inner parsec of the AGN."
" Upper limits to the component speeds relative to the apparent core are 0.0506 and 0.0286 at respective distances of 0.16 pe and 6.3 pe [rom the AGN. implving that the NGC! 4151 jet is non-relativistic. and dominated bv thermal plasma. all the way down to near (he broad-line region,"," Upper limits to the component speeds relative to the apparent core are $0.050c$ and $0.028c$ at respective distances of 0.16 pc and 6.8 pc from the AGN, implying that the NGC 4151 jet is non-relativistic, and dominated by thermal plasma, all the way down to near the broad-line region."
 This is consistent with (he approximately svimuuetric radio morphology about the apparent center of activity., This is consistent with the approximately symmetric radio morphology about the apparent center of activity.
 The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities. Inc. We thank the stalls ol the VLA. VLBA. GBT. and Effelshere telescopes that made these observations possible: we are especially erateful to Frank Ghigo for his efforts in making these VLBI observations a success verv soon after (he 15 GlIIz capability [fist became available at the GBT.," The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. We thank the staffs of the VLA, VLBA, GBT, and Effelsberg telescopes that made these observations possible; we are especially grateful to Frank Ghigo for his efforts in making these VLBI observations a success very soon after the 15 GHz capability first became available at the GBT."
 DSW acknowledges support from the NRAQO summer research program and from the National science and Engineering Research Council of Canada., DSW acknowledges support from the NRAO summer research program and from the National Science and Engineering Research Council of Canada.
 CGAL acknowledges financial support from the Roval Society., CGM acknowledges financial support from the Royal Society.
 We thank the anouvmous referee for verv useful suggestions about the analvsis of the nuclear radio spectrum and other issues., We thank the anonymous referee for very useful suggestions about the analysis of the nuclear radio spectrum and other issues.
 The pair of interacting galaxies NGC 4410a/b belongs to a group of 11 members (Hummel et al., The pair of interacting galaxies NGC 4410a/b belongs to a group of 11 members (Hummel et al.
 1986. hereafter HKGS86) which are located behind the Virgo cluster.," 1986, hereafter HKG86) which are located behind the Virgo cluster."
 It consists of a peculiar Sab (NGC 4410a) (Thuan Sauvage 1992) and an E galaxy (NGC 4410b) (HKG86) located in east-west direction and separated by 18777 (8.8 kpe at a distance of 97 Mpe) (Mazzarella Boroson 1993. hereafter MB93).," It consists of a peculiar Sab (NGC 4410a) (Thuan Sauvage 1992) and an E galaxy (NGC 4410b) (HKG86) located in east-west direction and separated by 7 (8.8 kpc at a distance of 97 Mpc) (Mazzarella Boroson 1993, hereafter MB93)."
" NGC 4410a is located at RA = 12! 26"" 27:99, Dec = ((J2000)."," NGC 4410a is located at RA = $^\mathrm{h}$ $^\mathrm{m}$ 9, Dec = (J2000)."
 Spectral analysis of the nucle: of both components led to the classification as two LINERs (Mazzarella et al., Spectral analysis of the nuclei of both components led to the classification as two LINERs (Mazzarella et al.
 1991: Bicay et al., 1991; Bicay et al.
 1995: Thuan Sauvage 1992)., 1995; Thuan Sauvage 1992).
 In the eastern component NGC 4410b a supernova type has been detected in 1965 (SN 1965 A) from which Turatto et al. (, In the eastern component NGC 4410b a supernova type has been detected in 1965 (SN 1965 A) from which Turatto et al. (
1989) derived a distance of 139 Mpe.,1989) derived a distance of 139 Mpc.
 The system has a radial velocity of about 7300 kms + (Mazzarella et al., The system has a radial velocity of about 7300 km $^{-1}$ (Mazzarella et al.
 1991; Batuski et al., 1991; Batuski et al.
 1992: Thuan Sauvage 1992: MB93)., 1992; Thuan Sauvage 1992; MB93).
 With a Hubble constant of 75 kms + ? this leads to a distance of 97 Mpe., With a Hubble constant of 75 km $^{-1}$ $^{-1}$ this leads to a distance of 97 Mpc.
 In this paper we apply the latter value to all distance-dependent parameters. like e.g. luminosities ete.," In this paper we apply the latter value to all distance-dependent parameters, like e.g. luminosities etc."
 A distance of 97 Mpe for NGC 4410 results in an absolute length scale of 470 pe +., A distance of 97 Mpc for NGC 4410 results in an absolute length scale of 470 pc $^{-1}$.
 HKG$806 found a spatial coincidence of the western optical component NGC 4410a with a radio point source of luminosity Lg ~l0O” eres. + embedded in a strong. extended radio source around NGC 4410a with a total radio luminosity Ly;7 ergs |," HKG86 found a spatial coincidence of the western optical component NGC 4410a with a radio point source of luminosity $L_{\mathrm R} \approx$ $^{39}$ erg $^{-1}$ embedded in a strong, extended radio source around NGC 4410a with a total radio luminosity $L_{\mathrm R} \approx$ erg $^{-1}$."
 The phenomenon of interaction between galaxies is closely related to the occurrence of starbursts (SBs): A large fraction of interacting galaxies (~70%)) exhibits typical characteristica of SBs (Bushouse 1986) and vice versa., The phenomenon of interaction between galaxies is closely related to the occurrence of starbursts (SBs): A large fraction of interacting galaxies $\sim$ ) exhibits typical characteristica of SBs (Bushouse 1986) and vice versa.
 It is also. striking that the majority of infrared-bright galaxies shows evidence for recent interactions as indicated by the presence of close neighbours. or by their disturbed morphology and tidal tails (Joseph et al.," It is also striking that the majority of infrared-bright galaxies shows evidence for recent interactions as indicated by the presence of close neighbours, or by their disturbed morphology and tidal tails (Joseph et al."
 1984: Lonsdale et al., 1984; Lonsdale et al.
 1984: Telesco 1988)., 1984; Telesco 1988).
" The fraction of mergers increases drastically in the infrared luminosity range £L;j; from 10!""L; (12%)) to 1012L.. (95%) (Sanders Mirabel 1996).", The fraction of mergers increases drastically in the infrared luminosity range $L_{IR}$ from $^{10} L_{\sun}$ ) to $^{12} L_{\sun}$ ) (Sanders Mirabel 1996).
 Although a large IR luminosity is not necessarily a tracer for enhanced star formation. it i5 one of the typical features for SB galaxies.," Although a large IR luminosity is not necessarily a tracer for enhanced star formation, it is one of the typical features for SB galaxies."
 Norman Scoville (1988) demonstrated that gas inflow from the galactic disk toward the central region. as required," Norman Scoville (1988) demonstrated that gas inflow from the galactic disk toward the central region, as required"
"Alost Active Galactic Nuelei (ACN) display a 7core|jet"" structure in Very Long Baseline Interferometry (VLBI) images.",Most Active Galactic Nuclei (AGN) display a “core+jet” structure in Very Long Baseline Interferometry (VLBI) images.
 In the standard interpretation. the core is taken to be the optically thick base of the jet (Blandford&Ixónigl 1979).," In the standard interpretation, the core is taken to be the optically thick base of the jet \citep{BK_1979}."
. Due to synchrotron self-absorption. the absolute position of the observed. VLDBI core (7=1 surface) shifts systematically with frequency. moving increasingly outward along the VLBI jet with lower frequency. (IXónigl.1981).," Due to synchrotron self-absorption, the absolute position of the observed VLBI core $\tau=1$ surface) shifts systematically with frequency, moving increasingly outward along the VLBI jet with lower frequency \citep{Konigl_1981}."
. This frequeney-dependent core shift. has a direct effect on astrometric measurements performed in the radio and optical., This frequency-dependent core shift has a direct effect on astrometric measurements performed in the radio and optical.
 In the near future. the GALA astrometry. mission and the Space Interferometry. Mission will begin.," In the near future, the GAIA astrometry mission and the Space Interferometry Mission will begin."
 For both missions. matching the optical astrometric catalogues to the radio catalogues (c.g.Fevetal.2001). presents a very important problem.," For both missions, matching the optical astrometric catalogues to the radio catalogues \citep[e.g.][]{Fey_2001} presents a very important problem."
 The core shifts can introduce. olfsets between the optical ancl radio positions of AGN of up to several rilliareseconcs (Ixovalevetal.2008)... which will strongly alfect the accuracy of matching the radio and optical catalogues.," The core shifts can introduce offsets between the optical and radio positions of AGN of up to several milliarcseconds \citep{Kovalev_2008}, which will strongly affect the accuracy of matching the radio and optical catalogues."
 Core shifts are also needed for the correct reconstruction of VLBI spectral-index αμα rotation-measure maps., Core shifts are also needed for the correct reconstruction of VLBI spectral-index and rotation-measure maps.
 Moreover. knowledge of the [requenev-dependent core shifts can be used to derive physical parameters of the jet. such as the core magnetic field and the distance from the VLBI core to the base of the jet (Lobanov1998:LHirotani2005).," Moreover, knowledge of the frequency-dependent core shifts can be used to derive physical parameters of the jet, such as the core magnetic field and the distance from the VLBI core to the base of the jet \citep{Lobanov_1998,Hirotani_2005}."
. Therefore. precise measurements of the core shifts are necessary.," Therefore, precise measurements of the core shifts are necessary."
 One wav to obtain core shifts is through phase-referencing VLBI observations. however this is a complex ancl resource-intensive technique. and phasc-relerencing core shifts have been determined. for only a few GN. such as 10381528 (Marcaide&Shapiro1984).. 4€ 39.25 (Cuiracloetal. 1995).. 3€ 395 (Laractal.1994)... 3C 390.1. &Lobanov 2001). and AL SL (Dietenholz.Bartel&Itu-pen 2004).," One way to obtain core shifts is through phase-referencing VLBI observations, however this is a complex and resource-intensive technique, and phase-referencing core shifts have been determined for only a few AGN, such as 1038+528 \citep{Marcaide_1984}, 4C 39.25 \citep{Guirado_1995}, 3C 395 \citep{Lara_1994}, 3C 390.1 \citep{Ros_2001}, and M 81 \citep{Bietenholz_2004}."
. Another indirect method to measure core shifts is to align optically thin parts of an AGN jet at dilferen frequencies (e.g.Kovalevetal.2008:Croke&Gatbuzcla2008:OSullivan&Cabuzela 2009).," Another indirect method to measure core shifts is to align optically thin parts of an AGN jet at different frequencies \citep[e.g.][]{Kovalev_2008,Croke_2008,Osullivan_2009}."
. Llowever. this methoc requires simultaneous. nmulti-lrequeney VLBI observations. which are likewise fairly resource intensive. anc does no always vield. unambiguous results.," However, this method requires simultaneous multi-frequency VLBI observations, which are likewise fairly resource intensive, and does not always yield unambiguous results."
 Phe limitations of these techniques are exacerbateck by the fact that the core shif may well depend on the activity state of an ACN. anc therefore be time dependent. whereas at present only isolated core-shift measurements for individual ον are," The limitations of these techniques are exacerbated by the fact that the core shift may well depend on the activity state of an AGN, and therefore be time dependent, whereas at present only isolated core-shift measurements for individual AGN are"
use the published value of 0.23 (?)..,use the published value of 0.23 \citep{daddi07a}.
" As for BX/BM galaxies, the scatter is observed to be z 0.46 dex, about larger than that for BzKs. It is evident from Figure 7bb that the CSF and DLY model predict z0.5 and 0.7 dex decline in the amplitude of the Ψ-Μ., scaling relation, clearly too steep to be supported by the observations at z~2 and 3.7."," As for BX/BM galaxies, the scatter is observed to be $\approx$ 0.46 dex, about larger than that for $BzK$ s. It is evident from Figure \ref{sfh_models}b b that the CSF and DLY model predict $\approx 0.5$ and $0.7$ dex decline in the amplitude of the $\Psi$ $M_*$ scaling relation, clearly too steep to be supported by the observations at $z\sim 2$ and $3.7$."
" In particular, the CSF model requires that the formation redshift is zpe4.8 (500 Myr prior to the observations) to reproduce the observed relation at z~3.729 The implication of the relatively low formation redshift (σε5”4.8 for the Bw-band dropouts, and zp&2.3 for z~2 galaxies) is that the galaxy samples observed at different redshift bins cannot be connected to one another through cosmic time."," In particular, the CSF model requires that the formation redshift is $z_f \approx 4.8$ $\approx$ 500 Myr prior to the observations) to reproduce the observed relation at $z\sim 3.7$ The implication of the relatively low formation redshift $z_f \approx 4.8$ for the $B_W$ -band dropouts, and $z_f \approx 2.3$ for $z\sim2$ galaxies) is that the galaxy samples observed at different redshift bins cannot be connected to one another through cosmic time."
" Such a scenario would not only contradict long duty cycles suggested by the tight W-M, scaling relation but also would require an unrealistic picture in which the majority of the galaxies observed at z~3.7 would suddenly start forming stars at a very short time interval around z—4.8.", Such a scenario would not only contradict long duty cycles suggested by the tight $\Psi$ $M_*$ scaling relation but also would require an unrealistic picture in which the majority of the galaxies observed at $z\sim3.7$ would suddenly start forming stars at a very short time interval around $z=4.8$.
 The EXP model provides a good description of the observations at both redshifts when 7=0.50 Gyr is assumed with the age , The EXP model provides a good description of the observations at both redshifts when $\tau=0.50$ Gyr is assumed (consistent with the age constraints).
A slight change of the (consistentformation redshift (zr=7 or 11 constraints).instead of 8) does not change the timescale more than 50 Myr., A slight change of the formation redshift $z_f=7$ or $11$ instead of $8$ ) does not change the timescale more than 50 Myr.
 The POW model also provides a good description at z~3.7 ? 7bb ? (??)..," The POW model also provides a good description at $z\sim 3.7$ \citet{papovich10} \ref{sfh_models}b \citet{reddy06a} \citep{mannucci09, magdis10}."
by the huninosity ratio of the two stars. 1.0. 7=Lo/Lp = 0.099 + 0.005.,"by the luminosity ratio of the two stars, i.e., $l = L_2/L_{\rm R}$ = 0.099 $\pm$ 0.005."
 The uncertainty is estimated taking the shape of the helt curve outside the eclipse iuto account., The uncertainty is estimated taking the shape of the light curve outside the eclipse into account.
 Iu addition to the depth. we measured the time ciring which the secondary is fully obscured: 1.6140.01 cel. The ingress and egress are sviuuetrie and cach lasts for 0.27640.007 dd. The svnuuetry of the ingress aud egress indicates that the relative acceleration of the linary componcnts between ingress and eeress is equal to zero. Le. it is justified to assmue the skv-projected relative velocity of the two stars to be constant during the eclipse.," In addition to the depth, we measured the time during which the secondary is fully obscured: $1.64
\pm 0.01$ d. The ingress and egress are symmetric and each lasts for $0.276 \pm
0.007$ d. The symmetry of the ingress and egress indicates that the relative acceleration of the binary components between ingress and egress is equal to zero, i.e. it is justified to assume the sky-projected relative velocity of the two stars to be constant during the eclipse."
 The eclipse time depends on the radii of both stars aud the geometry of the system., The eclipse time depends on the radii of both stars and the geometry of the system.
" Kuowine that the eclipse lasts only during  or less of the total orbital period. ic. only a very small seeient of the orbit is covered during the eclipse. aud that the svsteim is viewed close to the orbital plane. προς that the time of total eclipse (Total) Cal be expressed as: with P the orbital period. α the semi-major axis. E the complete elliptic integral. € the /ecceutricitv and oó the latitude of the eclipse ou the stellar dise and Rp aud Ry the radius of the red giant and the secondary. respectively,"," Knowing that the eclipse lasts only during $\sim$ or less of the total orbital period, i.e., only a very small segment of the orbit is covered during the eclipse, and that the system is viewed close to the orbital plane, implies that the time of total eclipse $\tau_{\rm total}$ ) can be expressed as: with $P$ the orbital period, $a$ the semi-major axis, $E$ the complete elliptic integral, $\epsilon$ the eccentricity and $\delta$ the latitude of the eclipse on the stellar disc and $R_{\rm R}$ and $R_2$ the radius of the red giant and the secondary, respectively."
 The total time of iugress. total eclipse aud egress Craperat jog} froin the same geometric considerations can be expressed. as: Dividing Eq. (1))," The total time of ingress, total eclipse and egress $\tau_{\rm in+total+eg}$ ) from the same geometric considerations can be expressed as: Dividing Eq. \ref{tautot}) )"
 by Eq. (2)), by Eq. \ref{tautotal}) )
 provides au estimate of Ro as a fuuction of cosà: with ¢ = RofRp., provides an estimate of $R_2$ as a function of $\cos \delta$: with $r$ = $R_2/R_{\rm R}$.
 In this way we fouud that where e=0.25£0.03., In this way we found that where $x = 0.75 \pm 0.03$.
 Using à = 0 (central eclipse) and the value of the radius of the red-giant star derived in the previous section. we then fid au upper nuit of Rydg XUlhh..," Using $\delta$ = 0 (central eclipse) and the value of the radius of the red-giant star derived in the previous section, we then find an upper limit of $R_2 \le 1.7 \pm
0.1$ $_{\odot}$."
 To coufirin this geometric analysis we computed a basic model of the eclipse signal., To confirm this geometric analysis we computed a basic model of the eclipse signal.
 We neglected lamb darkening and computed the fractional overlap between the two discs. taking iuto account the relative huninositv of the star being eclipsed.," We neglected limb darkening and computed the fractional overlap between the two discs, taking into account the relative luminosity of the star being eclipsed."
 As explained above. we assiuned the skv-projected relative velocity (0) of the two stars to be constant.," As explained above, we assumed the sky-projected relative velocity $v$ ) of the two stars to be constant."
 This iiodoel has been fitted to the portion of the light curve near the eclipse using a \larkov-Chain \Loute Carlo approach (seee.g.Torresetal.2008.andreferences which vields the joiut posterior probability density of all the paramcters. given thedata.," This model has been fitted to the portion of the light curve near the eclipse using a Markov-Chain Monte Carlo approach \citep[see
e.g.][and references therein]{torres2008}, which yields the joint posterior probability density of all the parameters, given thedata."
 The physical parameters in our model are r. ον Ff. and b=sind (the impact parameter).," The physical parameters in our model are $r$, $v$ , $l$ , and $b=\sin\delta$ (the impact parameter)."
 In order to avoid strong correlatious amoug these parameters (in particular between r. c. aud 5). when performing the fit we replace e with COHbey and r with ος.," In order to avoid strong correlations among these parameters (in particular between $r$, $v$, and $b$ ), when performing the fit we replace $v$ with $v^2/(1-b^2)$ and $r$ with $r/v^2$."
 The values of the physical paramicters resulting from this fif are b— r=Lllsz. emΟδqunRe daw. and |=0.10060ono consistent with the values obtained from the ecometric analvsis.," The values of the physical parameters resulting from this fit are $b=0.0^{+0.15}$ , $r=0.1435_{-0.0027}^{+0.0008}$, $v=1.0338_{-0.011}^{+0.0005} R_{\rm R}$ /day, and $l=0.10060_{-0.00006}^{+0.00006}$, consistent with the values obtained from the geometric analysis."
 To test our asstuuption that ο is constant. we repeated the ft with allowing ο to change linearly with time.," To test our assumption that $v$ is constant, we repeated the fit with allowing $v$ to change linearly with time."
 The result was a deceleration of 0.015NESdav? (i.e. ~3% slower at egress than at ingress)., The result was a deceleration of $0.015_{-0.004}^{+0.005} R_{\rm R}/\rm day^2$ (i.e. $\sim 3$ slower at egress than at ingress).
 This may be areal αποαν in the eclipse. Πιο an eccentric orbit.," This may be a real asymmetry in the eclipse, implying an eccentric orbit."
 However. it could also be due to the pulsation signal altering the apparcut shapes of the iugress and egress.," However, it could also be due to the pulsation signal altering the apparent shapes of the ingress and egress."
 We converted the fitted value of 7 into a bolometric huninosity ratio by folding blackbody curves with the spectral respouse curve., We converted the fitted value of $l$ into a bolometric luminosity ratio by folding blackbody curves with the spectral response curve.
 This is a function of the secoudarys temperature. as shown in Fig.," This is a function of the secondary's temperature, as shown in Fig."
 2. (dot-dashlied lines)., \ref{fluxosc} (dot-dashed lines).
" With the constraint from the radius ratio ancl we Bud Lo, = 5.2 4 0.7 L..", With the constraint from the radius ratio and we find $L_2$ = 5.2 $\pm$ 0.7 $_{\odot}$.
 The secondary is thus probably au FE main-sequeuce star., The secondary is thus probably an F main-sequence star.
" Using the masshuuinosity relation for stars with masses between 0.5 aud DOMAL.. Le. GLAEL0)=GUZM.)E, we found a mass for the secondary Mo of T.EE23:0.05 MAL... where we did not take the unucertaiutv of the mass-luuinosity relation iuto account."," Using the mass-luminosity relation for stars with masses between 0.5 and $_{\odot}$, i.e., $(L/L_{\odot})=(M/M_{\odot})^{4.5}$, we found a mass for the secondary $M_2$ of $1.44 \pm 0.05$ $_{\odot}$, where we did not take the uncertainty of the mass-luminosity relation into account."
 We also computed the surface eravity for the secondary aud found log(g») = L2 + 0.1., We also computed the surface gravity for the secondary and found $\log$ $_2$ ) = 4.2 $\pm$ 0.1.
 The binary also has to obey Keplers third law: in which we still have & as unknown. aud we take a nuiunuuni value of Toad for P.," The binary also has to obey Kepler's third law: in which we still have $a$ as unknown, and we take a minimum value of d for $P$ ."
 With this value weconrputed aminimi seniü-najor axis for the svstem of AAT, With this value wecomputed aminimum semi-major axis for the system of AU.
", On the other haud. if we assuue a circular orbit. we can conipute the period."," On the other hand, if we assume a circular orbit, we can compute the period."
 From the eclipse fit we know the, From the eclipse fit we know the
ie. ox. Equations (15)) aud (16)) simply reduce to which corresponds to the propagating kink wave iu a longitudinally homogeneous tube with coustaut kiuk velocity ej.,"i.e., $\Lambda \to \infty$, Equations \ref{eq:vrassymapp}) ) and \ref{eq:wavelengthapp}) ) simply reduce to which corresponds to the propagating kink wave in a longitudinally homogeneous tube with constant kink velocity ${\vk}_0$."
 Both the amplitude and the wavelength are constants in this case., Both the amplitude and the wavelength are constants in this case.
" We compare in Fieure 1 the exact ο). given w Equation (13)) with the expression in the WKB approximation (Equation (15))) for a particular set of xuanmeters,", We compare in Figure \ref{fig:comp} the exact $v_r (z)$ given by Equation \ref{eq:vrgen}) ) with the expression in the WKB approximation (Equation \ref{eq:vrassymapp}) )) for a particular set of parameters.
 We see that there is a very good agreemoeut tween both Equations., We see that there is a very good agreement between both Equations.
 The effect of longitudinal stratification ou both the wavelength and the amplitude is clearly seen in Figur Ἰ., The effect of longitudinal stratification on both the wavelength and the amplitude is clearly seen in Figure \ref{fig:comp}.
", Tere. we iuclude the effect of diuupiug by resonant absorption."," Here, we include the effect of damping by resonant absorption."
 As au exact solution of Equation (12)) is very difficult to obtain. we use the expressions derived in the WISB approximation.," As an exact solution of Equation \ref{eq:vrfull}) ) is very difficult to obtain, we use the expressions derived in the WKB approximation."
 First of all. the expression for ÀA(:) is the same as eiven in Equation (16)) in the case without resonant damping.," First of all, the expression for $\lambda (z)$ is the same as given in Equation \ref{eq:wavelengthapp}) ) in the case without resonant damping."
 Now we compute the damping leusth. {οίτὸν due to resonant absorption uxiug Equation (33)) with the kink velocity given in Equation (12)).," Now we compute the damping length, $\ld (z)$, due to resonant absorption using Equation \ref{eq:damplen}) ) with the kink velocity given in Equation \ref{eq:kinkspeed}) )."
 We obtain We note again that the ratio ZLp(:)/A(:)ds independent of 2., We obtain We note again that the ratio $\ld (z) / \lambda (z)$is independent of $z$.
" Finally. using Equatious (37)) aud (38)) we obtain the expression for ¢,(2) and As). namely with ντ) the amplitude as a function of 2 given by Iu Equation (51)) we see that there are two compoetiug effects that determine the amplitude of the propagating hank wave."," Finally, using Equations \ref{eq:vrexp}) ) and \ref{eq:amptot}) ) we obtain the expression for $v_r (z)$ and $\mathcal{A} (z)$, namely with $\mathcal{A} (z)$ the amplitude as a function of $z$ given by In Equation \ref{eq:amptotres}) ) we see that there are two competing effects that determine the amplitude of the propagating kink wave."
 Ou the oue haud. deusity stratification causes the amplitude to increase with height: on the other hand. resonant absorption damps the kink wave. so its effect is to decrease the amplitude.," On the one hand, density stratification causes the amplitude to increase with height; on the other hand, resonant absorption damps the kink wave, so its effect is to decrease the amplitude."
 Whereas the merease of the amplitude due to longitudinal stratification is independent of w. the damping by resonant absorption docs depend on z.," Whereas the increase of the amplitude due to longitudinal stratification is independent of $\omega$, the damping by resonant absorption does depend on $\omega$."
 Thus. we can anticipate that for a particular. critical frequency. weir. the amplitude mav be a constant independent of +.," Thus, we can anticipate that for a particular, critical frequency, $\omega_{\rm crit}$, the amplitude may be a constant independent of $z$."
 However. due to the functional depeudeuce of Equation (51)) on +. we clearly sce that the amplitude caunot remain coustaut for all :.," However, due to the functional dependence of Equation \ref{eq:amptotres}) ) on $z$, we clearly see that the amplitude cannot remain constant for all $z$."
 Despite this fact. it is still possible to eive an expression for the critical frequency for which the wuplitude is a approximately coustaut for small + only.," Despite this fact, it is still possible to give an expression for the critical frequency for which the amplitude is a approximately constant for small $z$ only."
 To do so. we approximate exp|.z/(2A)|z2/(2A) in Equation (51)).," To do so, we approximate $ 1 - \exp \left[ - z/(2 \Lambda) \right] \approx z/(2 \Lambda)$ in Equation \ref{eq:amptotres}) )."
 Then. we obtaind. For wZweir longitudinal stratification is the dominant effect and the amplitude increase with :.," Then, we obtain For $\omega \lesssim \omega_{\rm crit}$ longitudinal stratification is the dominant effect and the amplitude increase with $z$."
 On the contrary. for x2wai damping by resonant absorption is more cfiicicut and the amplitude decreases ii ;.," On the contrary, for $\omega \gtrsim
\omega_{\rm crit}$ damping by resonant absorption is more efficient and the amplitude decreases in $z$."
 We must bear in müud that Equation (52)) is oulv valid for s12all i. 1.6.. close to the footpoiut of the loop. but gives us some qualitative information about the behavior of the amplitude depending ou the value of the frequelcy.," We must bear in mind that Equation \ref{eq:relationamp0}) ) is only valid for small $z$, i.e., close to the footpoint of the loop, but gives us some qualitative information about the behavior of the amplitude depending on the value of the frequency."
" In Fieure 20 we plot ce,(:) for fixed frequency and loueitudinal imhomogcucity scale height. but for different values of 7/R."," In Figure \ref{fig:reso} we plot $v_r (z)$ for fixed frequency and longitudinal inhomogeneity scale height, but for different values of $l/R$."
 Iu the case 1/R=0 there is no resonant damping., In the case $l/R = 0$ there is no resonant damping.
 As 7/R increases. the wave amplitude decreases as a result of resonant absorption.," As $l/R$ increases, the wave amplitude decreases as a result of resonant absorption."
 However. we see that the waveleneth is independent of the value of //R.," However, we see that the wavelength is independent of the value of $l/R$ ."
 This means that. in the TTTD approximation. resonant absorption does not affect the value of the wavelength. which is exclusively determined bv the longitudinal inhomogeneity scale height.," This means that, in the TTTB approximation, resonant absorption does not affect the value of the wavelength, which is exclusively determined by the longitudinal inhomogeneity scale height."
 This is au important result from the observational point of, This is an important result from the observational point of
region of increasing longitudinal field at (he southern tip of the region of negative polarity.,region of increasing longitudinal field at the southern tip of the region of negative polarity.
 The field changes vary. widely in duration and some variation in start times is evident in the n| and fy maps. respectively.," The field changes vary widely in duration and some variation in start times is evident in the $n^{-1}$ and $t_0$ maps, respectively."
 Some field changes that occur early in the largest region of positive polarity close to the neutral line appear to propagate soull west across this region., Some field changes that occur early in the largest region of positive polarity close to the neutral line appear to propagate south west across this region.
 This phenomenon is similar to that observed in the 2001 December 11 flare by SII05., This phenomenon is similar to that observed in the 2001 December 11 flare by SH05.
 The a7 map shows the scatter in (he data with respect to the fit of Equation (1)) to the data., The $\sigma^2$ map shows the scatter in the data with respect to the fit of Equation \ref{atancurve}) ) to the data.
 The scatter (the noise) is greatest where the field is strongest and the field gradient is steepest., The scatter (the noise) is greatest where the field is strongest and the field gradient is steepest.
 Therefore the σ” map tends to resemble the absolute value of the α map., Therefore the $\sigma^2$ map tends to resemble the absolute value of the $a$ map.
 This is the case in our example in Figure 4 except that the strong positive region in the south-west of the active region does not appear stronelv in the 6? map because the noise level in the South-West is unusually low., This is the case in our example in Figure \ref{bigarray} except that the strong positive region in the south-west of the active region does not appear strongly in the $\sigma^2$ map because the noise level in the South-West is unusually low.
 The GONG instrumentation is identical in design across the network so that images taken simultaneously by (wo different telescopes should be nearly identical., The GONG instrumentation is identical in design across the network so that images taken simultaneously by two different telescopes should be nearly identical.
 We compared pairs of parameter maps lor each of the six [lares observed. by (wo sites sinnltaneously., We compared pairs of parameter maps for each of the six flares observed by two sites simultaneously.
 While instrumental differences and differences in seeing conditions inevitably prevent perfect malches between the image pairs. the close resemblance between each pair provides a foundation for confidence in our results.," While instrumental differences and differences in seeing conditions inevitably prevent perfect matches between the image pairs, the close resemblance between each pair provides a foundation for confidence in our results."
 $1105 already. verified that (he analvsis gave very similar results when applied to GONG and ALDI data for the 2003 October 29 flare., SH05 already verified that the analysis gave very similar results when applied to GONG and MDI data for the 2003 October 29 flare.
 The remapped images for a given [lare are stacked (o form a space-time data cube., The remapped images for a given flare are stacked to form a space-time data cube.
 Figure 5 shows the evolution of a 16x subset of pixels in the form of a 16x mosaic of plots of field strength against time arranged to reflect the spatial distribution of (he pixels., Figure \ref{mosaic} shows the evolution of a $16\times 16$ subset of pixels in the form of a $16\times 16$ mosaic of plots of field strength against time arranged to reflect the spatial distribution of the pixels.
 In each individual plot of the mosaic. the horizontal axis is lime. spanning the four-hour duration of the time series centered at the GOES start Gime of the flare. aud (he vertical axis is field intensity.," In each individual plot of the mosaic, the horizontal axis is time, spanning the four-hour duration of the time series centered at the GOES start time of the flare, and the vertical axis is field intensity."
 The region chosen for this particular mosaic straddles (he neutral line of the field-chanee map (parameter c) in Figure 4.., The region chosen for this particular mosaic straddles the neutral line of the field-change map (parameter $c$ ) in Figure \ref{bigarray}.
 In the mosaic the neutral line appears as a swath of plots without well-defined stepwise changes. extending from the south east corner to (he north west corner of the mosaic.," In the mosaic the neutral line appears as a swath of plots without well-defined stepwise changes, extending from the south east corner to the north west corner of the mosaic."
 This swath separates a contiguous region of posiüve field changes in the North-East. whose boundary is marked with a red line. and a contiguous region of negative changes in the South-West. whose boundary is marked with a blue line.," This swath separates a contiguous region of positive field changes in the North-East, whose boundary is marked with a red line, and a contiguous region of negative changes in the South-West, whose boundary is marked with a blue line."
 The positive changes above the left part of the red line are significantly stronger (han anvthing reported in $1105., The positive changes above the left part of the red line are significantly stronger than anything reported in SH05.
 There is also a large. contiguous group of beautiful. low-noise field changes in the bottom-right of the mosaic.," There is also a large, contiguous group of beautiful, low-noise field changes in the bottom-right of the mosaic."
 Some plots show spikes because of [Iare-induced line profile changes: the line goes into emission rather (han absorption. resulting in unphvsical measurements (Edelinan et al.," Some plots show spikes because of flare-induced line profile changes; the line goes into emission rather than absorption, resulting in unphysical measurements (Edelman et al."
 2004)., 2004).
 Examples of this phenomenon include the pixels al the bottom left of the mosaic., Examples of this phenomenon include the pixels at the bottom left of the mosaic.
 The noise is almost all seeing-velatecd and its strength is sensitive to local intensity gradients and magnetic field gradients., The noise is almost all seeing-related and its strength is sensitive to local intensity gradients and magnetic field gradients.
"Shapiro (1991; AS91 henceforth) estimated As,=0.91 keV. 2.9 keV and 4.9 keV for Bo=107 G. 5x10 G and LOM G. respectively.","Shapiro (1991; AS91 henceforth) estimated $\Delta\varepsilon_c=0.91$ keV, 2.9 keV and 4.9 keV for $B_s=10^{12}$ G, $5\times 10^{13}$ G and $10^{13}$ G, respectively."
" These values were approximated. by Usov&Melrose(1995) in the form As,~(0.9keV)(B,/10P7.Co!) which leads to critical LeniperaturesKN.()On the other hand. Jones (1986: J86 henceforth) obtained much lower cohesive energies As,=0.29 keV. 0.60 keV and 0.92 keV [or B;=2x107 G. 5x107 G and 105 G. respectively."," These values were approximated by \citet{um95} in the form $\Delta\varepsilon_c\simeq(0.9{\rm keV})(B_s/10^{12}~{\rm
G})^{0.73}$, which leads to critical temperatures On the other hand, Jones (1986; J86 henceforth) obtained much lower cohesive energies $\Delta\varepsilon_c=0.29$ keV, 0.60 keV and 0.92 keV for $B_s=2\times 10^{12}$ G, $5\times 10^{12}$ G and $10^{13}$ G, respectively."
" They can be approximated by As,c(0.18keV)(B,/10P7CO)!"" and converted (o critical temperatures79."," They can be approximated by $\Delta\varepsilon_c\simeq(0.18\ {\rm keV})(B_s/10^{12}{\rm
G})^{0.7}$ and converted to critical temperatures."
IK. (4)Delow we consider the condition. T;/T;>1. using both expressions for critical temperatures described bv equations (3) and (4). for CI- and ICS-dominated NTVG models. separately.," Below we consider the condition $T_i/T_s>1$, using both expressions for critical temperatures described by equations (3) and (4), for CR- and ICS-dominated NTVG models, separately."
" In this case the gap height /—fey is determined by the condition that f—με. where lyn2sinR=(D/D,yR is the mean Iree path [or pair production by a photon propagating al an angle 8 to the local surface magnetic field (RS75)."," In this case the gap height $h=h_{CR}$ is determined by the condition that $h=l_{ph}$, where $l_{ph}\approx\sin\theta\ {\cal
R}=(B_\perp/B_s){\cal R}$ is the mean free path for pair production by a photon propagating at an angle $\theta$ to the local surface magnetic field (RS75)."
" The CR-NTWVG model is described bv the following parameters: the height of a quasi steady. gap(ay, (notice (vpographical errors in eq. [", The CR-NTVG model is described by the following parameters: the height of a quasi steady gap (notice typographical errors in eq. [
6] of GMOL. which are corrected here). the gap potential drop (Gand the surface temperature,"6] of GM01, which are corrected here), the gap potential drop and the surface temperature"
value; the 1:3 ratio of amplitudes of the [OIII]4959À and [OIIIJ5007À narrow components is fixed.,value; the 1:3 ratio of amplitudes of the $\AA$ and $\AA$ narrow components is fixed.
" After adjusting the narrow components, broad Gaussian components are added to the Hf line, and the joint fit is further adjusted until the relative residuals are reduced to below 0.02-0.03."," After adjusting the narrow components, broad Gaussian components are added to the $\beta$ line, and the joint fit is further adjusted until the relative residuals are reduced to below 0.02-0.03."
" The STARLIGHT model for the observed spectra also yields thelight fraction xj, mass fraction Mini;, age τι, and metallicity Zj, of the stellar populations used in the fit."," The STARLIGHT model for the observed spectra also yields thelight fraction $x_\mathrm{j}$, mass fraction $M\mathrm{ini}_\mathrm{j}$, age $\tau_\mathrm{j}$, and metallicity $Z_\mathrm{j}$, of the stellar populations used in the fit."
 We use these parameters to derive starburst histories and estimate the epochs of the most recent starbursts in the studied galaxies., We use these parameters to derive starburst histories and estimate the epochs of the most recent starbursts in the studied galaxies.
 We apply Gaussian smoothing to the individual starburst events (see Fig. 2)), We apply Gaussian smoothing to the individual starburst events (see Fig. \ref{fig11}) )
 and determine the epoch of the most recent starburst episode., and determine the epoch of the most recent starburst episode.
" Most of the X-shaped radio sources and some objects from the control sample are type II AGN (weakly beamed radio sources), for which STARLIGHT cannot provide reliable estimates of the AGN continuum flux."," Most of the X-shaped radio sources and some objects from the control sample are type II AGN (weakly beamed radio sources), for which STARLIGHT cannot provide reliable estimates of the AGN continuum flux."
" We estimate the frame continuum flux at 5100 ffrom the SDSS photometry, with the relation (Wu Liu 2004)) where is the redshift and the and fiber magnitudes are obtained from the SDSS and corrected for the Galactic extinction Ay (taken from Schlegel et al. 1998))."," We estimate the rest-frame continuum flux at 5100 from the SDSS photometry, with the relation (Wu Liu \cite{wu}) ) where is the redshift and the and fiber magnitudes are obtained from the SDSS and corrected for the Galactic extinction $A_{V}$ (taken from Schlegel et al. \cite{schlegel}) )."
" It should be noted that the flux obtained with this method also contains a contribution from the host galaxy, but this does not introduce a strong bias in our estimates."," It should be noted that the flux obtained with this method also contains a contribution from the host galaxy, but this does not introduce a strong bias in our estimates."
" To assess the spectral classification of the X-shaped and control host galaxies, we measure the Ca II break of their absoption optical spectrum."," To assess the spectral classification of the X-shaped and control host galaxies, we measure the Ca II break of their absoption optical spectrum."
" This break is typically seenin the spectrum of elliptical galaxies and is described by a factor Cean=(f+—f/f. where f- and f, are the fluxes in the rest frame wavelength regions 3750-3950 A and 4050-4250 À, respectively (Landt et al. 2002))."," This break is typically seenin the spectrum of elliptical galaxies and is described by a factor $C_\mathrm{Ca\,II} = (f_{+} - f_{-})/f_{+}$, where $f_{-}$ and $f_{+}$ are the fluxes in the rest frame wavelength regions 3750-3950 $\AA$ and 4050-4250 $\AA$, respectively (Landt et al. \cite{landt}) )."
 The Ca II break was used as an additional criterion to separate blazars from radio galaxies., The Ca II break was used as an additional criterion to separate blazars from radio galaxies.
 Stocke et al. (1991)), Stocke et al. \cite{stocke}) )
 adopted a maximum value of σι=0.25 for BL Lacs to ensure the presence of a substantial non-thermal jet continuum in addition to the thermal spectrum of the elliptical host galaxy.," adopted a maximum value of $C_\mathrm{Ca\,II} = 0.25$ for BL Lacs to ensure the presence of a substantial non-thermal jet continuum in addition to the thermal spectrum of the elliptical host galaxy."
 This limit was later increased to Ccar<0.4 by other authors (Marcha et al. 1996;;," This limit was later increased to $C_\mathrm{Ca\,II} <0.4$ by other authors (Marcha et al. \cite{marcha};"
 Plotkin et al. 2008))., Plotkin et al. \cite{plotkin}) ).
 Landt et al. (2010)), Landt et al. \cite{landt2010}) )
 provide the Ca II break values of 16 of the X-shaped sources studied here., provide the Ca II break values of 16 of the X-shaped sources studied here.
" For the rest of the X-shaped sources and control objects, we measure the C factor of the rest- optical spectra using the IRAF task guiapps.spectool."," For the rest of the X-shaped sources and control objects, we measure the $C$ factor of the rest-frame optical spectra using the IRAF task guiapps.spectool."
" The measured stellar velocity dispersion, σ.., can be connected with the mass, Mgg, of the central black hole through an empirical relation (Gebhardt et al. 2000;;"," The measured stellar velocity dispersion, $\sigma_{*}$, can be connected with the mass, $M_\mathrm{BH}$, of the central black hole through an empirical relation (Gebhardt et al. \cite{gebhardt}; ;"
 Tremaine et al. 2002)): .., Tremaine et al. \cite{tremaine}) ): .
 This relation is valid under the assumption that the kinematics of the stars in the bulge of the host galaxy is dominated by, This relation is valid under the assumption that the kinematics of the stars in the bulge of the host galaxy is dominated by
in the VIS. the Fraunhofer A-band of Os. and the Chappuis band of O;.,"in the VIS, the Fraunhofer A-band of $\mathrm{O_2}$, and the Chappuis band of $\mathrm{O_3}$."
 Owing to the high resolution of their spectra. ? were also able to identify the weak Fraunhofer B-band of Os. which. however. is too narrow and too weak to be observable at low resolution.," Owing to the high resolution of their spectra, \citet{Tinetti2006a} were also able to identify the weak Fraunhofer B-band of $\mathrm{O_2}$, which, however, is too narrow and too weak to be observable at low resolution."
 Our results also agree with the principle radiative effects of clouds reported by ?? and ?.. namely that they cause an increase in scattered radiation and depths of absorption bands.," Our results also agree with the principle radiative effects of clouds reported by \citet{Tinetti2006a,Tinetti2006b} and \citet{Kaltenegger2007ApJ}, namely that they cause an increase in scattered radiation and depths of absorption bands."
 Our simplified radiative transfer model ts therefore suitable for studying the basic effects of the considered two cloud types on the reflection spectra of like extrasolar planets., Our simplified radiative transfer model is therefore suitable for studying the basic effects of the considered two cloud types on the reflection spectra of Earth-like extrasolar planets.
 The present study 1s focused on the effect of water and ice clouds 1n. Earth-like planetary atmospheres., The present study is focused on the effect of water and ice clouds in Earth-like planetary atmospheres.
 Given a present Earth-like chemical composition of the atmosphere. only the molecules Oo. HO. and in principle also O; have detectable features in the NUV-VIS wavelength range at low resolution.," Given a present Earth-like chemical composition of the atmosphere, only the molecules $\mathrm{O_2}$, $\mathrm{H_2 O}$, and in principle also $\mathrm{O_3}$ have detectable features in the NUV-VIS wavelength range at low resolution."
" However. as pointed out by ? CO» or CH, should also be visible at low resolution if their abundances im the atmosphere wereinereased."," However, as pointed out by \citet{Kaltenegger2009} $\mathrm{CO_2}$ or $\mathrm{CH_4}$ should also be visible at low resolution if their abundances in the atmosphere were."
". During an earlier epoch of the Earth. CH, might have been visible (see 2)). whereas CO» could be observed in the ΝΙΚ of the reflection spectrum of a CO: ""Sominated atmosphere such as Venus (?).."," During an earlier epoch of the Earth, $\mathrm{CH_4}$ might have been visible (see \citet{Kaltenegger2007ApJ}) ), whereas $\mathrm{CO_2}$ could be observed in the NIR of the reflection spectrum of a $\mathrm{CO_2}$ dominated atmosphere such as Venus \citep{Vasquez2010ASPC}."
" The effect of other cloud types (such as CO» ice clouds) ""Sepend in general on their optical properties (scattering phase >unction. scattering and absorption coefficients. and optical ""Sepths). which can be very different from those of the water and ice clouds considered here."," The effect of other cloud types (such as $\mathrm{CO_2}$ ice clouds) depend in general on their optical properties (scattering phase function, scattering and absorption coefficients, and optical depths), which can be very different from those of the water and ice clouds considered here."
 These properties. though. are Complicated functions of particle size distribution. refractive dices. or particle shape. which in turn depend strongly on the atmospheric conditions.," These properties, though, are complicated functions of particle size distribution, refractive indices, or particle shape, which in turn depend strongly on the atmospheric conditions."
 The effects of clouds on a reflection spectrum are also largely determined by the cloud altitude within the atmosphere., The effects of clouds on a reflection spectrum are also largely determined by the cloud altitude within the atmosphere.
 Only spectral features originating from molecules above the cloud layer(s) can be enhanced in the reflection spectra by the increase in back-scattered radiation caused by cloud particles., Only spectral features originating from molecules above the cloud layer(s) can be enhanced in the reflection spectra by the increase in back-scattered radiation caused by cloud particles.
 We now study the effects of single and multi-layered clouds on the reflection spectra and spectral albedos of Earth-like extrasolar planets orbiting different types of central stars., We now study the effects of single and multi-layered clouds on the reflection spectra and spectral albedos of Earth-like extrasolar planets orbiting different types of central stars.
 To illustrate the basic effects of the two different cloud types on the reflection spectra and planetary albedos. we first present calculations using only single cloud layers.," To illustrate the basic effects of the two different cloud types on the reflection spectra and planetary albedos, we first present calculations using only single cloud layers."
 We then discuss the corresponding effects of multi-layered clouds yielding mean Earth surface temperatures of 288K., We then discuss the corresponding effects of multi-layered clouds yielding mean Earth surface temperatures of $288 \ \mathrm{K}$.
 For each stellar type we calculated low-resolution reflection spectra of Earth-like planets for single low-level water and high-level ice clouds., For each stellar type we calculated low-resolution reflection spectra of Earth-like planets for single low-level water and high-level ice clouds.
 In Fig., In Fig.
 + we depict the resulting spectra for three representative cloud coverages(3066...70%.. and 100%)) and the respective clear sky cases.," \ref{spectra_single_layer} we depict the resulting spectra for three representative cloud coverages, and ) and the respective clear sky cases."
 This shows that clouds have a strong impact on the reflection spectra by increasing the amount of reflected incident stellar radiation due to the scattering of cloud particles and leading to deeper molecular absorption. bands. such as O» and H:O.," This shows that clouds have a strong impact on the reflection spectra by increasing the amount of reflected incident stellar radiation due to the scattering of cloud particles and leading to deeper molecular absorption bands, such as $\mathrm O_2$ and $\mathrm H_2 \mathrm O$."
 The reflection spectra depend directly on the spectral energy distribution of the incident stellar radiation., The reflection spectra depend directly on the spectral energy distribution of the incident stellar radiation.
 The incident stellar spectra. therefore. determine the spectral signatures that can be found in the reflection spectra.," The incident stellar spectra, therefore, determine the spectral signatures that can be found in the reflection spectra."
 In case of the M-type star. for example. only the HO absorption features (~0.95yam. ~1.1gm. -1.4um. and ~2wm) can be seen at low resolution.," In case of the M-type star, for example, only the $\mathrm H_2 \mathrm O$ absorption features $\sim 0.95 \ \mathrm{\mu m}$, $\sim 1.1 \ \mathrm{\mu m}$, $\sim 1.4 \ \mathrm{\mu m}$, and $\sim 2 \ \mathrm{\mu m}$ ) can be seen at low resolution."
 In contrast. these bands are almost invisible for the F-type star spectrum because this stellar type emits very little in that wavelength region (see Fig. 1).," In contrast, these bands are almost invisible for the F-type star spectrum because this stellar type emits very little in that wavelength region (see Fig. \ref{stellar_spectra}) )."
 The K-type star is particularly interesting because of its spectral maximum near the Chappuis band of Ox at 9.6ym., The K-type star is particularly interesting because of its spectral maximum near the Chappuis band of $\mathrm O_3$ at $9.6 \ \mathrm{\mu m}$.
 Therefore. this is the only case where ozone can be directly detected in the low-resolution reflection spectra for high cloud covers.," Therefore, this is the only case where ozone can be directly detected in the low-resolution reflection spectra for high cloud covers."
 For large cloud coverages the O» signature at 0.76pm can also be identified in the spectra for all types of central stars with the exception of the M-star case., For large cloud coverages the $\mathrm O_2$ signature at $0.76 \ \mathrm{\mu m}$ can also be identified in the spectra for all types of central stars with the exception of the M-star case.
 In general. the low-level water clouds have a larger overall effect on the reflection spectra than the high-level ice because of their much higher scattering optical depth.," In general, the low-level water clouds have a larger overall effect on the reflection spectra than the high-level ice because of their much higher scattering optical depth."
 Since the optical depths of both clouds is almost constant in. the wavelength range of the maxima of the incident stellar (i.e. t« 25m». clouds basically scatter the incident stellar radiation without changing its spectral distribution. in contrast to the effect of Rayleigh scattering.," Since the optical depths of both clouds is almost constant in the wavelength range of the maxima of the incident stellar (i.e. $\lambda < 2 \mu \mathrm m$ ), clouds basically scatter the incident stellar radiation without changing its spectral distribution, in contrast to the effect of Rayleigh scattering."
 The Rayleigh scattering by molecules results in the well-known blue shift of the reflected light caused by the 277-dependence of the Rayleigh scattering cross-section., The Rayleigh scattering by molecules results in the well-known blue shift of the reflected light caused by the $\lambda^{-4}$ -dependence of the Rayleigh scattering cross-section.
 For small cloud coverages this effect dominates the reflection spectra., For small cloud coverages this effect dominates the reflection spectra.
 Figure 5. also shows that in the M-star case considerably less radiation is back-scattered. even though the overall energy input is the same at the top of the planetary atmospheres for all central stars.," Figure \ref{ratio_single_layer} also shows that in the M-star case considerably less radiation is back-scattered, even though the overall energy input is the same at the top of the planetary atmospheres for all central stars."
 This is a direct consequence of the ο -dependence of the Rayleigh scattering., This is a direct consequence of the $\lambda^{-4}$ -dependence of the Rayleigh scattering.
 For longer wavelengths. Rayleigh scattering becomes inefficient leading to much less back-scattered incident stellar radiation for the M-type star (maximum of stellar spectrum at about 1im. see Fig. 1))," For longer wavelengths, Rayleigh scattering becomes inefficient leading to much less back-scattered incident stellar radiation for the M-type star (maximum of stellar spectrum at about $1 \ \mathrm{\mu m}$, see Fig. \ref{stellar_spectra}) )"
 than for instance the F-star case (maximum at ca., than for instance the F-star case (maximum at ca.
 0.4 μη)., $0.4 \ \mathrm{\mu m}$ ).
 The planetary albedos presented in Fig., The planetary albedos presented in Fig.
 5 have been calculated for the same cloud cover scenarios as in Fig. 4.., \ref{ratio_single_layer} have been calculated for the same cloud cover scenarios as in Fig. \ref{spectra_single_layer}.
 Por presentational reasons. the results for all four stellar types are plotted here in a single diagram for each cloud coverage.," For presentational reasons, the results for all four stellar types are plotted here in a single diagram for each cloud coverage."
 For a given cloud cover. the planetary albedos are obviously almost independent of the spectral energy distribution of the incident stellar radiation in contrast to the reflection spectra (cf.," For a given cloud cover, the planetary albedos are obviously almost independent of the spectral energy distribution of the incident stellar radiation in contrast to the reflection spectra (cf."
 Fig. 4)., Fig. \ref{spectra_single_layer}) ).
 They depend mainly on only the atmospheric chemical composition and the optical properties of the cloud, They depend mainly on only the atmospheric chemical composition and the optical properties of the cloud
Tn stars such as SV. Vul (Fie. 2)),In stars such as SV Vul (Fig. \ref{fig2}) )
 aud DC Cre (Fie. D) , and BC Cyg (Fig. \ref{fig4}) )
the computed values of fale)? initially increase directly in proportion to increasing differences in evele count25 as predicted for a stochastic process (Eddington&Plakidis1929).," the computed values of $\langle u(x) \rangle^2$ initially increase directly in proportion to increasing differences in cycle count, as predicted for a stochastic process \citep{1}."
. At lareer evele differences. however. the trend is reversed as the dominant pulsation iu such stars relmposcs its reguluidtv in the observed times of light maxinuun.," At larger cycle differences, however, the trend is reversed as the dominant pulsation in such stars reimposes its regularity in the observed times of light maximum."
 The observed values of (μὴ) therefore become very sinall for large cvele differences., The observed values of $\langle u(x) \rangle$ therefore become very small for large cycle differences.
 Sinuilu characteristics are observed in inany different pulsating stars. and was also noted by Eddineton&Plakidis(1929).," Similar characteristics are observed in many different pulsating stars, and was also noted by \citet{1}."
. Stochastic fluctuations iu period appear to be a colon feature of nearly all pulsating stars. but thev are invariably dominated by the regular pulsation iu such stars.," Stochastic fluctuations in period appear to be a common feature of nearly all pulsating stars, but they are invariably dominated by the regular pulsation in such stars."
 The physical processes respousible for such fluctuations are uncertain. but prestunably they originate in temporal modifications of envelope convection m such stars.," The physical processes responsible for such fluctuations are uncertain, but presumably they originate in temporal modifications of envelope convection in such stars."
The coellicients αν ave presented in Table 1.,The coefficients $a_{ij}$ are presented in Table 1.
 The accuracy of the fitting is generally better than0., The accuracy of the fitting is generally better than.
14. ]toh et al. (, Itoh et al. (
1979) analvzed the results of the Monte Carlo computations for the screening potentials of the ionic mixtures of various charge ratios and concentration ratios carried oul bv them and also by Hansen. Torrie. Vieillelosse (1977).,"1979) analyzed the results of the Monte Carlo computations for the screening potentials of the ionic mixtures of various charge ratios and concentration ratios carried out by them and also by Hansen, Torrie, Vieillefosse (1977)."
" They have established that the screening potential at intermediate distances //;;(r) lor a mixture of two kinds of ions with charges and imunber densities (Z,¢.nq) ancl (Zoe.ns) given below fits the Monte Carlo results excellently within the inherent Monte Carlo noise: We also clefine (he parameter where 45; 1s the reduced mass for the two ions with charges Z; and Z;."," They have established that the screening potential at intermediate distances $H_{ij}(r)$ for a mixture of two kinds of ions with charges and number densities $(Z_{1}e, n_{1})$ and $(Z_{2}e, n_{2})$ given below fits the Monte Carlo results excellently within the inherent Monte Carlo noise: We also define the parameter where $\mu_{ij}$ is the reduced mass for the two ions with charges $Z_{i}$ and $Z_{j}$."
 Then the enhancement factor for the resonant thermonuclear rates of the (wo nuclei Z; and Z; is given bv, Then the enhancement factor for the resonant thermonuclear rates of the two nuclei $Z_{i}$ and $Z_{j}$ is given by
representative pixels represent (he [fastest and strongest field changes. [ree of artifacts. bul do not present a complete picture of the changes to the magnetic field in an active region.,"representative pixels represent the fastest and strongest field changes, free of artifacts, but do not present a complete picture of the changes to the magnetic field in an active region."
 Magnetic [Iux calculations capture the effects of (Iares on entire active regions., Magnetic flux calculations capture the effects of flares on entire active regions.
 In this section. we estimate the change in the magnetic flux during each flare.," In this section, we estimate the change in the magnetic flux during each flare."
 Because all of the pixels in a remapped image have equal area. the net [lux is just the sum of the field changes over all of (he pixels in the remapped image.," Because all of the pixels in a remapped image have equal area, the net flux is just the sum of the field changes over all of the pixels in the remapped image."
 We eliminate from consideration. of course. those pixels for which (he parameters of the fit of Equation (1)) to the time series plot do not satislv all of the criteria (a-c) described in Section 4..," We eliminate from consideration, of course, those pixels for which the parameters of the fit of Equation \ref{atancurve}) ) to the time series plot do not satisfy all of the criteria (a-d) described in Section \ref{fieldchanges}."
 These flix caleulations no doubt include some false positives. but we expect these {ο average out.," These flux calculations no doubt include some “false positives”, but we expect these to average out."
 Figure 7 shows histograms of the net (bottom left) and unsigned (bottom right) magnetic flux changes for all 77 flaves in this study., Figure \ref{fchangehist} shows histograms of the net (bottom left) and unsigned (bottom right) magnetic flux changes for all 77 flares in this study.
 The vast majority of the flix changes are towards the weak end of the scale., The vast majority of the flux changes are towards the weak end of the scale.
 About half of the flares fall into the first bin in each histogram., About half of the flares fall into the first bin in each histogram.
 Like the histogram of field changes in the same figure. these histograms resemble power laws but with a stronger power index.," Like the histogram of field changes in the same figure, these histograms resemble power laws but with a stronger power index."
 The flux changes have a greater range of values than the field changes do because the area is a varving parameter in the flux calculations but not in the field intensity calculations., The flux changes have a greater range of values than the field changes do because the area is a varying parameter in the flux calculations but not in the field intensity calculations.
 Table 5. shows the statistics for the increases and decreases in net ancl unsigned flux., Table \ref{fluxincdectable} shows the statistics for the increases and decreases in net and unsigned flux.
 The net [Iuxes increase in approximately equal numbers in general (compare the first two columns of Table 5))., The net fluxes increase in approximately equal numbers in general (compare the first two columns of Table \ref{fluxincdectable}) ).
 Unsigned fIuxes. on the other hand. decrease lor nearly (wo thirds of (he flares overall (see the top line of Table 5)). aud for those near disk-center as well as those near the limb (lines 4 and 5 of Table 5)).," Unsigned fluxes, on the other hand, decrease for nearly two thirds of the flares overall (see the top line of Table \ref{fluxincdectable}) ), and for those near disk-center as well as those near the limb (lines 4 and 5 of Table \ref{fluxincdectable}) )."
 For X-class flares the ratio of [ιν decreases to increases is ereater (han 2:1 while for M-class flares (he ratio is closer to 1:1 (compare lines 2 and 3 of Table 5))., For X-class flares the ratio of flux decreases to increases is greater than 2:1 while for M-class flares the ratio is closer to 1:1 (compare lines 2 and 3 of Table \ref{fluxincdectable}) ).
 X-class flares near disk-center show three times as many decreases as increases in unsigned (lux whereas X-class flares near the limb show fewer than twice as many (lines 6 and 8 of Table 5.., X-class flares near disk-center show three times as many decreases as increases in unsigned flux whereas X-class flares near the limb show fewer than twice as many (lines 6 and 8 of Table \ref{fluxincdectable}.
 The corresponding M-class statistics are closer (o 1:1. perhaps," The corresponding M-class statistics are closer to 1:1, perhaps"
the parallax. and τμ can be caleulated.,"the parallax, and $T_{\rm eff}$ can be calculated."
 We combine our results with those from stellar oscillation frequencies to more completely unclerstand the svstem through a description of the central stars and exoplanets masses ancl the extent of the habitable zone., We combine our results with those from stellar oscillation frequencies to more completely understand the system through a description of the central star's and exoplanet's masses and the extent of the habitable zone.
 Section 2 details our observing procedure. Section 3D discusses how + Dra's angular diameter and Zr were determined. ancl Section 4 explores the physical implications of (he new measurements.," Section 2 details our observing procedure, Section 3 discusses how $\iota$ Dra's angular diameter and $T_{\rm eff}$ were determined, and Section 4 explores the physical implications of the new measurements."
 Observations were obtained using the CIARA Array. a six element Y-shaped optical- interferometer located on Mount Wilson. California (tenDrimnmelaarοἱal.2005).," Observations were obtained using the CHARA Array, a six element Y-shaped optical-infrared interferometer located on Mount Wilson, California \citep{2005ApJ...628..453T}."
". We used the CILARA Classic and CLIMB beam combiners in the A""-band (2.13 jan) while visible wavelengths (470-800 nm) were used for tracking ancl tip/üilt corrections.", We used the CHARA Classic and CLIMB beam combiners in the $K'$ -band (2.13 $\mu$ m) while visible wavelengths (470-800 nm) were used for tracking and tip/tilt corrections.
 The observing procedure and data reduction process employed. here are described in (2005).., The observing procedure and data reduction process employed here are described in \citet{2005ApJ...628..439M}.
 We observed + Dra over four nights spanning four vears wilh two baselines: in 2007 and 2008. we used the longest telescope pair $1-E1 with a maximum baseline of 331 m and in 2011. we used a shorter telescope pair WI1-W2 with a maximunm baseline of 108 Chosing proper calibrator stars is vital because they act as (he standard against which (he scientific target is measured.," We observed $\iota$ Dra over four nights spanning four years with two baselines: in 2007 and 2008, we used the longest telescope pair S1-E1 with a maximum baseline of 331 m and in 2011, we used a shorter telescope pair W1-W2 with a maximum baseline of 108 Chosing proper calibrator stars is vital because they act as the standard against which the scientific target is measured."
 We selected four calibrators (ID 1239985. IID 139778. ID 141472. ancl IID 145454) because thev are single stars with expected visibility amplitudes 2804. so they were verv nearly unresolved on the baseline used.," We selected four calibrators (HD 128998, HD 139778, HD 141472, and HD 145454) because they are single stars with expected visibility amplitudes $>$ $\%$ so they were very nearly unresolved on the baseline used."
 This meant uncertainties in (he calibrators ciameters did not affect the target's diameter caleulation as much as if the calibrator stars had a significant angular size on the sky., This meant uncertainties in the calibrators' diameters did not affect the target's diameter calculation as much as if the calibrator stars had a significant angular size on the sky.
 We interleaved calibrator aud target star observations so that every target was flanked by calibrator observations macle as close in time as possible. which allowed us to convert instrumental target and calibrator visibilities to calibrated visibilities for the target.," We interleaved calibrator and target star observations so that every target was flanked by calibrator observations made as close in time as possible, which allowed us to convert instrumental target and calibrator visibilities to calibrated visibilities for the target."
 To check for possible unseen close companions that would contaminate our observations. we created spectral energy distribution (SED) fits based on published UBWRIJIL photometric values obtained from the literature for each calibrator to establish diameter estimates.," To check for possible unseen close companions that would contaminate our observations, we created spectral energy distribution (SED) fits based on published $UBVRIJHK$ photometric values obtained from the literature for each calibrator to establish diameter estimates."
 We combined the photometry with Nurnez model based on Ti and log g values to caleulate angular diameters for (he calibrators., We combined the photometry with Kurucz model based on $T_{\rm eff}$ and log $g$ values to calculate angular diameters for the calibrators.
 The stellar models were fit to observed, The stellar models were fit to observed
The model used i the simulations is the same as that of Draudeuburg e al. (1996)).,The model used in the simulations is the same as that of Brandenburg et al. \cite{brandenburg96}) ).
 T1ο shuulatiou domain consists of a recaneular box wuch is defined on a Cartesian grid.wi hoe aud y denoting the two horizontal coordinates (corres»ondius to latiude and longitude im spherical coordinates). and +denoting depth. respecively (Fig. 1)).," The simulation domain consists of a rectangular box which is defined on a Cartesian grid,with $x$ and $y$ denoting the two horizontal coordinates (corresponding to latitude and longitude in spherical coordinates), and $z$denoting depth, respectively (Fig. \ref{fig1}) )."
" Tn ios Cases, convectivele stable laverspA are included. below ane above the uusable laver."," In most cases, convectively stable layers are included below and above the unstable layer."
 The upper laver (region 1) is stabiized by a cooling term i1 the cherey equation. Wwuch eads to an almost isotheriual. highly stable stratificatio1.," The upper layer (region 1) is stabilized by a cooling term in the energy equation, which leads to an almost isothermal, highly stable stratification."
 The lower stable laver (regiou 3) represcuts au overshoo zoue. Whose thickuess is €105011 such that overshoolue yhunes do not reach the lower iupenetrable boneary.," The lower stable layer (region 3) represents an overshoot zone, whose thickness is chosen such that overshooting plumes do not reach the lower impenetrable boundary."
 The box rotates about an axis O. that makes anauele () with the z-axis.," The box rotates about an axis $\vec{\Omega}$, that makes an angle $\theta$ with the $z$ -axis."
 Ileuce 0= corresponds to a sittlatioi where the box is located at the south pole of the $1n., Hence $\theta=0$ corresponds to a situation where the box is located at the south pole of the Sun.
 In the present paper we treat ouly this special case., In the present paper we treat only this special case.
 The governing equatious are those describing maguctic iuduction. nussconiuitv. aud the balauce of moment and energy: where JV«Béjty is the current deusity. 5 is the maenuctic diffusivity. 7 is the kincmatic viscosity. CuofCy is the adiabatic iudex. aud # ds the radiative conductivity.," The governing equations are those describing magnetic induction, masscontinuity, and the balance of momentum and energy: where $\vec{J}=\nabla\times\vec{B}/\mu_0$ is the current density, $\eta$ is the magnetic diffusivity, $\nu$ is the kinematic viscosity, $\gamma=C_p/C_V$ is the adiabatic index, and $\kappa$ is the radiative conductivity."
 Tn all sunulatious. 5 and p are taken constant. and # is a prescribed function of depth.," In all simulations, $\eta$ and $\nu$ are taken constant, and $\kappa$ is a prescribed function of depth."
" The stress tensor S is given hiv and S7 stands for $,,,57,.", The stress tensor $\tens{S}$ is given by and $\tens{S}^2$ stands for $\sum_{ij}{\sf S}_{ij}^2$.
 The equation of state is that of an ideal eas. 1.6.. The term Q. given by represcuts cooling or heating. depending ou whether the internal cuerey density exceeds ο or falls below it. respectively: oy veprescuts the cooling/heating rate.," The equation of state is that of an ideal gas, i.e., The term $Q$, given by represents cooling or heating, depending on whether the internal energy density exceeds $e_1$ or falls below it, respectively; $\sigma_0$ represents the cooling/heating rate."
 The deptl-dependent function f eusures that Q is vauishing only iu region 1l. aud το)0.," The depth-dependent function $f$ ensures that $Q$ is non-vanishing only in region 1, and $f(z_2)=0$."
" The inc""son of this term leads to the presence of a highly stable. thin overshoot laver. tιο providing a realistic uupper boundary condition for the convection zone."," The inclusion of this term leads to the presence of a highly stable, thin overshoot layer, thereby providing a realistic upper boundary condition for the convection zone."
 lu the horizontal directions. veriodic boundary couditious are inposed.," In the horizontal directions, periodic boundary conditions are imposed."
 The upper aid lower boundaries of the domain are nmupenetrable and. stress-free. aud the horizoutal coniponeuts of he magnetic8 field variation are set to zero.," The upper and lower boundaries of the domain are impenetrable and stress-free, and the horizontal components of the magnetic field variation are set to zero."
 At t1e lower boundary. the energy flux is prescribed. and at the top boundary the internal energv (Gwhich is proportional to the temperature) is fixed.," At the lower boundary, the energy flux is prescribed, and at the top boundary the internal energy (which is proportional to the temperature) is fixed."
" Iu the actual ruus we (5-)set Dy,=0: By, is cither 0 or the imposed horizontal field.", In the actual runs we set $B_{0y}=0$; $B_{0x}$ is either 0 or the imposed horizontal field.
 A] quautities are made dimeusiouless by setting where py is the initial deusity at a depth <ταν the ottou of the uustable laver.," All quantities are made dimensionless by setting where $\rho_0$ is the initial density at a depth $z=z_3$, the bottom of the unstable layer."
 Thus leieth is expressed im eris of d=iapool the thiekuess of the convectivelv ustade zone (region 2).," Thus length is expressed in terms of $d=z_3-z_2$, the thickness of the convectively unstable zone (region 2)."
" It follows that time is measured interus of \fd/g. velocity iu feriis ο Vgd. the magnetic fieldl strength in terms of popogd. aid eutropy in ternis of C,."," It follows that time is measured in terms of $\sqrt{d/g}$, velocity in terms of $\sqrt{gd}$, the magnetic field strength in terms of $\sqrt{\mu_0\rho_0 gd}$ and entropy in terms of $C_p$ ."
 Oji several occasions we shall consider the ΟΠΟΙΟΥ: valance. Which is governed by a conservation law. where ess=©|[ulDotsoj /21]|B[/2ugpisH the total specific(n energv. aud the fluxes. ἔτι are given by," On several occasions we shall consider the energy balance, which is governed by a conservation law, where $e_{\rm tot}= e+ |\vec{u}|^2/2+|\vec{B}|^2/2\mu_0\rho$ is the total specific energy, and the fluxes, $\vec{F}_i$ , are given by"
Reeious appareutly devoid of galaxies (IXirsliuer ct al.,Regions apparently devoid of galaxies (Kirshner et al.
 1981) aud clusters (Eiuasto. Joevecr Saar 1980) were discovered in the early 1980s. and the existence of voids was confirmed by subsequent huger surveys at a variety of wavelengths (de Lappareut. Geller. IDIuchra 1986: da Costa et al.," 1981) and clusters (Einasto, Joeveer Saar 1980) were discovered in the early 1980's, and the existence of voids was confirmed by subsequent larger surveys at a variety of wavelengths (de Lapparent, Geller, Huchra 1986; da Costa et al."
 1988: Celler Thichra 1989: Davis ct al., 1988; Geller Huchra 1989; Davis et al.
 1992: \lauroeordato et al., 1992; Maurogordato et al.
 1992: da Costa et al., 1992; da Costa et al.
 1991: see Rood 1988 aud references therein for a discussion of the history of void detection aud interpretation)., 1994; see Rood 1988 and references therein for a discussion of the history of void detection and interpretation).
 Though their relative paucity has meant that void galaxies have larecly gone overlooked. they remain oue of the best probes of the effect of environment aud cosmology ou galaxy. evolution. and are perhaps one of the most intrigue new probes into our wuderstaucing of structure formation.," Though their relative paucity has meant that void galaxies have largely gone overlooked, they remain one of the best probes of the effect of environment and cosmology on galaxy evolution, and are perhaps one of the most intriguing new probes into our understanding of structure formation."
 Voids have been studied statistically using techniques such as the void probability function (Maurogordato Lachi¢zzce-Rev 1987: Lachiezze-Bev. da Costa. Alaurogordato 1992: Voecley ct al.," Voids have been studied statistically using techniques such as the void probability function (Maurogordato Lachièzze-Rey 1987; Lachièzze-Rey, da Costa, Maurogordato 1992; Vogeley et al."
 1991: Croton et al., 1994; Croton et al.
 2001: Πον]ο Voecley 2001). found. using void-finding techniques (Pellegrini. da Costa de Carvalho L989: Slezak. de Lappareut Bijaowi 1993: ELAd. Piran da Costa 1996: ELAd. Piran and da Costa 1997: Mülller et al.," 2004; Hoyle Vogeley 2004), found using void-finding techniques (Pellegrini, da Costa de Carvalho 1989; Slezak, de Lapparent Bijaoui 1993; El-Ad, Piran da Costa 1996; El-Ad, Piran and da Costa 1997; Mülller et al."
 2000: Plionis Basilalos 2002: Tlovle Voecley 2002: 2001) aud studied using semi-analvtic or N-body simulations (Mathis White 2002: Benson et al., 2000; Plionis Basilakos 2002; Hoyle Vogeley 2002; 2004) and studied using semi-analytic or N-body simulations (Mathis White 2002; Benson et al.
 2003: Cottlobber et al., 2003; Gottlöbber et al.
 2003)., 2003).
 Rojas et al. |, Rojas et al. [
"2001a. (photometric data). 20010. (spectroscopic data). 20010 (catalog)] have cousidered the properties of galaxies that reside in extremely low density environments,","2004a (photometric data), 2004b (spectroscopic data), 2004c (catalog)] have considered the properties of galaxies that reside in extremely low density environments."
 They (Rojas et al., They (Rojas et al.
" 2001a) ideutify a suuple of LO? void ealaxies. bc. galaxies that are found in regions that have deusity coutrast. à,=δρίρ—0.6 detected using the Sloan Digital Sky Survey (York ct al."," 2004a) identify a sample of $^3$ void galaxies, i.e. galaxies that are found in regions that have density contrast, $\delta_v\equiv
\delta \rho /\rho < -0.6$ detected using the Sloan Digital Sky Survey (York et al."
 2000. Stoughton et al.," 2000, Stoughton et al."
 2002. Abazajian et al.," 2002, Abazajian et al."
 2003. Strauss et al.," 2003, Strauss et al."
 2001)., 2004).
 The properties of galaxies in voids clearly differ from those in higher-denusitv regions. as seen iu previous studies of void galaxies that include examination of spectral and photometric properties (Moody ct al.," The properties of galaxies in voids clearly differ from those in higher-density regions, as seen in previous studies of void galaxies that include examination of spectral and photometric properties (Moody et al."
 1987: Weistrop et al., 1987; Weistrop et al.
 1995: Popescu. Hopp Elsassscr 1997. Croein Celler 1999. 2000) and TT coutent (Szoiioru ct al.," 1995; Popescu, Hopp Elsässser 1997, Grogin Geller 1999, 2000) and HI content (Szomoru et al."
 1996: IIuchitineier. Hopp. Kulu 1997).," 1996; Huchtmeier, Hopp, Kuhn 1997)."
 Grogin Celler (1999. 2000) analyze a sample of 16 galaxies iu regions with deusity less than half of the mean density (ic. dpfp«— 0.5) aud fined that these void galaxies are bluer. of earlier type. and have a larecr fraction of emission lue svstenis than galaxies in dense regions.," Grogin Geller (1999, 2000) analyze a sample of 46 galaxies in regions with density less than half of the mean density (i.e. $\delta \rho/\rho < -0.5$ ) and find that these void galaxies are bluer, of earlier type, and have a larger fraction of emission line systems than galaxies in dense regions."
 Sinularly. Rojas et al. (," Similarly, Rojas et al. ("
2001α) find void galaxies are bluer. fainter aud have morphologies. as classified by their Sérrsic aud concentration indices. that more closely resenüble late-type galaxies as compared to galaxies that reside in higher deusitv euvirounieuts (wall galaxies).,"2004a) find void galaxies are bluer, fainter and have morphologies, as classified by their Sérrsic and concentration indices, that more closely resemble late-type galaxies as compared to galaxies that reside in higher density environments (wall galaxies)."
 Rojas ct al. (, Rojas et al. (
2001b) also find that void ealaxies have stronger equivalent widths of Ho and ΟΠ aud have higherspecific star formation rates.,2004b) also find that void galaxies have stronger equivalent widths of $\alpha$ and OII and have higher star formation rates.
 Hovle et al. (, Hoyle et al. (
"2003) measure the Luminositv Fuuction (hereafter LF) of these galaxies and find that the LE's of the wall aud void galaxies have different values of AM, (where iaguitudes are in SDSS bauds unless stated otherwise) i. void galaxies are f£ünter than wall ealaxics. but the values of the faint cud slopes are τον simular: a—LISEOA anda=1.1930.07 respectively.","2003) measure the Luminosity Function (hereafter LF) of these galaxies and find that the LF's of the wall and void galaxies have different values of $M_r*$ (where magnitudes are in SDSS bands unless stated otherwise) i.e. void galaxies are fainter than wall galaxies, but the values of the faint end slopes are very similar: $\alpha=-1.18\pm 0.13$ and $\alpha=-1.19\pm0.07$ respectively."
 This suggests that voids are not dominated by a large population of low huninositv galaxies., This suggests that voids are not dominated by a large population of low luminosity galaxies.
 An important question is whether voids ive strongly auti-biased., An important question is whether voids are strongly anti-biased.
 Do they contain significant amounts of Dark Matter even though they are larecly devoid of light?, Do they contain significant amounts of Dark Matter even though they are largely devoid of light?
 We would like to test this question by determining the mass fiction of void ealaxies and estimating their local bias parameter., We would like to test this question by determining the mass function of void galaxies and estimating their local bias parameter.
 The bias paraiucter. b is defined as the ratio of galaxy perturbations to the perturbations in the uuderlviug dark matter distribution.," The bias parameter, $b$ is defined as the ratio of galaxy perturbations to the perturbations in the underlying dark matter distribution."
 For au uubiased distribution. 6=1. the density coutrast of galaxies reflects the density contrast in dark matter.," For an unbiased distribution, $b=1$, the density contrast of galaxies reflects the density contrast in dark matter."
 Void regions also provide an important testbed for the overall picture of galaxy. formation. because Dirkhoff's (1923) theorem sugeests that the behavior of structure erowtl within an uuder- or overdeuse region will mimic that of a universe with the same mean properties.," Void regions also provide an important testbed for the overall picture of galaxy formation, because Birkhoff's (1923) theorem suggests that the behavior of structure growth within an under- or overdense region will mimic that of a universe with the same mean properties."
 Goldberg Voecley (2001) suggest a prescription to eficieutlv simulate the exowth of, Goldberg Vogeley (2004) suggest a prescription to efficiently simulate the growth of
SNla should explode in globular clusters. corresponding to | supernova in à globular cluster within 100 Mpe every year. and that a dedicated HST program would be able to find the connection. if each SNIa was observed a few years after the explosion.,"SNIa should explode in globular clusters, corresponding to 1 supernova in a globular cluster within 100 Mpc every year, and that a dedicated HST program would be able to find the connection, if each SNIa was observed a few years after the explosion."
 With their assumptions such a program would require deep HST observations of ~100 fields every year., With their assumptions such a program would require deep HST observations of $\sim$ 100 fields every year.
 They did not account for the fact that some SNIa suffer from significant extinction. and that observations inside galaxies where there is a high background are much less sensitive than in the field., They did not account for the fact that some SNIa suffer from significant extinction and that observations inside galaxies where there is a high background are much less sensitive than in the field.
 These effects are difficult to model for the full sample of type [a supernovae. and it is therefore unclear if the proposed observational program would be succesful despite the high costs.," These effects are difficult to model for the full sample of type Ia supernovae, and it is therefore unclear if the proposed observational program would be succesful despite the high costs."
 We therefore use the currently available HST data to observe or put limits on the fraction of SNlae in. globular clusters. and to make it possible to estimate the sensitivity that can be achieved with a dedicated observational program.," We therefore use the currently available HST data to observe or put limits on the fraction of SNIae in globular clusters, and to make it possible to estimate the sensitivity that can be achieved with a dedicated observational program."
 To be able to exclude a GC origin. it is necessary to know the observable properties of the GCs.," To be able to exclude a GC origin, it is necessary to know the observable properties of the GCs."
 Being old stellar systems. there are only relatively small variations in the mass-to-light ratios of different clusters. with the main difference being related to the globular cluster metallicity.," Being old stellar systems, there are only relatively small variations in the mass-to-light ratios of different clusters, with the main difference being related to the globular cluster metallicity."
 However. the mass distribution of globular clusters is wide. with several orders of magnitude difference between the brightest and the faintest clusters (e.g.??)..," However, the mass distribution of globular clusters is wide, with several orders of magnitude difference between the brightest and the faintest clusters \citep[e.g.][]{Harris1991,Jordan2007}."
 In the more distant galaxies or in shallow observations it will not be possible to observe the faint clusters and it is necessary to calculate the incompleteness caused by this., In the more distant galaxies or in shallow observations it will not be possible to observe the faint clusters and it is necessary to calculate the incompleteness caused by this.
 The most straight-forward way to do this is to use the observed luminosity function of globular clusters (?).., The most straight-forward way to do this is to use the observed luminosity function of globular clusters \citep{Pfahl2009}.
 However. while the definition of 7 as the enhancement per unit mass is a useful measure. it is misleading in terms of the physical interpretation. as the number of compact binaries does not scale linearly with the mass of the globular cluster.," However, while the definition of $\eta$ as the enhancement per unit mass is a useful measure, it is misleading in terms of the physical interpretation, as the number of compact binaries does not scale linearly with the mass of the globular cluster."
 Instead it is related to the stellar encounter rate D inside the clusters., Instead it is related to the stellar encounter rate $\Gamma$ inside the clusters.
 The distribution of structural parameters (and hence I? of clusters is not well known., The distribution of structural parameters (and hence $\Gamma$ ) of clusters is not well known.
" Since also the exact processes of compact binary formation are poorly constrained. itis therefore not possible to make theoretical estimates of the relation between GC mass and the probability of hosting SNla progenitors,"," Since also the exact processes of compact binary formation are poorly constrained, it is therefore not possible to make theoretical estimates of the relation between GC mass and the probability of hosting SNIa progenitors."
 We instead attempt to do this on an empirical basis., We instead attempt to do this on an empirical basis.
 The only compact binaries that have been surveyed in large samples of GCs are LMXBs., The only compact binaries that have been surveyed in large samples of GCs are LMXBs.
 We use the results of ? and ? to estimate the mass distribution of GCs that contribute to the population of compact binaries. and thereby to estimate 4 completeness levels. CL25. 6150. CL75 and 61.100. meaning the GC masses/luminosities above which25%..506c.. and of the compact binaries are expected to reside.," We use the results of \citet{Peacock2010} and \citet{Sivakoff2007} to estimate the mass distribution of GCs that contribute to the population of compact binaries, and thereby to estimate 4 completeness levels, CL25, CL50, CL75 and CL100, meaning the GC masses/luminosities above which, and of the compact binaries are expected to reside."
 We strongly caution that this is based on observations of LMXBs alone. and that it is very possible that SNIa progenitors could have a different mass-dependence.," We strongly caution that this is based on observations of LMXBs alone, and that it is very possible that SNIa progenitors could have a different mass-dependence."
 However. currently there are no models that predict a different behaviour. and the populations of faint X-ray sources in Galactic GCs do seem to follow the distribution of bright LMXBs.," However, currently there are no models that predict a different behaviour, and the populations of faint X-ray sources in Galactic GCs do seem to follow the distribution of bright LMXBs."
 To estimate the completeness masses. we use the K-band data of ? and the z-band data of ?..," To estimate the completeness masses, we use the K-band data of \citet{Peacock2010} and the z-band data of \citet{Sivakoff2007}."
 We give the completeness values for the K-band observations of M31 and z-band observations of Virgo in table 1.., We give the completeness values for the K-band observations of M31 and z-band observations of Virgo in table \ref{tab:CL}.
 To compare these results and extrapolate them to other wavelengths we use the integrated simple stellar population magnitudes of ??..," To compare these results and extrapolate them to other wavelengths we use the integrated simple stellar population magnitudes of \citet{Girardi2000,Marigo2008}."
 The values are in good agreement. assuming a 12 Gyr stellar population with a Chabrier initial mass function and a metallicity of 0.012.," The values are in good agreement, assuming a 12 Gyr stellar population with a Chabrier initial mass function and a metallicity of 0.012."
 We also provide estimates of the corresponding (initial) globular cluster masses. using the K-band magnitudes and two different metallicities.," We also provide estimates of the corresponding (initial) globular cluster masses, using the K-band magnitudes and two different metallicities."
 These are then used to find the colours in all the different bands used in the following analysis., These are then used to find the colours in all the different bands used in the following analysis.
 As the metal-rich GCs are redder. they are fainter than the metal-poor GCs in the used bands. for a given K-band luminosity.," As the metal-rich GCs are redder, they are fainter than the metal-poor GCs in the used bands, for a given K-band luminosity."
 We therefore use the calculations for z=0.012 to determine the confidence limits in all the bands. noting that in this way the confidence limits will be underestimated. decreasing our sensitivity somewhat.," We therefore use the calculations for z=0.012 to determine the confidence limits in all the bands, noting that in this way the confidence limits will be underestimated, decreasing our sensitivity somewhat."
 Younger clusters would be brighter for a given stellar mass. similarly leading to an underestimation of the confidence limits.," Younger clusters would be brighter for a given stellar mass, similarly leading to an underestimation of the confidence limits."
 The magnitudes for CL100 are given in table 2.., The magnitudes for CL100 are given in table \ref{tab:CL100}.
 From table 1. it can be seen that subtracting 1.5. 2.5 and 3.0 from these magnitudes yields CL75. CL50 and CL25. respectively.," From table \ref{tab:CL} it can be seen that subtracting 1.5, 2.5 and 3.0 from these magnitudes yields CL75, CL50 and CL25, respectively."
 The observations of globular clusters at the positions of type la supernovae can be performed before the explosions. but also after. since the light of the globular clusters is provided by stars. which are not affected by the explosion.," The observations of globular clusters at the positions of type Ia supernovae can be performed before the explosions, but also after, since the light of the globular clusters is provided by stars, which are not affected by the explosion."
 As the luminosity of the SNIae are very high just after the explosion. it is necessary to wait until they have become fainter than a globular cluster.," As the luminosity of the SNIae are very high just after the explosion, it is necessary to wait until they have become fainter than a globular cluster."
 This typically takes less than two years. although SNIae with light-echoes might be bright enough to hide globular clusters for a longer time.," This typically takes less than two years, although SNIae with light-echoes might be bright enough to hide globular clusters for a longer time."
 To facilitate comparisons and thereby the use of type Ia supernova as standard candles in cosmology. their lightcurves are observed using BVRI photometry.," To facilitate comparisons and thereby the use of type Ia supernova as standard candles in cosmology, their lightcurves are observed using BVRI photometry."
 While most studies are limited to less than ~100 days. a number of SNlae have published late-time data.," While most studies are limited to less than $\sim100$ days, a number of SNIae have published late-time data."
 We have surveyed the litterature to, We have surveyed the litterature to
from measurements restricted. to limited wavelength ranges. whieh is an ill-conditioned deconvolution problem. raising important computational difficullies.,"from measurements restricted to limited wavelength ranges, which is an ill-conditioned deconvolution problem, raising important computational difficulties."
 Since then. three different approaches have been proposed to solve this problem.," Since then, three different approaches have been proposed to solve this problem."
 A first approach uses an adaptation of ihe ILogbom CLEAN algorithm (Hogbom1974). to the RM deconvolution (leald2009)., A first approach uses an adaptation of the Hogbom CLEAN algorithm \citep{Hogbom1974} to the RM deconvolution \citep{Heald2009}.
.. The second approach is wavelet-based. ancl assumes field svaumnetries in order to project the observed data onto A?<0 (Fricketal. 2010)...," The second approach is wavelet-based, and assumes field symmetries in order to project the observed data onto $\lambda^{2}<0$ \citep{Frick2010}. ."
 The third approach Lietal.2011) is based on the compressed sensing paradigm Tao 2006)..," The third approach \citep{Wiaux2009,Li2011} is based on the compressed sensing paradigm \citep{Donoho2006,Candes2006}."
 All these methods are more or less successful in the case of mixed problems. i.e. when both thin and thick components are included in the model.," All these methods are more or less successful in the case of mixed problems, i.e. when both thin and thick components are included in the model."
 For example. in a recent paper it has been shown that RAI Synthesis may vield an erroneous Faraday. structure in the presence of multiple. interfering HM. components. even when cleaning of (he Faraday spectrum is performed (Farnsworthetal.2011).," For example, in a recent paper it has been shown that RM Synthesis may yield an erroneous Faraday structure in the presence of multiple, interfering RM components, even when cleaning of the Faraday spectrum is performed \citep{Farnsworth2011}."
.. Also. to our knowledge these methods have not been evaluated in the presence of noise added (o the observed. data. a situation that makes the deconvolution problem even more difficult.," Also, to our knowledge these methods have not been evaluated in the presence of noise added to the observed data, a situation that makes the deconvolution problem even more difficult."
 Thus. the development of robust deconvolution methods for the recovery of the Faraday dispersion function in a given spectral range becomes crucial for the RAL synthesis applications.," Thus, the development of robust deconvolution methods for the recovery of the Faraday dispersion function in a given spectral range becomes crucial for the RM synthesis applications."
 Inspired bv the above mentioned contributions. in (his paper we discuss (he case of sparse approximation of the complex Faraday dispersion ΠΟΙΟ. i.e. we assume that F(6) can be approximated by a small number of discrete components. which can be both thin or Chick.," Inspired by the above mentioned contributions, in this paper we discuss the case of sparse approximation of the complex Faraday dispersion function, i.e. we assume that $F(\phi)$ can be approximated by a small number of discrete components, which can be both thin or thick."
 Also. we present the implementation of a greedy. deconvolution algorithm. and we illustrate the described method with several numerical simulations which emphasize the effect of the covered range and sampling resolution in the Faraday. depth space. ancl the effect of noise on the observed data.," Also, we present the implementation of a greedy deconvolution algorithm, and we illustrate the described method with several numerical simulations which emphasize the effect of the covered range and sampling resolution in the Faraday depth space, and the effect of noise on the observed data."
 The numerical results show that the described method performs quite well for simple component mixtures. al (vpical sampling resolution values and coverage range in the Faraday depth space. and it is quite robust in the presence of noise.," The numerical results show that the described method performs quite well for simple component mixtures, at typical sampling resolution values and coverage range in the Faraday depth space, and it is quite robust in the presence of noise."
 We show that the described technique is well suited [or exploratory data. analvsis. where prior information about the component distributions is not available. ancl it can be used as a complement to the previously proposed methods.," We show that the described technique is well suited for exploratory data analysis, where prior information about the component distributions is not available, and it can be used as a complement to the previously proposed methods."
 Although a sparse solution is an idealized model of a complex astrophysical svstem. the potential complexity of the solutions is aclequate Lor a wide range of astvoplivsical situations.," Although a sparse solution is an idealized model of a complex astrophysical system, the potential complexity of the solutions is adequate for a wide range of astrophysical situations."
 The sparseness requirement steers the solution to include the siiallest number of components required to fit an observed Faraday depth spectrum., The sparseness requirement steers the solution to include the smallest number of components required to fit an observed Faraday depth spectrum.
 Double-Iobed radio galaxies that are nol resolved by the telescope may experience different Faraday rotation in each lobe because the differences in the foreground on scales smaller than the beam., Double-lobed radio galaxies that are not resolved by the telescope may experience different Faraday rotation in each lobe because the differences in the foreground on scales smaller than the beam.
 The lobes themselves may be extended and experience differential Faraday rotation as well., The lobes themselves may be extended and experience differential Faraday rotation as well.
 A sparse solution may consist of (wo discrete Faraday components representing each lobe., A sparse solution may consist of two discrete Faraday components representing each lobe.
 If the data are good enough to detect differential Faraday rotation across the source. the solution max includeone or more," If the data are good enough to detect differential Faraday rotation across the source, the solution may includeone or more"
Chemically peculiar (CP) stars are an important class of stars that occupy the upper main sequence. where radiative diffusion and gravitational settling. result in. atmospheric chemical abundances that differ remarkably from the Sun's.,"Chemically peculiar (CP) stars are an important class of stars that occupy the upper main sequence, where radiative diffusion and gravitational settling result in atmospheric chemical abundances that differ remarkably from the Sun's."
 According to their patterns of chemical anomalies. CP stars are classified into several subclasses that also follow a temperature sequence.," According to their patterns of chemical anomalies, CP stars are classified into several subclasses that also follow a temperature sequence."
 Among them. SrCrEu. Si. He-weak. and He-strong stars have strong global magnetic fields.," Among them, SrCrEu, Si, He-weak, and He-strong stars have strong global magnetic fields."
" These ""magnetic"" CP (mCP) stars also exhibit synchronous variability in. their spectra and brightness with periods longer than one half of a day.", These “magnetic” CP (mCP) stars also exhibit synchronous variability in their spectra and brightness with periods longer than one half of a day.
 Their photometric amplitudes are a few hundredths of magnitude., Their photometric amplitudes are a few hundredths of magnitude.
 mCP stars have inhomogeneous surface distributions of chemical elements as determined from their rotationally modulated spectral-line variability (e.g..Lüftingeretal. 2010a.b).," mCP stars have inhomogeneous surface distributions of chemical elements as determined from their rotationally modulated spectral-line variability \citep[e.g.,][]{lufta,luftb}."
. The uneven surface distribution of various elements. together with rotation. has been presumed to be the main cause of these stars’ light variability.," The uneven surface distribution of various elements, together with rotation, has been presumed to be the main cause of these stars' light variability."
 Line blanketing caused by overabundant elements. mainly iron-group metals and transitions. may induce the flux redistribution providing the mechanism for the light variability (Lanzetal.1996).," Line blanketing caused by overabundant elements, mainly iron-group metals and transitions, may induce the flux redistribution providing the mechanism for the light variability \citep{lanko}."
.. A strong magnetic field may also influence thelight curves (e.g..Kochukhovetal. 2005).," A strong magnetic field may also influence thelight curves \citep[e.g.,][]{malablaj}."
. Krtiékaetal.(2007.2009) used surface abundance maps to simulate successfully the light curves of the He-strong star and the Si star7224.," \citet{krt,eedra} used surface abundance maps to simulate successfully the light curves of the He-strong star and the Si star."
. They demonstrated that the inhomogeneous surface distribution of silicon. iron. and helium. along with the and transitions of these elements. accounted for most of the light variability in these CP stars.," They demonstrated that the inhomogeneous surface distribution of silicon, iron, and helium, along with the and transitions of these elements, accounted for most of the light variability in these CP stars."
 The light curves of magnetic CP stars are stable on a timescale of decades or more and so indicate persistency of their spectroscopic and photometric spots., The light curves of magnetic CP stars are stable on a timescale of decades or more and so indicate persistency of their spectroscopic and photometric spots.
 We can observe period changes in their light curves in only a few cases (Mikulaseketal.2008b.andreferencestherein).., We can observe period changes in their light curves in only a few cases \citep[][and references therein]{mikbra}.
 It is generally expected that the meridional currents induced by the rapid rotation of hot MS stars are able to erase the effects of the slow diffusion of chemical elements and thus prevent the formation of CP abundance anomalies., It is generally expected that the meridional currents induced by the rapid rotation of hot MS stars are able to erase the effects of the slow diffusion of chemical elements and thus prevent the formation of CP abundance anomalies.
 We study therefore the light variability of7355.. which is one of the most rapidly rotating mCP stars.," We study therefore the light variability of, which is one of the most rapidly rotating mCP stars."
 1182180. 995480) is a bright (V.=6.02 mag) but poorly studied southern B2V star.," 182180, 95480) is a bright $V=6.02$ mag) but poorly studied southern B2V star."
" It is known to be a rapid rotator, Oksalaetal.(2010) evaluating its projected equatorial velocity to be vsini=(300€15)kms7!."," It is known to be a rapid rotator, \citet{oks} evaluating its projected equatorial velocity to be $v\,\sin\,i=(300\pm15)\,\mathrm{km\,s}^{-1}$."
" The Hipparcos catalog (ESA1997) classified the star as an “unsolved variable"". but Koen&Eyer(2002) reanalysed the Hipparcos photometry and found a frequency of variation of 1/0!26072."," The Hipparcos catalog \citep{ESA} classified the star as an “unsolved variable”, but \citet{koen} reanalysed the Hipparcos photometry and found a frequency of variation of $1/0\fd26072$."
 The first detailed study of wwas performed by Riviniusetal.(2008).. who describe the star às a helium-strong CP star with Balmer emission.," The first detailed study of was performed by \citet{riv}, who describe the star as a helium-strong CP star with Balmer emission."
 They argue that the true period. corresponding to the star’s rotational period. is twice that derived by Koen&Eyer(2002):: (!521428(6).," They argue that the true period, corresponding to the star's rotational period, is twice that derived by \citet{koen}: $P=0\fd521428(6)$ ."
 This suggests that iis the most rapidly rotating He-strong CP star known., This suggests that is the most rapidly rotating He-strong CP star known.
 In the present study. we analyse our new and archival photometry of tto determine the star’s periodicity and light curve shape at various epochs between 1990 and 2009.," In the present study, we analyse our new and archival photometry of to determine the star's periodicity and light curve shape at various epochs between 1990 and 2009."
 We estimate the mass and age of uusing the revised version of the Hipparcos catalogue (vanLeeuwen 2007). the Geneva and Str6mmeren photometry (from GCPD')). and the isochrones of the Padova group (Marigoetal.2008).," We estimate the mass and age of using the revised version of the Hipparcos catalogue \citep{leeuwen}, , the Geneva and Strömmgren photometry (from ), and the isochrones of the Padova group \citep{marigo}."
. The Geneva colours (Cramer1999) are consistent with a VV star., The Geneva colours \citep{cramer} are consistent with a V star.
 The Z index shows no peculiarity beyond what we would expect for a classical CP4 star (Paunzenetal. 2005)., The $Z$ index shows no peculiarity beyond what we would expect for a classical CP4 star \citep{paun}. .
. From the various Geneva indices and the availableStrómmgren photometry. we deduce a reddening of E(b—v»)=0.05 mag," From the various Geneva indices and the availableStrömmgren photometry, we deduce a reddening of $E(b-y)\,=\,0.05$ mag"
"using this alternative concentration-mass relation, hereafter referred to as B01-M05.","using this alternative concentration-mass relation, hereafter referred to as B01-M05."
 Fig., Fig.
" 6 shows how these different assumptions for the mass, density profile and concentration-mass relation of a perturber change the total critical curves produced by a primary lens at z=0.6 and the perturbing halo located at the same redshift and with a mass of Msoo=[10°Mo,10)Μο,1019 Μο]."," \ref{fig:CCprofiles} shows how these different assumptions for the mass, density profile and concentration-mass relation of a perturber change the total critical curves produced by a primary lens at $z=0.6$ and the perturbing halo located at the same redshift and with a mass of $M_{200}=[10^8 M_{\odot},~ 10^9 M_{\odot},~ 10^{10}
M_{\odot}]$ ."
" A different density profile (a truncated singular isothermal sphere, a truncated NFW profile with the M08 concentration-mass relation and a truncated NFW profile with the B01-MO05 concentration-mass relation) is assumed in each row of Fig. 6.."," A different density profile (a truncated singular isothermal sphere, a truncated NFW profile with the M08 concentration-mass relation and a truncated NFW profile with the B01-M05 concentration-mass relation) is assumed in each row of Fig. \ref{fig:CCprofiles}."
 Different distortions to the critical curve correspond to different levels of violations in the smooth-lens flux-ratio relationship., Different distortions to the critical curve correspond to different levels of violations in the smooth-lens flux-ratio relationship.
" The mass dependence of the violation pattern has been studied systematically, with results presented in 86, which also includes a discussion of effects from different concentration-mass relations and from allowing scatter in the concentration on the overall cusp-violation probabilities."," The mass dependence of the violation pattern has been studied systematically, with results presented in $\S$ 6, which also includes a discussion of effects from different concentration-mass relations and from allowing scatter in the concentration on the overall cusp-violation probabilities."
" In this section we have illustrated the effects of varying the redshift, impact parameter, mass and density profile of a single perturbing halo."," In this section we have illustrated the effects of varying the redshift, impact parameter, mass and density profile of a single perturbing halo."
" In practice, perturbations could arise anywhere along the line of sight and from many different haloes."," In practice, perturbations could arise anywhere along the line of sight and from many different haloes."
 The overall perturbation is far more complicated than any of the simple cases presented here., The overall perturbation is far more complicated than any of the simple cases presented here.
" In the following sections, we use cosmological N-body simulations to obtain self-consistent and realistic distributions of perturbers along strong lensing sight lines, and estimate the net perturbation and the likelihood of the observed flux ratio violations."," In the following sections, we use cosmological $N$ -body simulations to obtain self-consistent and realistic distributions of perturbers along strong lensing sight lines, and estimate the net perturbation and the likelihood of the observed flux ratio violations."
" The Millennium-II simulation (MS-IL; ?)) is an N-body simulation of a cubic cosmological volume with a comoving side length of 100h~'Mpc, at a spatial resolution of 1hkpc and mass resolution of 6.89x109!Mc."," The Millennium-II simulation (MS-II; \citealt{Millennium2}) ) is an $N$ -body simulation of a cubic cosmological volume with a comoving side length of $h^{-1}~\Mpc$, at a spatial resolution of $h^{-1}~\kpc$ and mass resolution of $6.89\times10^6
h^{-1}M_{\odot}$."
" The cosmological! parameters of MS-II are the same as those of the earlier Millennium and Aquarius simulations, consistent with the WMAP-1 results."," The cosmological parameters of MS-II are the same as those of the earlier Millennium and Aquarius simulations, consistent with the WMAP-1 results."
 MS-II provides us with the large-scale distributions of a cosmological sample of dark matter haloes., MS-II provides us with the large-scale distributions of a cosmological sample of dark matter haloes.
" When tracing lensing sight lines through this simulation, we use the following method to determine where haloes cross the past light cone of a fiducial observer (for more details, see ?))."," When tracing lensing sight lines through this simulation, we use the following method to determine where haloes cross the past light cone of a fiducial observer (for more details, see \citealt{Raul2008thesis}) )."
" We start by replicating the 100! Mpc simulation box in its X, Y and Z dimensions, as many times as we need to cover the desired redshift range (along the sight line) and angular size (transverse to the sight line)."," We start by replicating the $h^{-1}$ Mpc simulation box in its $X$, $Y$ and $Z$ dimensions, as many times as we need to cover the desired redshift range (along the sight line) and angular size (transverse to the sight line)."
" For computational efficiency we only let the combined box go to the source redshift in the X and Y dimensions, and keep the number of replications in the Z dimension to a minimum."," For computational efficiency we only let the combined box go to the source redshift in the $X$ and $Y$ dimensions, and keep the number of replications in the $Z$ dimension to a minimum."
" As illustrated in Fig. 7,,"," As illustrated in Fig. \ref{fig:RepBoxMSII}, ,"
" the observer is located at the origin (0, 0, 0) in one corner of this replicated box."," the observer is located at the origin (0, 0, 0) in one corner of this replicated box."
" Assuming a source redshift ofZs=2, the total dimension of the combined box is chosen to be 38x8, in units of one Millennium-II simulation box."," Assuming a source redshift of$z_s=2$, the total dimension of the combined box is chosen to be $38\times38\times8$, in units of one Millennium-II simulation box."
" The position angles (0,4) of a given line-of-sight vector are defined as the angles measured from the Z X- and XY -plane, respectively."," The position angles $(\theta, \phi)$ of a given line-of-sight vector are defined as the angles measured from the $ZX$ - and $XY$ -plane, respectively."
" The simulated sky into which we trace sight lines is then two 2?x30? stripes, which cover 10?«040? and 50?<080°, and 10?<¢12°."," The simulated sky into which we trace sight lines is then two $2^{\circ} \times 30^{\circ}$ stripes, which cover $10^{\circ} \leqslant \theta \leqslant 40^{\circ}$ and $50^{\circ} \leqslant \theta \leqslant 80^{\circ}$, and $10^{\circ}
\leqslant \phi \leqslant 12^{\circ}$."
 Directions along the X and Y axes (with «10°) and along 40?«0<50? have been excluded to avoid significant repetition of structures in the replicated box.," Directions along the $X$ and $Y$ axes (with $\leqslant 10^{\circ}$ ) and along $40^{\circ} \leqslant
\theta \leqslant 50^{\circ}$ have been excluded to avoid significant repetition of structures in the replicated box."
 Haloes at each simulation snapshot (corresponding to a particular redshift) are identified using the Friends-of-Friends algorithm (?))., Haloes at each simulation snapshot (corresponding to a particular redshift) are identified using the Friends-of-Friends algorithm \citealt{Davis1985FoF}) ).
 Haloes also contain many subhaloes; these are identified using theSUBFIND algorithm (?))., Haloes also contain many subhaloes; these are identified using the algorithm \citealt{VolkerGADGET2}) ).
 The minimum mass of subhaloes resolved by the simulation is 1.4x105Η (corresponding to 20 particles)., The minimum mass of subhaloes resolved by the simulation is $1.4\times10^8 h^{-1}M_{\odot}$ (corresponding to 20 particles).
 Haloes at different snapshots1Mc are linked together by an algorithm for defining their merging history (?))., Haloes at different snapshots are linked together by an algorithm for defining their merging history \citealt{Helly03}) ).
 We follow haloes in each of these merger trees and predict their trajectories (in the replicated box) between every two adjacent snapshots., We follow haloes in each of these merger trees and predict their trajectories (in the replicated box) between every two adjacent snapshots.
" In this way, we can find the exact redshift and comoving position of a halo at the moment it crosses the past light cone of the observer."," In this way, we can find the exact redshift and comoving position of a halo at the moment it crosses the past light cone of the observer."
" When a halo crosses the light cone, all its subhaloes are assumed to cross at the same redshift."," When a halo crosses the light cone, all its subhaloes are assumed to cross at the same redshift."
 We assume that the relative positions of these subhaloes at the light-cone crossing time are the same as in the previous snapshot., We assume that the relative positions of these subhaloes at the light-cone crossing time are the same as in the previous snapshot.
" Hereafter, we will use the term ""lensing cone"" to refer to the observer's light cone that encloses a particular lensing sight line towards a certain direction in the sky (and out to the source redshift)."," Hereafter, we will use the term “lensing cone” to refer to the observer's light cone that encloses a particular lensing sight line towards a certain direction in the sky (and out to the source redshift)."
 All haloes that cross the past light cone are checked to see if they are physically within a given lensing cone., All haloes that cross the past light cone are checked to see if they are physically within a given lensing cone.
" If so, their positions, redshifts, masses and half mass radii are stored for lens modelling."," If so, their positions, redshifts, masses and half mass radii are stored for lens modelling."
" All lensing cones are 50""x 50""-wide, out to a source redshiftz,= 2, and contain a primary lens around redshift z;—0.6 (typical source and lens redshifts for the observed quasar lensing systems)."," All lensing cones are $50\arcsec\times 50\arcsec$ -wide, out to a source redshift$z_s=2$ , and contain a primary lens around redshift $z_d=0.6$ (typical source and lens redshifts for the observed quasar lensing systems)."
" 'To build up our lensing cone catalogue, we randomly"," To build up our lensing cone catalogue, we randomly"
"the umber deusity of Chuups. i,xc? where r. i& the chunup radiis. whilst the mass injection rate frou each chump nii.xre.","the number density of clumps, $n_{c} \propto r_{c}^{-3}$ where $r_{c}$ is the clump radius, whilst the mass injection rate from each clump $\dot{m}_{c} \propto r_{c}$."
 Thus we can only couuaenut that or small chumps. it is more Likely that this πα mass-loacding luit will actually occur.," Thus we can only comment that for small clumps, it is more likely that this maximum mass-loading limit will actually occur."
 We further note that the radial profile of t1ο Mac[um uuuber oft1e flow relative to the clumps cau take many different forus. depenine on the iuput parameters used.," We further note that the radial profile of the Mach number of the flow relative to the clumps can take many different forms, depending on the input parameters used."
 Iu Fie., In Fig.
 7 we show several examples., \ref{fig:mach} we show several examples.
 The profile of the Mach wmuber is influenced by the fact that mass-loading tends to drive the Mach number towards unity. whilst the spherical divergence teuds to drive it away from unity ILutquist al.1986)).," The profile of the Mach number is influenced by the fact that mass-loading tends to drive the Mach number towards unity, whilst the spherical divergence tends to drive it away from unity Hartquist \cite{HDPS1986}) )."
 Panel a) is for a case iu which niass-loadiug is snall., Panel a) is for a case in which mass-loading is small.
 In this case the divergeuce term wins. and drives the Mach παπανο towards zero.," In this case the divergence term wins, and drives the Mach number towards zero."
 Panel b} is for a similar situation. but iu this case because the inner shock is very close to the CD. the initial postshock Mach uunuberis ereater than unity so the divereeuce term drives it owards infinity.," Panel b) is for a similar situation, but in this case because the inner shock is very close to the CD, the initial postshock Mach number is greater than unity so the divergence term drives it towards infinity."
 In paucl c) we see that the divergence is initially dominant. but as the flow approaches the CD the Mach. uuuber is driven back towards unity.," In panel c) we see that the divergence is initially dominant, but as the flow approaches the CD the Mach number is driven back towards unity."
" However. this behaviour is no due to the flow iniss-loadiug (although d,= 2.61). nut is rather because ie density increases near the CD wulst the pressure remalus constant. producing a decrease in the sound specd {ie sale effect occurs for the flow srown in Fie."," However, this behaviour is not due to the flow mass-loading (although $\Phi_{\rm b} = 2.64$ ), but is rather because the density increases near the CD whilst the pressure remains constant, producing a decrease in the sound speed (the same effect occurs for the flow shown in Fig."
 2 which Las no mnass-loacding)., \ref{fig:johns_results} which has no mass-loading).
 The same situation occurs iu panel where the fall iu sound speed is ereat chough to drive 1ο flow through a sonic transition., The same situation occurs in panel d) where the fall in sound speed is great enough to drive the flow through a sonic transition.
 The flow correspondis to panel ο) is very simular to that associated with panel d) exceat we now have two sonic trausitious due to 1ο initial post-shock flow being supersonic with respect to the chuups., The flow corresponding to panel e) is very similar to that associated with panel d) except we now have two sonic transitions due to the initial post-shock flow being supersonic with respect to the clumps.
" In plot £) the flow is siguificautly wass-loacded (Pj,= 7.86). and the mass-loacing term dominates the divergence term such that the Mach iuuuber is driven towards unity."," In plot f) the flow is significantly mass-loaded $\Phi_{\rm b} = 7.86$ ), and the mass-loading term dominates the divergence term such that the Mach number is driven towards unity."
 . ⋮∐⋯∐⋅↖↽∙↖↖⇁↸∖∐⋜↧↖↽↸∖↸⊳⋜↧↕↸⊳∏↕⋜↧↑↸∖≼↧ xofiles of the N-rav ↸∖↕⊔↕↴∖∷∖↴↕↖↽↕↑⋅↖↽⋜↧↴∖↴⋜↧↕⋟∏∐↸⊳↑↕∪∐∪↕⋟↥⋅⋜⊔∐∏↴∖↴≺↴∖↴↸∖↸∖⊟∶↴∙⊾∙≺∖," Finally, we have calculated profiles of the X-ray emissivity as a function of radius (see Fig. \ref{fig:xray}) )."
"∖⋝⋝∙ We asstune that fie enudssivitv A0XwT5V?, which. is. aeood approximation over the teuperature range 5r\10=T5«10'K Kalu 1976))."," We assume that the emissivity $\Lambda \propto n^{2} T^{-1/2}$, which is agood approximation over the temperature range $5 \times 10^{5} {\rm K} \ltsimm T \ltsimm 5 
\times 10^{7}{\rm K}$ Kahn \cite{K1976}) )."
 Also plotted in Fig., Also plotted in Fig.
 8 are the radial temperature profiles., \ref{fig:xray} are the radial temperature profiles.
 A bubble wn-affected by mass-loading expanding iuto a surrounding medium with aur profile ofdensity has a higher ceutral eniperature but a lower central enüssivitv than at its lamb., A bubble un-affected by mass-loading expanding into a surrounding medium with an $r^{-2}$ profile of density has a higher central temperature but a lower central emissivity than at its limb.
 Couversely. if it is expanding iuto a medium with an rt profie of density. the situation is reversed. as the central temperature is lower aud the central cuissivity is ligher than at its lub.," Conversely, if it is expanding into a medium with an $r^{1}$ profile of density, the situation is reversed, as the central temperature is lower and the central emissivity is higher than at its limb."
 Tf the bubble is mass-loadecd. the [m]general trend is for a reduction iu the central cuussivity aud an increase in the central temperature relative to the limb.," If the bubble is mass-loaded, the general trend is for a reduction in the central emissivity and an increase in the central temperature relative to the limb."
 To date. the only stellar wind bubbles which have becu successfully observed iu N-ravs are two WolfRavet ring nebulae. NCC 6888 Wrieeeao 1998)) and S308 (Wrieee 1999)).," To date, the only stellar wind bubbles which have been successfully observed in X-rays are two Wolf-Rayet ring nebulae, NGC 6888 Wrigge \cite{WCMK1998}) ) and S308 (Wrigge \cite{W1999}) )."
 Both lave Nav nuiunosities ower than expected from the stzudard: nioclel (Weaver 1977))., Both have X-ray luminosities lower than expected from the standard model (Weaver \cite{WMCSM1977}) ).
 This discreuulev ds normally atributed to wo possibilities either conducivo evaporation of gas youn the cold dense outer shell iito the bube interior. or euhauced cooling resulting fi1u high meallicities iu he cooling gas (sce MacLow 200 )).," This discrepancy is normally attributed to two possibilities: either conductive evaporation of gas from the cold dense outer shell into the bubble interior, or enhanced cooling resulting from high metallicities in the cooling gas (see MacLow \cite{M2000}) )."
 It is no surprise. herefore. that our mass-loadiug simulations 1xdicate that evaporation from clumps he bubble nay also be conipatible with current observaions.," It is not surprising, therefore, that our mass-loading simulations indicate that evaporation from clumps the bubble may also be compatible with current observations."
 The atest N-rav, The latest X-ray
"Compton thick, i.e. Ng~1/or=1.5x1024cm?.","Compton thick, i.e. $N_{\rm H}\sim 1/{\sigma_{\rm T}} =
1.5\times 10^{24}\psqcm$."
" Under the assumptions used, the main reduction of A with column density Ng is merely due to the increased column acting as a dead weight since the UV part of the spectrum is used up after traversing a column of a few 10?!cm?."," Under the assumptions used, the main reduction of $A$ with column density $N_{\rm H}$ is merely due to the increased column acting as a dead weight since the UV part of the spectrum is used up after traversing a column of a few $10^{21}\pcmsq$."
 The outer 'dead weight’ is then pushed by the inner gas which experiences the full force of the radiation., The outer 'dead weight' is then pushed by the inner gas which experiences the full force of the radiation.
 In this paper we explore further the implications of the boost factor on the limit to the column density of dusty gas that can remain close to an AGN without being ejected by radiation pressure., In this paper we explore further the implications of the boost factor on the limit to the column density of dusty gas that can remain close to an AGN without being ejected by radiation pressure.
 The key feature is to cast the inverse of the boost factor as the (classical) Eddington ratio A: A cloud is long lived if Αλ<1., The key feature is to cast the inverse of the boost factor as the (classical) Eddington ratio $\lambda$: A cloud is long lived if $A\lambda<1$.
 If the boost factor for a particular cloud is 100 then it will be blown away when the Eddington ratio exceeds 1/100., If the boost factor for a particular cloud is 100 then it will be blown away when the Eddington ratio exceeds 1/100.
 This determines a relation between the column density of long-lived absorbing gas close to a nucleus and its Eddington ratio., This determines a relation between the column density of long-lived absorbing gas close to a nucleus and its Eddington ratio.
 ? have previously noted the role of the Eddington ratio when explaining the geometrical thickness of the torus around AGN by the action of radiation pressure., \cite{1992ApJ...399L..23P} have previously noted the role of the Eddington ratio when explaining the geometrical thickness of the torus around AGN by the action of radiation pressure.
 ? have estimated the effective Eddington limit for a torus around an AGN considering both smooth and clumpy dust distributions.," \cite{2007MNRAS.380.1172H}
 have estimated the effective Eddington limit for a torus around an AGN considering both smooth and clumpy dust distributions."
" Previous work on the luminosity dependence of absorption has found that the incidence of absorption drops with luminosity citealt2003ApJ...598..886U;; citealt2005ApJ...635..864L,, but see citealt2006MNRAS.372.1755D., citealt2005 ApJ...630..115T))."," Previous work on the luminosity dependence of absorption has found that the incidence of absorption drops with luminosity \\citealt{2003ApJ...598..886U}; ; \\citealt{2005ApJ...635..864L}, but see \\citealt{2006MNRAS.372.1755D}, \\citealt{2005ApJ...630..115T}) )."
 The ’receding torus’ model citealt199 IMNRAS.252..586L;; citealt1998MNRAS.297L..39S)) is often invoked to explain why quasars may show less absorption., The 'receding torus' model \\citealt{1991MNRAS.252..586L}; \\citealt{1998MNRAS.297L..39S}) ) is often invoked to explain why quasars may show less absorption.
 In that model the reduction in absorbed objects is attributed to (heating) destruction of dust within the inner regions of a torus of absoring gas surrounding the nucleus., In that model the reduction in absorbed objects is attributed to (heating) destruction of dust within the inner regions of a torus of absoring gas surrounding the nucleus.
 Here we consider the relation between luminosity and absorption from the point of view of the effective Eddington limit on dusty gas., Here we consider the relation between luminosity and absorption from the point of view of the effective Eddington limit on dusty gas.
 We determine the boost factor A as detailed in Cite2006MNRAS.373L..16F using and AGN spectral energy distributions obtained by cite2007MNRAS.381.1235V.., We determine the boost factor $A$ as detailed in \\cite{2006MNRAS.373L..16F} using and AGN spectral energy distributions obtained by \\cite{2007MNRAS.381.1235V}.
 A is obtained from absorption only (the input spectrum minus the transmitted one) and assumes that the gas is optically thin to the infrared radiation thereby produced., $A$ is obtained from absorption only (the input spectrum minus the transmitted one) and assumes that the gas is optically thin to the infrared radiation thereby produced.
 Trapping of radiation is assumed to be negligible and the ionization parameter £—L/nr? is arranged to be about 10 (thereby fixing the gas density for a given incident AGN flux)., Trapping of radiation is assumed to be negligible and the ionization parameter $\xi=L/nr^2$ is arranged to be about 10 (thereby fixing the gas density for a given incident AGN flux).
" Cite2007MNRAS.381.1235V find that the UV — X-ray spectral energy distributions (SEDs) of AGN depend on Eddington ratio, with much more ionizing radiation — and therefore higher boost factors — occurring at higher A."," \\cite{2007MNRAS.381.1235V} find that the UV – X-ray spectral energy distributions (SEDs) of AGN depend on Eddington ratio, with much more ionizing radiation – and therefore higher boost factors – occurring at higher $\lambda$."
 We adopt mean SEDs for high (> 0.1) and low (« 0.1) A when computing A as a function of absorption column density., We adopt mean SEDs for high $>0.1$ ) and low $<0.1$ ) $\lambda$ when computing $A$ as a function of absorption column density.
 Ng is plotted against A=A! in Fig., $N_{\rm H}$ is plotted against $\lambda=A^{-1}$ in Fig.
 2., 2.
" The drift velocity of the grains relative to the gas is computed byCLOUDY and found to be low (about 0.1kms""! where most of the radiative force is applied) justifying our assumption that the dust and gas are coupled.", The drift velocity of the grains relative to the gas is computed by and found to be low (about $0.1\kmps$ where most of the radiative force is applied) justifying our assumption that the dust and gas are coupled.
 Long-lived absorbing clouds can survive against radiation pressure in the shaded region of the Figure., Long-lived absorbing clouds can survive against radiation pressure in the shaded region of the Figure.
" Clouds to the right of the dividing line,in the unshaded part, see the nucleus as above"," Clouds to the right of the dividing line,in the unshaded part, see the nucleus as above"
"From a morphological point of view, the pillars in the simulations with a higher flux (ie. when the computational volume is located closer to the ionizing source) are smaller than in the case of a lower flux (Fig. 3,,","From a morphological point of view, the pillars in the simulations with a higher flux (i.e. when the computational volume is located closer to the ionizing source) are smaller than in the case of a lower flux (Fig. \ref{FIG_compare},"
" panel 8, panel 1 and panel 7 in decreasing flux order)."," panel 8, panel 1 and panel 7 in decreasing flux order)."
" In addition, they gain more momentum away from the source and move faster away from the source as the photo-evaporation is stronger."," In addition, they gain more momentum away from the source and move faster away from the source as the photo-evaporation is stronger."
" At the same time the density of the hot gas is higher, leading to denser, more compressed structures with a smaller diameter."," At the same time the density of the hot gas is higher, leading to denser, more compressed structures with a smaller diameter."
 Due to the higher photo-evaporation rate their average masses are as well lower (see Table 2))., Due to the higher photo-evaporation rate their average masses are as well lower (see Table \ref{TAB_compare}) ).
" Changing the initial flux is expected to have a similar effect as changing the mean density, as p«z? (cf Eq. 2))."," Changing the initial flux is expected to have a similar effect as changing the mean density, as $\rho\propto x^2$ (cf Eq. \ref{x_Stroem}) )."
 In we reduced the mean density by a factor of three., In we reduced the mean density by a factor of three.
 At the same time we reduced the flux by a factor of three to avoid an extremely high level of ionization degree., At the same time we reduced the flux by a factor of three to avoid an extremely high level of ionization degree.
" In total, this corresponds to the same penetration length as influx."," In total, this corresponds to the same penetration length as in."
". T'hus, we expect a similar morphology to evolve, but the densities should be lower."," Thus, we expect a similar morphology to evolve, but the densities should be lower."
 In Fig., In Fig.
 3 (panel 9) this can be clearly seen., \ref{FIG_compare} (panel 9) this can be clearly seen.
" The morphology is similar toflux, the front is at a similar position."," The morphology is similar to, the front is at a similar position."
" Again, the density (Fig. 4))"," Again, the density (Fig. \ref{rho_evol}) )"
 in the hot gas evolves similarly to the expectation for a homogeneous medium., in the hot gas evolves similarly to the expectation for a homogeneous medium.
 The mass assembled in the most prominent structure (Table 2)) is lower and the density of the structure fits the findings of pressure equilibrium (see §3.4))., The mass assembled in the most prominent structure (Table \ref{TAB_compare}) ) is lower and the density of the structure fits the findings of pressure equilibrium (see \ref{RES_T}) ).
 Combining these findings with the results of 83.1 allows us to make an interesting prediction.," Combining these findings with the results of \ref{RES_general}
 allows us to make an interesting prediction."
" As the density of the hot gas behaves similarly to the case of a homogeneous medium and as the structures are in approximate pressure equilibrium with the surrounding hot gas, we can predict the density of the structures from the initial mean density of the medium, the flux of the source, and the time since the ignition of the source or the position of the ionization front."," As the density of the hot gas behaves similarly to the case of a homogeneous medium and as the structures are in approximate pressure equilibrium with the surrounding hot gas, we can predict the density of the structures from the initial mean density of the medium, the flux of the source, and the time since the ignition of the source or the position of the ionization front."
 The density of the forming structures is thus given as where we used Eq. 10.., The density of the forming structures is thus given as where we used Eq. \ref{rho_front}.
 z; depends on the initial density(18) and the impinging flux (see Eq. 2))., $x_\mathrm{s}$ depends on the initial density and the impinging flux (see Eq. \ref{x_Stroem}) ).
" As we expect the assumption of pressure equilibrium to hold in the case of a point source, the three-dimensional expression taking into account geometrical dilution is given by where Rg is the Strómmgren radius a detailed derivation of the three-dimensional front position(for see e.g. 7))."," As we expect the assumption of pressure equilibrium to hold in the case of a point source, the three-dimensional expression taking into account geometrical dilution is given by where $R_\mathrm{S}$ is the Strömmgren radius (for a detailed derivation of the three-dimensional front position see e.g. \citealt{1991pagd.book.....S}) )."
" 'To study the effect of the largest scales of the initial turbulence (the turbulent input scales) we compare with ky44:4, a run in which we populate modes k—4..8, instead of k—1..4 as usual."," To study the effect of the largest scales of the initial turbulence (the turbulent input scales) we compare with 4, a run in which we populate modes $k=4...8$, instead of $k=1..4$ as usual."
 The resulting surface density in the first 2pc facing the star is shown in Fig. 5.., The resulting surface density in the first $2\pc$ facing the star is shown in Fig. \ref{turb_surf}.
 Already in the initial conditions (left column) a clear difference can be seen., Already in the initial conditions (left column) a clear difference can be seen.
" Whereas the power on the larger k modes leads to large, distinct structures (top panel), power on the smaller modes show already a much more diversified density distribution (lower panel)."," Whereas the power on the larger k modes leads to large, distinct structures (top panel), power on the smaller modes show already a much more diversified density distribution (lower panel)."
 After tinal=500kyr (right column) the ionization leads to an enhancement of the pre-existing structure., After $t_\mathrm{final}=500\kyr$ (right column) the ionization leads to an enhancement of the pre-existing structure.
" The densest filaments survive, while the other material is swept away by the ionization."," The densest filaments survive, while the other material is swept away by the ionization."
" In (top panel) this leads to an(G09b) excavation of the few, but bigger structures and thus to the creation of few, but distinct pillars."," In (top panel) this leads to an excavation of the few, but bigger structures and thus to the creation of few, but distinct pillars."
" On the other hand, in kmax4((bottom panel) more structures, but of smaller scales survive, which leads to several, but more diffuse structures."," On the other hand, in (bottom panel) more structures, but of smaller scales survive, which leads to several, but more diffuse structures."
" Together with refRESy achthisshows, thatonlyastrongenoughturbulentdrivingon radiation"," Together with \\ref{RES_Mach} this shows, that only a strong enough turbulent driving ona large enough driving scale leads to the formation of coherent structures as seen in observations."
is, As has been shown in \ref{RES_res} this is not an effect of the resolution.
dominatedbythelargermodes.," The turbulence is well enough resolved to allow for small enough modes to produce fuzzy structure in, but the evolution under the influence of UV-radiation is dominated by the larger modes."
 Another possibility to change the input scale of the turbulence is to simply increase or decrease the size of the simulation domain., Another possibility to change the input scale of the turbulence is to simply increase or decrease the size of the simulation domain.
 In the box size is doubled to 8pc., In the box size is doubled to $8\pc$.
" Since the particle number is kept constant, this leads to a factor of two lower spatial resolution."," Since the particle number is kept constant, this leads to a factor of two lower spatial resolution."
" So the resolution in the part of the domain shown in Fig 3 (panel 12) is comparable to the low resolution case ,((panel 2).", So the resolution in the part of the domain shown in Fig \ref{FIG_compare} (panel 12) is comparable to the low resolution case (panel 2).
 In the box size is halved to 2pc., In the box size is halved to $2\pc$.
 This corresponds to doubling the spatial resolution., This corresponds to doubling the spatial resolution.
" The domain has a smaller extent in the x-direction as well, which we compensate by taking two times the evolved turbulent box in the x-"," The domain has a smaller extent in the x-direction as well, which we compensate by taking two times the evolved turbulent box in the x-direction."
" This is valid, since the initial conditions were evolved with periodic boundary conditions."," This is valid, since the initial conditions were evolved with periodic boundary conditions."
" The particle number is thus 4x 109, twice as high as in most other cases."," The particle number is thus $4\times10^6$ , twice as high as in most other cases."
is an interval of dipping activity (the modulation is much stronecr in the LECS than the MECS. consistent with the known cucrey dependence of dipping). followed by a dip-free iuterva and a longer interval of deep dipping at the eud of the oservation.,"is an interval of dipping activity (the modulation is much stronger in the LECS than the MECS, consistent with the known energy dependence of dipping), followed by a dip-free interval and a longer interval of deep dipping at the end of the observation."
 The short-ou state observation covers parts of l orbital evcles aud 1icludes 3 eclipse intervals., The short-on state observation covers parts of 4 orbital cycles and includes 3 eclipse intervals.
 Both he LECS aud the MECS show a eradual reduction iu οςmut rate. with this ctΠοοτ Deluge more pronounced in tlie LECS. such that the femath orbital cvele appears to be absent. whereas a sinall modulation is still visible iu the MECS.," Both the LECS and the MECS show a gradual reduction in count rate, with this effect being more pronounced in the LECS, such that the fourth orbital cycle appears to be absent, whereas a small modulation is still visible in the MECS."
 Superposed on this decay are the eclipses and what is normally taken to e dipping activity., Superposed on this decay are the eclipses and what is normally taken to be dipping activity.
 However. this appears to be presen or up to 20 hrs diving each orbital cvele. whereas the nalu-ou state dip duration is usually 5.10 hr (see e.g.. Revnolks Parmar 1995: Scott Leal 19993).," However, this appears to be present for up to 20 hrs during each orbital cycle, whereas the main-on state dip duration is usually 5–10 hr (see e.g., Reynolds Parmar \cite{r:95}; Scott Leahy \cite{s:99}) )."
 During the first τος orbital eveles. the ceutroid ofthe cussion occurs at successively earlier orbital phases. while for the fourth orbital evele no strong variation within the cvcle is observed.," During the first three orbital cycles, the centroid of the emission occurs at successively earlier orbital phases, while for the fourth orbital cycle no strong variation within the cycle is observed."
 This is also seen in the hardness ratio plot which shows intervals of increased hardness (consistent with increased absorption) at occur progressively earlier iu each of the first 3 (aud xossiblv the fourth) orbital eveles., This is also seen in the hardness ratio plot which shows intervals of increased hardness (consistent with increased absorption) that occur progressively earlier in each of the first 3 (and possibly the fourth) orbital cycles.
 The peaks of the NECS enutroids and the mereases in LECS larducss ratio secu —1 Fig., The peaks of the MECS centroids and the increases in LECS hardness ratio seen in Fig.
 2 are separated by an average of ~1.1 davs., \ref{fig:lc} are separated by an average of $\sim$ 1.4 days.
 This ucaus that the intervals of strong absorption marcl back Nor dr each orbital evele., This means that the intervals of strong absorption march back by $\sim$ 7 hr each orbital cycle.
 This rapid marching back is oei strong contrast to the iizin-ou state dips which have a iod only 0.5 hr less than the orbital oue (Scott Leal 1999))., This rapid marching back is in strong contrast to the main-on state dips which have a period only 0.5 hr less than the orbital one (Scott Leahy \cite{s:99}) ).
 There max also be a narrow intensity dip iu the AIECS lightcurve. similar to those seen in the on-state. owards the cud of the second evele of the short-on state.," There may also be a narrow intensity dip in the MECS lightcurve, similar to those seen in the on-state, towards the end of the second cycle of the short-on state."
 Iu order to study the spectral evolution duriug the parts of the 35 dav cvele observed here. 5 plase averaged spectra were extracted.," In order to study the spectral evolution during the parts of the 35 day cycle observed here, 5 phase averaged spectra were extracted."
 The selected iutervals are indicated iu Fig., The selected intervals are indicated in Fig.
 2. and are labelled as AIL aud $1 to $8., \ref{fig:lc} and are labelled as M1 and S1 to S4.
 Intersa AIL covers a dip-free part of the main-on state. while S1 and 82 cover the peaks of the first two short-on orbita evcles aud have a similar overall iuteusitv to MI.," Interval M1 covers a dip-free part of the main-on state, while S1 and S2 cover the peaks of the first two short-on orbital cycles and have a similar overall intensity to M1."
 Iuterva, Interval
one can decompose the mean electromotive loree into distinct components proportional to the large-scale field ancl (o its gradient. as suggested by equation (3)). although the caveats discussed. above regarding the dillieulties of this approach at high. values of i need to be borne in mind.,"one can decompose the mean electromotive force into distinct components proportional to the large-scale field and to its gradient, as suggested by equation \ref{eq:emf_expansion}) ), although the caveats discussed above regarding the difficulties of this approach at high values of $Rm$ need to be borne in mind."
 For instability-driven dvnamos. the whole picture is very dillerent since the perturbations to the flow and magnetic fiekl needed to drive the emf come about only through an initial instabilitw of the field itself)," For instability-driven dynamos, the whole picture is very different since the perturbations to the flow and magnetic field needed to drive the emf come about only through an initial instability of the field itself."
 There is therelore no concept of a strictly kinematic regime in which the flow can be described independently of the magnetic field., There is therefore no concept of a strictly kinematic regime in which the flow can be described independently of the magnetic field.
 Furthermore. although. as we shall show below. it is possible to describe such dxnamos within (he mean field framework. it is in general meaningful to speak of a ancl o-ellects.," Furthermore, although, as we shall show below, it is possible to describe such dynamos within the mean field framework, it is in general meaningful to speak of $\alpha$ and $\beta$ -effects."
 The instability. and hence the resulting emt. will (vpically have a complicated nonlinear dependence on the strength and eracients of the magnetic field. rendering meaningless a decomposition such as (3)).," The instability, and hence the resulting emf, will typically have a complicated nonlinear dependence on the strength and gradients of the magnetic field, rendering meaningless a decomposition such as \ref{eq:emf_expansion}) )."
 An exception to this might be (he magnetorotational instability. which is a weak fielcl instabilitv.," An exception to this might be the magnetorotational instability, which is a weak field instability."
 In this case. Drandenburg(2005) and Gressel(2010) have argued that a mean field expansion of the form (3)) is possible. allhough it should be stressed. as acknowledged by Gressel(2010).. that a more sviuimetric treatment Chat treats ihe momentum and induction equations on an equal fooling. an approach pioneered by Courvoisieretal.(2010a.b).. is requirecl.," In this case, \citet{Bburg05} and \citet{Gressel10} have argued that a mean field expansion of the form \ref{eq:emf_expansion}) ) is possible, although it should be stressed, as acknowledged by \citet{Gressel10}, that a more symmetric treatment that treats the momentum and induction equations on an equal footing, an approach pioneered by \citet{CHP10a,CHP10b}, is required."
 Obtaining a mathematical description of an instabilitv-«driven dvnanmo is less straightforward than for a standard. flow-driven dvnamo. where. al least in the kinematic reeime. the problem is tackled either via the induction equation or the mean induction equation.," Obtaining a mathematical description of an instability-driven dynamo is less straightforward than for a standard, flow-driven dynamo, where, at least in the kinematic regime, the problem is tackled either via the induction equation or the mean induction equation."
 For an instabilitv-driven dinamo. (he starting point is an analvsis of the pertinent instability.," For an instability-driven dynamo, the starting point is an analysis of the pertinent instability."
 The dillieulty then arises in describing how this instabilitv feeds back into the dvnamo process., The difficulty then arises in describing how this instability feeds back into the dynamo process.
 The initial phases of (he instability will be characterised bv exponential erowth. aud it therefore makes sense as a [ist step to consider (he nature of the emf (which will also be growing exponentially) resulting from the most uustable mode of instability and ils dependence on (he various parameters of (he problem.," The initial phases of the instability will be characterised by exponential growth, and it therefore makes sense as a first step to consider the nature of the emf (which will also be growing exponentially) resulting from the most unstable mode of instability and its dependence on the various parameters of the problem."
 The ulümate aim must be to trv, The ultimate aim must be to try
filling factor of metals. these results were fairly crucle as the study was focused on the properties of individual galaxies.,"filling factor of metals, these results were fairly crude as the study was focused on the properties of individual galaxies."
 Aguirre et ((2001a) and Aguirre et ((2001b) studied ICM. anetal enrichiment by superimposing an outflow model oun nmunuerical simulations that did not include SN-driven winds. but were only able to coustrain the contribution from late-forming (226) aud relatively large (AL2A0 AL. objects.," Aguirre et (2001a) and Aguirre et (2001b) studied IGM metal enrichment by superimposing an outflow model on numerical simulations that did not include SN-driven winds, but were only able to constrain the contribution from late-forming $z \lsim 6$ ) and relatively large $M
\gsim 10^{8.5} M_\odot$ ) objects."
 Con Ostriker (1999) studied metal curichment in even lower resolution soothed particle livdvodvuamic (SPIT) smmulatious with a dark unatter particle mass of 8.6«10537... Cuediu Ostriker (1997) studied the relationship between reiouization and carly inetal enrichment im high-resolution simulations. but did not adequately follow superuova explosious.," Cen Ostriker (1999) studied metal enrichment in even lower resolution smoothed particle hydrodynamic (SPH) simulations with a dark matter particle mass of $8.6 \times 10^8 M_\odot.$ Gnedin Ostriker (1997) studied the relationship between reionization and early metal enrichment in high-resolution simulations, but did not adequately follow supernova explosions."
 Finally. Thacker. Scanuapieco. Davis (2002) were able to estimate the filline factor of outflows at +>f purely in the context of high-resolution SPU simulations with a dark latter particle mass of 2.5«106AZ... but were not able to exanune its dependence ou model paramcters due to the lugh computational cost of this approach.," Finally, Thacker, Scannapieco, Davis (2002) were able to estimate the filling factor of outflows at $z \geq 4$ purely in the context of high-resolution SPH simulations with a dark matter particle mass of $2.5 \times 10^6 M_\odot$, but were not able to examine its dependence on model parameters due to the high computational cost of this approach."
 Earh-cnurichiment scenarios also lave important inplications for the thermal and velocity structure of the ICM. as first studied in Teguuuk. Silk. Evrard (1993) and Voit (1996) (see also Cen aud Bryan 2000).," Early-enrichment scenarios also have important implications for the thermal and velocity structure of the IGM, as first studied in Tegmark, Silk, Evrard (1993) and Voit (1996) (see also Cen and Bryan 2000)."
 The resulting feedback ou galaxy formation was first examined In Scaunapieco. Ferrara. Broadhurst (2000). SD. aud Scannapieco. Thacker. Davis (2001).," The resulting feedback on galaxy formation was first examined in Scannapieco, Ferrara, Broadhurst (2000), SB, and Scannapieco, Thacker, Davis (2001)."
" The nature of this effect is twofold: au impinging wind may shock-heat the eas of a nearby perturbation to above the virial temperature. thereby mechanically evaporating the gas. or the gas may be accelerated to above the escape velocity and stripped from the perturbation cutirely,"," The nature of this effect is twofold: an impinging wind may shock-heat the gas of a nearby perturbation to above the virial temperature, thereby mechanically evaporating the gas, or the gas may be accelerated to above the escape velocity and stripped from the perturbation entirely."
 The latter channel is considerably more effective. because shock-heated clouds that are too laree to be stripped are able to radiatively cool within a sound crossine time. thus liuiting evaporation.," The latter channel is considerably more effective, because shock-heated clouds that are too large to be stripped are able to radiatively cool within a sound crossing time, thus limiting evaporation."
 Note that tlis type of feedback is fundamentally differcut from the one commonly adopted in galaxy formation models. iu which hot gas is produced by supernovae iu the parent galaxy.," Note that this type of feedback is fundamentally different from the one commonly adopted in galaxy formation models, in which hot gas is produced by supernovae in the parent galaxy."
 Iu this paper we return to the issues of enrichniueut and feedback. adopting a more complete approach that conibines the detailed modeling of a typical object as in MER. with the more general spatially depeudent modeling described in SB.," In this paper we return to the issues of enrichment and feedback, adopting a more complete approach that combines the detailed modeling of a typical object as in MFR, with the more general spatially dependent modeling described in SB."
 Iu this wav we are able place coustraiuts ou the overall metal Πιο factor produced as well as investigate the liux between cosmic metal enrichment aud the feedback from outflows on galaxy. formation., In this way we are able place constraints on the overall metal filling factor produced as well as investigate the link between cosmic metal enrichment and the feedback from outflows on galaxy formation.
 The structure of the paper is as follows., The structure of the paper is as follows.
 In 822 and 833 we describe our somi-aualvtical simulations of galaxy formation with feedback aud ICAL enrichment., In 2 and 3 we describe our semi-analytical simulations of galaxy formation with feedback and IGM enrichment.
 Iu $814 we sumunarize the results of these simulatious and the constraints they place of the fraction of the universe inpacted by outflows: conclisions are eiven in 855., In 4 we summarize the results of these simulations and the constraints they place of the fraction of the universe impacted by outflows; conclusions are given in 5.
 Iu order to determine the distributiou of outflows as a function of cosmic time. we use the linear peaks model described in detail iu SB.," In order to determine the distribution of outflows as a function of cosmic time, we use the linear peaks model described in detail in SB."
 Note that it is nuportaut not ouly to have a nieasure of the overall uuuber deusitv of such objects. but also of their spatial distribution. as lüeh-redshift galaxies are expected to be highly clustered both from theory (6.9...BS. Kaiser 1981) and observations (ανακου et 11998).," Note that it is important not only to have a measure of the overall number density of such objects, but also of their spatial distribution, as high-redshift galaxies are expected to be highly clustered both from theory (e.g., Kaiser 1984) and observations (Giavalisco et 1998)."
" Using a standard fit to the Cold Dark Matter (CDM) power-spectrumi (Dardeen ct 11986). we construct a 256° linear deusity field spanning a (Ll + Mpce)? cubic comoving volume. where fis the IHubble coustant iu units of 100 kan + Mpeο,"," Using a standard fit to the Cold Dark Matter (CDM) power-spectrum (Bardeen et 1986), we construct a $^3$ linear density field spanning a (4 $h^{-1}$ $^3$ cubic comoving volume, where $h$ is the Hubble constant in units of 100 km $^{-1}$ $^{-1}$."
" Based mainly on the latest measurements of Cosmic Microwave Backeround (CMD) anisotropies DDalbi 2000: Netterfeld 2001: Prvke 2002) and the abundance of galaxy clusters (Viana Liddle 1996). we focus our attention on a cosmological model with parameters 5h=0.65. Qay = 0.35. O4 = 0.65. O,=0.05. σς=OAT. and 5»=1. where Qa;. O4. and 9, are the total matter. vacuna. aud xuvonie deusities in units of the critical deusitv. σς is the nass variance of linear fluctuatious ou the sh!Mpe scale. and is the tilt of the primordial power spectrum."," Based mainly on the latest measurements of Cosmic Microwave Background (CMB) anisotropies Balbi 2000; Netterfield 2001; Pryke 2002) and the abundance of galaxy clusters (Viana Liddle 1996), we focus our attention on a cosmological model with parameters $h=0.65$, $\Omega_M$ = 0.35, $\Omega_\Lambda$ = 0.65, $\Omega_b =
0.05$, $\sigma_8 = 0.87$, and $n=1$, where $\Omega_M$, $\Omega_\Lambda$, and $\Omega_b$ are the total matter, vacuum, and baryonic densities in units of the critical density, $\sigma_8$ is the mass variance of linear fluctuations on the $8 h^{-1}{\rm Mpc}$ scale, and $n$ is the tilt of the primordial power spectrum."
 This linear density field is convolved with spherical ‘topiat’ window functious correspouding to mine differeut total nlasses. spaced in equal logarithmic intervals from 3.0).LOOAL. to L3«10MAL... aud spanning the interesting ranee from objects that lie close to the lower limit set by photoionization and molecular cooling (e.$.. Darkaua Loeb 1999: Ciardi. Ferrara. Abel 2000) to the most massive ealaxies that lost outflows.," This linear density field is convolved with spherical `top--hat' window functions corresponding to nine different total masses, spaced in equal logarithmic intervals from $3.0 \times 10^7\,\msun$ to $4.3
\times 10^{11}\,\msun$, and spanning the interesting range from objects that lie close to the lower limit set by photoionization and molecular cooling (e.g., Barkana Loeb 1999; Ciardi, Ferrara, Abel 2000) to the most massive galaxies that host outflows."
 We assume that the formation of Population III (Pop IID objects. defined as halos with virial temperatures below 104 Ix. is completely suppressed by photodissociation of hydrogen molecules by UV radiation produced by nearby objects. aud we study the inupact of this assumption in further detail below.," We assume that the formation of Population III (Pop III) objects, defined as halos with virial temperatures below $10^4$ K, is completely suppressed by photodissociation of hydrogen molecules by UV radiation produced by nearby objects, and we study the impact of this assumption in further detail below."
 Usine the elliptical collapse imiodel of Sheth. Mo. Tormen (1999). we ideutifv all wvirialized peaks in the overdeusitv field. arrange them in order of decreasing collapse redshift. and exchide all uuplivsical objects collapsing within more massive. already virialized halos.," Using the elliptical collapse model of Sheth, Mo, Tormen (1999), we identify all `virialized' peaks in the overdensity field, arrange them in order of decreasing collapse redshift, and exclude all unphysical objects collapsing within more massive, already virialized halos."
 After collapse. we account for the finite gas cooling time using a simple insideout collapse model (White Freuls 1991: Somerville 1997).," After collapse, we account for the finite gas cooling time using a simple inside–out collapse model (White Frenk 1991; Somerville 1997)."
" The cooling eas initially relaxes to an isothermal distribution at the virial tempcrature Ti, aa Navarro. Frenk. White (1997. hereafter NEW) dark matter halo with concentration parameter e=5. aud with a uniform metallicity Z calculated as described in thle uext Section."," The cooling gas initially relaxes to an isothermal distribution at the virial temperature $T_{\rm vir}$ in a Navarro, Frenk, White (1997, hereafter NFW) dark matter halo with concentration parameter $c =5$, and with a uniform metallicity $Z$ calculated as described in the next Section."
 In this model.the gas within a radius resol cools due to radiative losses that accouut for metallicity as tabulated by Sutherland and Dopita (1993). aud the gas outside this radius stavs at the virial teniperature of the halo. with ro) moving outwards with time.," In this model,the gas within a radius $r_{\rm cool}$ cools due to radiative losses that account for metallicity as tabulated by Sutherland and Dopita (1993), and the gas outside this radius stays at the virial temperature of the halo, with $r_{\rm cool}$ moving outwards with time."
 This iiodel is described in further detail in SD., This model is described in further detail in SB.
" When the total mass contained within reo) equals the object's harvonic mass. a new galaxy is assumed to form with a eas mass AY,=(0,/03;)M. Iu the smaller halos at lieh redshift having logTj,<5.7 (e. masses AL<2.10M|:)/10|77 NES). rapid. cooling by. atomic lydrogen aud helm occurs ou timescales wach shorter than the eas freefall time. aud iufalliug eas collapses to the ceuter at the freefall rate rather than coming to hydrostatic equilibrium (MER)."," When the total mass contained within $r_{\rm cool}$ equals the object's baryonic mass, a new galaxy is assumed to form with a gas mass $M_b=({\Omega_b/\Omega_M})M.$ In the smaller halos at high redshift having $\log T_{\rm vir}<5.7$ (i.e. masses $M<2\times 10^{10}\,[(1+z)/10]^{-3/2}\,\msun$ ), rapid cooling by atomic hydrogen and helium occurs on timescales much shorter than the gas free–fall time, and infalling gas collapses to the center at the free–fall rate rather than coming to hydrostatic equilibrium (MFR)."
 The supply of cold gas for star formation is then only limited by the infall rate., The supply of cold gas for star formation is then only limited by the infall rate.
" We asstuue a Salpeter initial mass function (AIF) with upper and lower mass cutoffs equal to M,=120M. aud Ad;=0. AL... respectively."," We assume a Salpeter initial mass function (IMF) with upper and lower mass cut–offs equal to $M_u=120\,\msun$ and $M_l=0.1\,\msun$ respectively."
 Tn this case. oue SN occurs for every p|zm136M. of stars formed. releasing an cucrey," In this case, one SN occurs for every $\nu^{-1}\approx
136\,\msun$ of stars formed, releasing an energy"
the rather low inferred volume filling factor for which metals have been detected. about 20-40 of barvons must already be enriched with metals to explain the observed absorption.,"the rather low inferred volume filling factor for which metals have been detected, about 20-40 of baryons must already be enriched with metals to explain the observed absorption."
 We have used. a large sample of synthetic spectra which mimic the observational properties of four observed. 050 spectra to interpret the results of a search for in the ow density LGAL, We have used a large sample of synthetic spectra which mimic the observational properties of four observed QSO spectra to interpret the results of a search for in the low density IGM.
 Our results can be summarised as follows., Our results can be summarised as follows.
 We would like to thank Michael Rauch. Len Cowie and ESO for providing the observed spectra and the referee Anthony Aguiree for a helpful report.," We would like to thank Michael Rauch, Len Cowie and ESO for providing the observed spectra and the referee Anthony Aguiree for a helpful report."
 The authors would further like to thank Steve Warren for his useful suggestions and Alex Ixing and Thomas Babbecdge for helpful comments on the manuscript., The authors would further like to thank Steve Warren for his useful suggestions and Alex King and Thomas Babbedge for helpful comments on the manuscript.
" This work was supported by the European Community Research and ‘Training Network “Phe Physics of the Intergalactic Medium""", This work was supported by the European Community Research and Training Network “The Physics of the Intergalactic Medium”
All of these characteristics disagree with the observed (clnental abundances of these metal-poor DLAs.,All of these characteristics disagree with the observed elemental abundances of these metal-poor DLAs.
 Even i lueh+vedshift. there is no signature of the existence of PISNe.," Even at high-redshift, there is no signature of the existence of PISNe."
 The |Si/C] for PISNe is as large as. |1.5. which is also inconsistent with the observational estimate in the intergalactic medi ICAL (|Siο) ~O77. Aguirrectal.2001)).," The [Si/C] for PISNe is as large as $+1.5$, which is also inconsistent with the observational estimate in the intergalactic medium (IGM) ([Si/C] $\sim 0.77$, \citealt{agu04}) )."
 The ICAL abundance looks more conusisteut with nonual (uou-faimt) core-collapse superuovae witli [C/Fo] ~0 and |Si/Fe] ~0.7 (IX06)., The IGM abundance looks more consistent with normal (non-faint) core-collapse supernovae with [C/Fe] $\sim 0$ and [Si/Fe] $\sim 0.7$ (K06).
 We have shown that the eurchniuent source of the extremely metal-poor DLA is very likely a primordial supernova that is faint as a result of nüxiue-fallback to form a3GAL. black hole., We have shown that the enrichment source of the extremely metal-poor DLA is very likely a primordial supernova that is faint as a result of mixing-fallback to form a $3-6M_\odot$ black hole.
 It is interesting that the observed DLA abuudauce is very sinulax to those of EMP stars in the solar neighborhood including the ultra metal star HEQO557-IslO ΤΟΤΠ) 2.75. 0το =|1.6. Norrisetal. 2007)) and L17193 (Itoetal.2009).," It is interesting that the observed DLA abundance is very similar to those of EMP stars in the solar neighborhood including the ultra metal-poor star HE0557-4840 ([Fe/H] $=-4.75$, [C/Fe] $=+1.6$, \citealt{nor07}) ) and $^\circ$ 493 \citep{ito09}."
. Without rotation. the chenuücal eurichiueut from very luassbve stars {>50— 10037.) is very sinall because the central part is supposed to fall onto the black hole.," Without rotation, the chemical enrichment from very massive stars $\gtsim 50-100 M_\odot$ ) is very small because the central part is supposed to fall onto the black hole."
 Iu the carly stages of galaxw formation. chemical eurichineut is likely to be driven by core-collapse superuovae frou ~20FOAL. stars. although the mass range depeuds ou the rotation.," In the early stages of galaxy formation, chemical enrichment is likely to be driven by core-collapse supernovae from $\sim 20-50 M_\odot$ stars, although the mass range depends on the rotation."
 Wow did the first superuova enrich the first galaxy?, How did the first supernova enrich the first galaxy?
 Iu our supernova scenario. we assume that the first Supernova occurs a primordial gas cloud with the otal mass of 10°inAZ...," In our supernova scenario, we assume that the first supernova occurs in a primordial gas cloud with the total mass of $10^{6-7} M_\odot$."
 Iu. lyvdrocvuamical sinmulatious (0.8...MacLow&Ferrara1999).. the interstellar 1ediu (ISMD is ionized by the supernova explosion. aud the IIT nass rapidly decreases.," In hydrodynamical simulations \citep[e.g.,][]{mac99}, the interstellar medium (ISM) is ionized by the supernova explosion, and the HI mass rapidly decreases."
 Afterwards. the IT mass slightly Increases due to the recombination. and then decreases due to galactic mass-outflow.," Afterwards, the HI mass slightly increases due to the recombination, and then decreases due to galactic mass-outflow."
 Some of the ISAL could jiwe the Π ου density of logNCI)~20.5 and could be observed as DLAs., Some of the ISM could have the HI column density of $\log N({\rm HI})\sim 20.5$ and could be observed as DLAs.
 The observable III regions could have AZ(IID) ~300047... although the HI mass Πο] depends ou the total mass of the galaxy. the radial density profile. aud the imhomoeecucity of the ISM.," The observable HI regions could have $M({\rm HI})$ $\sim 3000M_\odot$, although the HI mass highly depends on the total mass of the galaxy, the radial density profile, and the inhomogeneity of the ISM."
" With our faint supernova models. the ejected € mass is 0ολ, which is roughly cousisteut with the observed C-rich DLA."," With our faint supernova models, the ejected C mass is $\sim 0.2M_\odot$, which is roughly consistent with the observed C-rich DLA."
 Iu Cookeetal.(2010b).. the masses of carbon aud neutral eas of the C-rich DLA are estimated as AL(CTI)~2(14TI)Lem5)aL and AVOID~2.5&104(μα)σαι72)>2| AL... which. are cousisteut. with- our scenario 1 ΕΠ)~3«0u5m ," In \citet{coo10b}, the masses of carbon and neutral gas of the C-rich DLA are estimated as $M({\rm CII}) \sim 2 \left(n({\rm H})/1\,{\rm cm}^{-3}\right)^{-2} M_\odot$ and $M({\rm HI}) \sim 2.5 \times 10^4 \left(n({\rm H})/1\,{\rm cm}^{-3}\right)^{-2} M_\odot$ , which are consistent with our scenario if $n({\rm H}) \sim 3\,{\rm cm}^{-3}$ ."
Are there anv signatures of the first stars in other metal-poor svstenis?, Are there any signatures of the first stars in other metal-poor systems?
" For globular cluster svstenis (CCS). the present stellar mass aud half-lieht radius are 104SAL. and 3.35 pe (eg.Cilinoreetal.2007).. respectively, which imply high deusities (09~ 1000)."," For globular cluster systems (GCSs), the present stellar mass and half-light radius are $10^{4-6}M_\odot$ and $1-35$ pc \citep[e.g.,][]{gil07}, respectively, which imply high densities $n \sim 1000$ )."
 Since the contribution of dark matter is small. the total mass would be 107?AZ. with the range of star formation efficiencies (0.001. 0.1).," Since the contribution of dark matter is small, the total mass would be $10^{5-9} M_\odot$ with the range of star formation efficiencies $0.001-0.1$ )."
 The progenitors of GCSs could be more massive if the CCS have lost a large fraction of stars bv the relaxation as shown in N-body smmlatious (Lamersetal.2010)., The progenitors of GCSs could be more massive if the GCS have lost a large fraction of stars by the relaxation as shown in N-body simulations \citep{lam10}.
. Star formation fakes place quickly and >101000 zuperuovae are expected to occur from the stellar mass with the Salpeter initial mass function. which mieht blow away the ISM and quench star formation.," Star formation takes place quickly, and $\gtsim 10-1000$ supernovae are expected to occur from the stellar mass with the Salpeter initial mass function, which might blow away the ISM and quench star formation."
 This is consistent with the narrow inctallicity distribution functions aud the lack. of the scatter iu clemental abundance ratios (Carrettaetal.2009)., This is consistent with the narrow metallicity distribution functions and the lack of the scatter in elemental abundance ratios \citep{car09}.
. In the clemeutal abundance patterus. no carbou eunhaucemieut that seenis to be originated from supernuovae is seen.," In the elemental abundance patterns, no carbon enhancement that seems to be originated from supernovae is seen."
" For dwart spheroidal galaxies (dSpls). the present stell: niass and hal£light radius are 10?""AL. and 20.—1000 pe (e...Culinoreetal.2007).. respectively. nupbiug nuch lower deusities than in GCss,"," For dwarf spheroidal galaxies (dSphs), the present stellar mass and half-light radius are $10^{3-7}M_\odot$ and $20-1000$ pc \citep[e.g.,][]{gil07}, respectively, implying much lower densities than in GCSs."
" The dark uatter mass is about 104Αν, independent of the stellar nass (Celaetal.2009).", The dark matter mass is about $10^7M_\odot$ independent of the stellar mass \citep{geh09}.
. Frou the stellar mass. 1.104 supernovae are expected.," From the stellar mass, $1-10^4$ supernovae are expected."
 As seen in tlie observed. color- diagrams (Tolstoyetal.2009).. star formation akes place slowly with a very low rate. aud thus the ISM is likely to be inhomogencous.," As seen in the observed color-magnitude diagrams \citep{tol09}, star formation takes place slowly with a very low rate, and thus the ISM is likely to be inhomogeneous."
 The elemental abundance oittern can be used for the abundance profiling., The elemental abundance pattern can be used for the abundance profiling.
 Iu ‘act. a few EMP stars at |Fo/TI] 3.5 in dSphs do show carbou cuhaneement (Norrisetal.2010).. which sugeests a contribution from faint supernovac.," In fact, a few EMP stars at [Fe/H] $\ltsim -3.5$ in dSphs do show carbon enhancement \citep{nor10}, which suggests a contribution from faint supernovae."
 Also iu he outer halo of the Mills. Wav Calaxy. three stars at |Fe/II| <2.5 do show |C/Fe| ~12 (Beers 2010. xivate conumuanication): such stars may boe disrupted roni 91211».," Also in the outer halo of the Milky Way Galaxy, three stars at [Fe/H] $\ltsim -2.5$ do show [C/Fe] $\sim +2$ (Beers 2010, private communication); such stars may be disrupted from dSphs."
" Tn the carly stages of chemical eurichineut. the interstellar miediuni ds. supposed to be highly inhomogencous.— so that the properties of tho first objects can be directly extracted frou, the comparison between the observed clemeutal abundances ancl nucleosvuthesis vields."," In the early stages of chemical enrichment, the interstellar medium is supposed to be highly inhomogeneous, so that the properties of the first objects can be directly extracted from the comparison between the observed elemental abundances and nucleosynthesis yields."
 We have shown that the observed abundance pattern of the very metal-poor C-rich DLA is in excelleut agreement with the uucleosvuthesis viclds of a primordial star that explodes as a fait core-collapse supernova owing to the cfiicient mixing aud fallback., We have shown that the observed abundance pattern of the very metal-poor C-rich DLA is in excellent agreement with the nucleosynthesis yields of a primordial star that explodes as a faint core-collapse supernova owing to the efficient mixing and fallback.
 The uucleosvuthesis vields of PISNe are not. consistcut with the observation., The nucleosynthesis yields of PISNe are not consistent with the observation.
 The contribution from rotating lnassive stars seenüs to be small because of the lack of N chhancement., The contribution from rotating massive stars seems to be small because of the lack of N enhancement.
 The contribution from ACB stars should be very small because of the N abundance aud of the chrichinent timescale., The contribution from AGB stars should be very small because of the N abundance and of the enrichment timescale.
 Since the DLA abuucdiauces reflect the chemical eurichineut im eas-plase. the binary or accretion scenarios of the EXP stars do not work.," Since the DLA abundances reflect the chemical enrichment in gas-phase, the binary or accretion scenarios of the EMP stars do not work."
 Thus. we conclude that eurichinent by primordial swpernovac is the best solution to explain the abundance pattern of the C-rich DLA.," Thus, we conclude that enrichment by primordial supernovae is the best solution to explain the abundance pattern of the C-rich DLA."
 The abuudauce pattern of the C-vich DLA is similay to those of EMP stars such as the ultra metal-poor star WEO557-1810., The abundance pattern of the C-rich DLA is similar to those of EMP stars such as the ultra metal-poor star HE0557-4840.
 Some of EMP stars in dSphs aud the Galactic outer halo also show similar carbon chhancement at [Fe/TI 3., Some of EMP stars in dSphs and the Galactic outer halo also show similar carbon enhancement at [Fe/H] $\ltsim -3$.
 Chemical euriclineut by the first stars m the first galaxies is likely o be driven by core-collapse supernovac., Chemical enrichment by the first stars in the first galaxies is likely to be driven by core-collapse supernovae.
 We would like to thank M. Pettini aud R. Cooke or providing their results prior to publication., We would like to thank M. Pettini and R. Cooke for providing their results prior to publication.
 We also hawk J. Norris. B. Sutherland. €. Da Costa. D. Yong.and D. Mackevy for fruitful discussion.," We also thank J. Norris, R. Sutherland, G. Da Costa, D. Yong,and D. Mackey for fruitful discussion."
 This work has been supported in part by WPI Initiative. MEXT. Japan. aud w the Craut-in-Aid for Scieutifio Research of the JSPS (18101003. 20510226) and MENT (1901700L. 22012003).," This work has been supported in part by WPI Initiative, MEXT, Japan, and by the Grant-in-Aid for Scientific Research of the JSPS (18104003, 20540226) and MEXT (19047004, 22012003)."
rresonance line emission was detected.,resonance line emission was detected.
 Tight upper limits were placed on the 1032 and 1038 llines (see Section 4)., Tight upper limits were placed on the 1032 and 1038 lines (see Section 4).
 The results of our searches for other cosmic lines within the bandpass are also reported (see Section 4)., The results of our searches for other cosmic lines within the bandpass are also reported (see Section 4).
 Our upper limit on the ddoublet intensitv is well below the 4x10! Ix. overionized model (Breitschwerdt2001) predictions.," Our upper limit on the doublet intensity is well below the $4 \times 10^4$ K, overionized model \citep{breitschwerdt}
 predictions."
 This discrepancy. as well as discrepancies in the intensities and (he ecolumn densitv. practically disallow models of this sort.," This discrepancy, as well as discrepancies in the intensities and the column density, practically disallow models of this sort."
 Our (wo sigma upper limit on the ddoublet intensity is only mareinally above the minimum intensity expected from the -rich zone around the most local cool cloud (Slavin1939). combined with the VI--rich regions in Smith&Cox (2001)s suite of simulations of a multiple supernovae induced hot bubble., Our two sigma upper limit on the doublet intensity is only marginally above the minimum intensity expected from the -rich zone around the most local cool cloud \citep{slavin} combined with the -rich regions in \citet{smith_cox}' 's suite of simulations of a multiple supernovae induced hot bubble.
 In the event that the line of sight intersects multiple cool clouds within the Local Bubble. as well as the Local Dubble's wall. (hen our doublet upper limit is well below the predicted intensity. and places a strong constraint on models of hot gas/cool gas transition zones.," In the event that the line of sight intersects multiple cool clouds within the Local Bubble, as well as the Local Bubble's wall, then our doublet upper limit is well below the predicted intensity and places a strong constraint on models of hot gas/cool gas transition zones."
 In order to determine if the upper limits require the Local Bubble to be undergoing unusual physical processes or contain unusual plasmas. we constructed and compared with a generalized multi-component (an VI-rich ~3x10? IX plasma and a soft X-ray emitting ~10° IX plasma) model of the Local Bubble.," In order to determine if the upper limits require the Local Bubble to be undergoing unusual physical processes or contain unusual plasmas, we constructed and compared with a generalized multi-component (an -rich $\sim 3\times 10^5$ K plasma and a soft X-ray emitting $\sim 10^6$ K plasma) model of the Local Bubble."
 This model's lintensitv and column censity and soft X-ray surface brightness were all consistent with observations (see Section 5)., This model's intensity and column density and soft X-ray surface brightness were all consistent with observations (see Section 5).
 Dv combining our intensity upper limit with other researchers ecolumu densitv estimates. we were able to calculate limits on the electron densitv. thermal pressure. pathlength. aud cooling timescale (also see Section 5).," By combining our intensity upper limit with other researcher's column density estimates, we were able to calculate limits on the electron density, thermal pressure, pathlength, and cooling timescale (also see Section 5)."
 By subtracting the Local Dubbles ddoublet intensity upper limit from measurements for longer. high latitude lines of sights. we lound the halo's intensity. [rom which its electron density. thermal pressure. pathlength. and cooling rate were estimated.," By subtracting the Local Bubble's doublet intensity upper limit from measurements for longer, high latitude lines of sights, we found the halo's intensity, from which its electron density, thermal pressure, pathlength, and cooling rate were estimated."
 The results of this project are summarized in Section 6., The results of this project are summarized in Section 6.
 The intensitv of resonance line photons [rom aalong extended lines of sight through the Local Bubble. the Galactic halo. and intervening regions is reported elsewhere (Sheltonetal.2001:al 2002).. Ile," 	The intensity of resonance line photons from along extended lines of sight through the Local Bubble, the Galactic halo, and intervening regions is reported elsewhere \citep{shelton_etal,dixon_etal,shelton,welsh_etal}."
re. we wish to measure (he iintensitv of the Local Bubble. aud so must block the photons from external regions.," Here, we wish to measure the intensity of the Local Bubble, and so must block the photons from external regions."
" To cdo so. we employ the ""shadowing sirategv oft-used in N-rayx. analvses."," To do so, we employ the “shadowing” strategy oft-used in X-ray analyses."
 In (he ideal shadowius, In the ideal shadowing
"13 Lots. where 77, is the electron density.",1.3 10^4 where $n_e$ is the electron density.
" We assume [ree-[all velocities on the order of 300 kins ο and electron densities of abbout 10em.? and 5xLO!em.7, respectively. and temperatures around 8000 Ix (Muzerroleetal.1998)."," We assume free-fall velocities on the order of 300 ${\rm km \; s}^{-1}$, ties and electron densities of bout $10^{12} \; {\rm cm}^{-3}$ and $5 \times 10^{11}
\; {\rm cm}^{-3}$, respectively, and temperatures around 8000 K \citep{muz..98}."
. The length of the tube is approximately 107? em., The length of the tube is approximately $10^{12}$ cm.
 Using these values in equation (28)). we obtain ox," Using these values in equation \ref{razao2}) ), we obtain 5."
"i) Therefore. the term related to thermal conductivity. (&/pe,)V7T. is very small. compared to the term |2vVT|."," Therefore, the term related to thermal conductivity, $(\kappa/ \rho c_v)
\nabla^2 T$ , is very small, compared to the term $|-{\bf v} \cdot \nabla
T|$."
 We thus conclude that temperature gradients are maintained in the tube because thermal conduction is not efficient., We thus conclude that temperature gradients are maintained in the tube because thermal conduction is not efficient.
 Estimating the time scale related (o this process. we obtain GNL))? 5.5 10*vears.," Estimating the time scale related to this process, we obtain )^2 5.5 10^7."
".(31) This (me scale is very long. compared to the free fall time scale (ip,9 hr)."," This time scale is very long, compared to the free fall time scale $t_{ff} \sim 9$ hr)."
 We conclude. therefore. that thermal conduction is not important for the region near the star and. consequently. Alfvénn waves generated near the shock region cannot contribute to an increase in temperature of the whole tube.," We conclude, therefore, that thermal conduction is not important for the region near the star and, consequently, Alfvénn waves generated near the shock region cannot contribute to an increase in temperature of the whole tube."
 Jaleliceetal.(1990.andreferences(herein) proposed (hat the Ixelvin-IHlelmholtz (Ix-11) instability produced in an extragalactic jet bv the shear in the plasma flow with respect to the ambient medium can generate MIDID waves., \citet[ and references therein]{jafe..90} proposed that the Kelvin-Helmholtz (K-H) instability produced in an extragalactic jet by the shear in the plasma flow with respect to the ambient medium can generate MHD waves.
 Thev suggested (hat these waves. once camped. can eive rise to currents capable of generating magnetic fields.," They suggested that these waves, once damped, can give rise to currents capable of generating magnetic fields."
 In the case of the magnetic funnels of T Tauri stars. there is also a shear between the gas falling onto the star and the external medium.," In the case of the magnetic funnels of T Tauri stars, there is also a shear between the gas falling onto the star and the external medium."
 This flow. however. is sub-Alfvénnic and. therelore. the development of Ixelvin-Hehlnholtz modes is not expected.," This flow, however, is sub-Alfvénnic and, therefore, the development of Kelvin-Helmholtz modes is not expected."
 In fact. Hardeeetal.(1992). performed an analvtical and numerical analvsis of the Ixelvin-Ilelmholtz instability in magnetized jets and show that the fundamental mode is completely stabilized if the magnetic Mach number[Mins=Crateνο+ UA] is less than unity.," In fact, \citet{hardee..92} performed an analytical and numerical analysis of the Kelvin-Helmholtz instability in magnetized jets and show that the fundamental mode is completely stabilized if the magnetic Mach number$M_{ms} = v_{tube} / \sqrt{c_{s}^2 + v_{A}^{2}}$ ] is less than unity."
We now need only to apply Algorithm 1 in order to compute the solution.,We now need only to apply Algorithm \ref{algo:primdual} in order to compute the solution.
" This requires computation of the three proximity operators, which are given by the following proposition: The application of Proposition 4 and Lemma 2 to the optimization problem in Equation(A4), using the the primal-dual scheme in Algorithm 1,, yields the reconstruction algorithm expressed in Algorithm 2.."," This requires computation of the three proximity operators, which are given by the following proposition: The application of Proposition \ref{prop:palg} and Lemma \ref{lem:decomp} to the optimization problem in Equation, using the the primal-dual scheme in Algorithm \ref{algo:primdual}, yields the reconstruction algorithm expressed in Algorithm \ref{alg:inversion}."
" Application of the method described in Appendix AppendixA: to the specific case of 3D lensing leads us to Algorithm 2,, where one can note the projection over the two constraints described above (data fidelity and minimum value of the solution), and the operator St,, which imposes a soft threshold at a level of λ/ω as: The main difficulty with the primal-dual scheme described above — indeed, with any iterative algorithm — is to define an appropriate convergence criterion."," Application of the method described in Appendix \ref{sec:solv-optim-probl} to the specific case of 3D lensing leads us to Algorithm \ref{alg:inversion}, where one can note the projection over the two constraints described above (data fidelity and minimum value of the solution), and the operator ${\cal S}t_{\lambda}$, which imposes a soft threshold at a level of $\lambda/\omega$ as: The main difficulty with the primal-dual scheme described above – indeed, with any iterative algorithm – is to define an appropriate convergence criterion."
" In this case, the difference between two successive iterates x’ and x/*! is not bounded."," In this case, the difference between two successive iterates $\bx^{t}$ and $\bx^{t+1}$ is not bounded."
" However, the partial primal-dual gap 654, defined by: (when solving (A3))) is bounded."," However, the partial primal-dual gap $\mathfrak{G}_{pd}$, defined by: (when solving ) is bounded."
" Here, G* is the convex conjugate of convex function G: Let us define two variables from the sequences (x’), and (£)« produced by Algorithm 1:: which are the at iteration N— 1."," Here, $G^*$ is the convex conjugate of convex function $G$: Let us define two variables from the sequences $(\bx^t)_t$ and $(\boldsymbol{\xi}^t)_t$ produced by Algorithm \ref{algo:primdual}: which are the at iteration $N-1$ ."
" ? have shown that the sequence defined by (6,4(x, is bounded, and decreases at a rate of O(1/t), where t €))is venthe iteration number."," \citet{cp10} have shown that the sequence defined by $\left(\mathfrak{G}_{pd} (\bx^N,\boldsymbol{\xi}^N)\right)_{N \in \mathbb{N}}$ is bounded, and decreases at a rate of $\mathcal{O}(1/t)$, where $t$ is the iteration number."
" In order to use in our context, the two indicatrice functions inside are not considered, as they play little role."," In order to use in our context, the two indicatrice functions inside are not considered, as they play little role."
" Therefore, in our case, we may rewriteO,4(x,y) as: We determine the algorithm to have converged when"," Therefore, in our case, we may rewrite$\mathfrak{G}_{pd} (\bx,\by)$ as: We determine the algorithm to have converged when"
van Kerkwijk et 22000: Bassa et 22006b).,van Kerkwijk et 2000; Bassa et 2006b).
 However. the space densities of these different samples are extremely different.," However, the space densities of these different samples are extremely different."
 The companions to pulsars have been discovered they are orbiting a pulsar. unlike the photometrically-discovered UCWD sample: Bassa. van KerkwiJk Kulkarni state that PSR JO751+1807 is ~0.6 kpe away. considerably further than any of our UCWD sample (see Table D). and PSR J0437-4715 is 150 pe away (Danziger et 11993). beyond all but one of the photometrically-discovered UCWDs.," The companions to pulsars have been discovered they are orbiting a pulsar, unlike the photometrically-discovered UCWD sample: Bassa, van Kerkwijk Kulkarni state that PSR J0751+1807 is $\sim$ 0.6 kpc away, considerably further than any of our UCWD sample (see Table \ref{tab:UCWD_dist}) ), and PSR J0437-4715 is 150 pc away (Danziger et 1993), beyond all but one of the photometrically-discovered UCWDs."
 A crude comparison between the possible detection volumes of the single UCWDs and the pulsar companions gives ~(600/70)=630.," A crude comparison between the possible detection volumes of the single UCWDs and the pulsar companions gives $\sim(600/70)^{3} \approx
630$."
 Here we have considered that COMBO-17 J1143. às a serendipitously discovered object. does not give a good measure of the systematic detection volume of the UCWDs in our sample.," Here we have considered that COMBO-17 J1143, as a serendipitously discovered object, does not give a good measure of the systematic detection volume of the UCWDs in our sample."
 This suggests that. even if the companions to PSR JO751+1807 and PSR J0437-4715 were cool enough to be UCWDs. the seven systematically discovered UCWDs in our sample are ~2200 times more abundant than those with pulsar companions.," This suggests that, even if the companions to PSR J0751+1807 and PSR J0437-4715 were cool enough to be UCWDs, the seven systematically discovered UCWDs in our sample are $\sim2200$ times more abundant than those with pulsar companions."
 This factor can be increased by another order of magnitude if one assumes that all the known nearby pulsars have been studied. but that only a tenth of the sky has been surveyed to the same depth as the field that produced the SDSS UCWD sample.," This factor can be increased by another order of magnitude if one assumes that all the known nearby pulsars have been studied, but that only a tenth of the sky has been surveyed to the same depth as the field that produced the SDSS UCWD sample."
 To only observe one pulsar in ~20.000 supposedly MSP-containing objects would imply extremely narrow-beam pulsar emission.," To only observe one pulsar in $\sim 20,000$ supposedly MSP-containing objects would imply extremely narrow-beam pulsar emission."
 Unless those unseen MSPs were somehow unusual. this would suggest that many more pulsars exist than we currently expect. significantly worsening any mismatch between the inferred birthrates of LMXBs and MSPs (e.g. Kulkarni Narayan 1988: Lorimer 1995; Pfahl. Rappaport Podsiadlowski If a NS was formed in the system through AIC and was not subsequently spun up. it could reasonably be expected not to emit pulsar radiation.," Unless those unseen MSPs were somehow unusual, this would suggest that many more pulsars exist than we currently expect, significantly worsening any mismatch between the inferred birthrates of LMXBs and MSPs (e.g. Kulkarni Narayan 1988; Lorimer 1995; Pfahl, Rappaport Podsiadlowski If a NS was formed in the system through AIC and was not subsequently spun up, it could reasonably be expected not to emit pulsar radiation."
 A black-hole companion would. of course. not be expected to emit pulsar radiation. but a local space density for such black-hole binaries of 1015pe (see section 4.4)) is highly unexpected (see. e.g.. Romani 1905).," A black-hole companion would, of course, not be expected to emit pulsar radiation, but a local space density for such black-hole binaries of $\rm \sim 10^{-5} ~pc^{-3}$ (see section \ref{sec:PopNumb}) ) is highly unexpected (see, e.g., Romani 1998)."
 Gates et ((2004) estimated a space density for UCWDs of 3x107pe from a sample of 6 objects found in the Sloan digital sky This rough figure does compare with an estimate of the SN Ia rate integrated over time and space.," Gates et (2004) estimated a space density for UCWDs of $\rm 3
\times 10^{-5} ~pc^{-3}$ from a sample of 6 objects found in the Sloan digital sky This rough figure does compare with an estimate of the SN Ia rate integrated over time and space."
 The local stellar density of 0.1M.pe? (Binney Merrifield 1998). combined with a mass for the thin disc of ~4x101M. and the assumption that the mass fraction of UCWDs ts constant throughout the disc. produces an estimate for the number of UCWDs of ~10.," The local stellar density of $\rm 0.1 ~{\rm M_{\odot}} ~pc^{-3}$ (Binney Merrifield 1998), combined with a mass for the thin disc of $\rm \sim
4 \times 10^{10} ~{\rm M_{\odot}}$ and the assumption that the mass fraction of UCWDs is constant throughout the disc, produces an estimate for the number of UCWDs of $\sim 10^{7}$ ."
 We approximate the current SN Ia rate in the Galactic disc as ~7x107/yr (using the same dise mass as above and the SN Ia rate per unit mass of Mannueei et 22005).," We approximate the current SN Ia rate in the Galactic disc as $\rm
\sim 7 \times 10^{-3} ~/ yr$ (using the same disc mass as above and the SN Ia rate per unit mass of Mannucci et 2005)."
 Multiplying this rate by a Galactic age of ~10Gyr leads to an estimate of a total of ~7x10) Even if we halve this number of remnants to allow for the WD cooling time (see section 4.2)). the number of single UCWDs ts easily consistent with them being produced through SN la. Indeed. these numbers suggest that only a subset of SNe la produces single UCWDs. which is as expected if only a subset of the SN Ia formation channels can produce LMWDs (see sections 3.1 3.2)).," Multiplying this rate by a Galactic age of $\rm \sim 10~Gyr$ leads to an estimate of a total of $\rm \sim 7 \times 10^{7}$ Even if we halve this number of remnants to allow for the WD cooling time (see section \ref{sec:UCWDsLMWDs}) ), the number of single UCWDs is easily consistent with them being produced through SN Ia. Indeed, these numbers suggest that only a subset of SNe Ia produces single UCWDs, which is as expected if only a subset of the SN Ia formation channels can produce LMWDs (see sections \ref{sec:formation} \ref{sec:RemMass}) )."
 The lack of lines in UCWD spectra means that we do not know the radial velocities for our sample., The lack of lines in UCWD spectra means that we do not know the radial velocities for our sample.
 However. we can examine the population kinematics using only the information from the tangential velocities.," However, we can examine the population kinematics using only the information from the tangential velocities."
 We now investigate whether their observed space velocities are consistent with single LMWDs released from binaries with a range of orbital periods., We now investigate whether their observed space velocities are consistent with single LMWDs released from binaries with a range of orbital periods.
 For à range of inital parameters. we integrated the motion of 10° assumed SN la remnants for up to 10 Gyr through the Galactic potential (using a similar procedure to Brandt Podsiadlowski 1995). orientating the orbital velocity vector of the donor at random wher the binary is disrupted.," For a range of inital parameters, we integrated the motion of $\rm
10^{5}$ assumed SN Ia remnants for up to 10 Gyr through the Galactic potential (using a similar procedure to Brandt Podsiadlowski 1995), orientating the orbital velocity vector of the donor at random when the binary is disrupted."
 For each integrated population. we used a single value of orbital period (and hence orbital velocity) at the time of the For calculating the orbital velocity at a given orbital period. donor stars are assumed to be 0.5M. at the time of the explosion. and the WDs are assumed to explode at a mass of 1.4M...," For each integrated population, we used a single value of orbital period (and hence orbital velocity) at the time of the For calculating the orbital velocity at a given orbital period, donor stars are assumed to be $\rm 0.5 ~{\rm M_{\odot}}$ at the time of the explosion, and the WDs are assumed to explode at a mass of $\rm 1.4 ~{\rm
M_{\odot}}$."
 Equation | shows that our results should be relatively insensitive to those assumptions. but in the future we intend to perform this procedure using the output of our binary population synthesis caleulations.," Equation \ref{eq:Vorb} shows that our results should be relatively insensitive to those assumptions, but in the future we intend to perform this procedure using the output of our binary population synthesis calculations."
 Each remnant is initially located at random within an axisymmetric Galaxy modelled by two exponential scale-heights (vertical and radial)., Each remnant is initially located at random within an axisymmetric Galaxy modelled by two exponential scale-heights (vertical and radial).
 The axisymmetry ts also exploited for computational efficiency: at each integration time-step the view from Earth is calculated at all points on the solar circle., The axisymmetry is also exploited for computational efficiency: at each integration time-step the view from Earth is calculated at all points on the solar circle.
 A further assumption ts that the remnants can be observed to a distance of 160 pe — broadly appropriate for UCWDs., A further assumption is that the remnants can be observed to a distance of 160 pc – broadly appropriate for UCWDs.
 Within sucha small volume. the space velocities should only be a very weak function of distance.," Within sucha small volume, the space velocities should only be a very weak function of distance."
" Aspluud(2005.ACSO5) Z/.X Grevesse&Nocls Crevesse&Sauval(L998.CSO) Aspluudetal.(2005) Aspluudctal.(2009.ACSO9) Z/.X Anders&Crevesse(1950). Aspluundetal.(2005) Asplundetal.(2009) Bahcalletal.(2005a) ""solar imaodel problemi which has been coufirmed iu many subsequent. indepeudeut. publiceatious."," \citet[AGS05]{ags:2005}
 $Z/X$ \citet[GN93]{gn:93} \citet[GS98]{gs:98} \citet{ags:2005} \citet[AGS09]{ags:2009} $Z/X$ \citet{ag:89}, \cite{ags:2005} \cite{ags:2009} \citet{bbps:2005} “solar model problem”, which has been confirmed in many subsequent, independent publications."
 Autia&Basu(2006) further demonstrated that helioseisuic data require the solar envelope to have a composition close to the old photospheric abundances. aud. Chaplinctal.(2007) used low-cegree p-modes peuctrating to the solar core to arrive at a similar conclusion.," \citet{ab:2006} further demonstrated that helioseismic data require the solar envelope to have a composition close to the old photospheric abundances, and \citet{csbev:2007} used low-degree p-modes penetrating to the solar core to arrive at a similar conclusion."
" To cure the ""trouble in paradise” (Asplundetal.2005) attempts were undertaken to confirm the previous. higherabundances of intermediate clemeuts. in particular of oxveen (eg. Conteuo&Socas-Nawiuro2008:Caffauetal. 2008)."," To cure the “trouble in paradise” \citep{ags:2005} attempts were undertaken to confirm the previous, higherabundances of intermediate elements, in particular of oxygen \citep[e.g.\ ][]{csn:2008,clsab:2008}."
. On the other haud. the lower abundances were recovered. too (Maiorcaetal.2009. for nitrogen: Socas-Navairo&Norton2007. for oxvgeu).," On the other hand, the lower abundances were recovered, too \citealt{mcbb:2009} for nitrogen; \citealt{snn:2007} for oxygen)."
 On the side of the solar model comumunuity. possible or necessary changes to the constitutional physics were discussed to restore the previous excellent agreement with helioseisiiologyv (see Carzik2008 for a stuuimary).," On the side of the solar model community, possible or necessary changes to the constitutional physics were discussed to restore the previous excellent agreement with helioseismology (see \citealt{guzik:2008} for a summary)."
 Iu uwtieular. an increase of opacities has been considered he most promising approach (Basu&Αα2001:Dali-Dalseaardetal. 2009).," In particular, an increase of opacities has been considered the most promising approach \citep{ba:2004,bbs:2005,ab:2006,cddmhp:2009}."
. But updated Bosselaud opacities or the solar interior are not enough to solve the solar abundance problem (Bahealletal.2005¢)., But updated Rosseland opacities for the solar interior are not enough to solve the solar abundance problem \citep{bsb:2005}.
. Also. a xostulated upward correction to theneonabundaucelas rotfoundobservationalsupport(Young 2005)..," Also, a postulated upward correction to theneonabundancehas notfoundobservationalsupport\citep{young:2005}. ."
 It is therefore reasonable to shift attention also to other stellarobjects. since any revision of the solar," It is therefore reasonable to shift attention also to other stellarobjects, since any revision of the solar"
As mentioned above. the observatious were united to the optical major axis: [or most galaxies. this is the axis with the largest. velocity eradient. and thus it is reasonable to assume that the rotation curves measured here are representaive.,"As mentioned above, the observations were limited to the optical major axis; for most galaxies, this is the axis with the largest velocity gradient, and thus it is reasonable to assume that the rotation curves measured here are representative."
 However. tje stellar rotation curves we'e tracecl out to only a modest radius whereas he neutral gas velocity widths include emission TOW fus that extends well bevond the optical galaxy.," However, the stellar rotation curves were traced out to only a modest radius whereas the neutral gas velocity widths include emission from gas that extends well beyond the optical galaxy."
 onetheless. ifi ie clwarl elliptical galaxies axl cbwart irregular galaxies have similar kilematic pro»erties. it slioul be pxsible to correct for this effect Ol à statistical basis.," Nonetheless, if the dwarf elliptical galaxies and dwarf irregular galaxies have similar kinematic properties, it should be possible to correct for this effect on a statistical basis."
 For comparison. we conside: (the 1eutral gas distributio1 and kinematics for a sample of 20 ealaxies selected [rou he optica imaglug samples of vauZeeetal.(1097a) aud vauZee(2001).. Le. a subset ol tle dwarf irregular gaaxies shown in Figre 6..," For comparison, we consider the neutral gas distribution and kinematics for a sample of 20 galaxies selected from the optical imaging samples of \citet{vHS97} and \citet{vZ01}, i.e., a subset of the dwarf irregular galaxies shown in Figure \ref{fig:tf}."
 The resolved HI distribution aud kilelatics were ¢Malued with Very Large Array duriug several observing runs (rom 1993 - 2000., The resolved HI distribution and kinematics were obtained with Very Large Array during several observing runs from 1993 - 2000.
 While the majority of the HI svnhesis data is as yet uupublished. the dI sample incluces the gaaxles in valZeeetal.(199b) with distances scaed to al Hy of 75 1.," While the majority of the HI synthesis data is as yet unpublished, the dI sample includes the galaxies in \citet{vHSB97} with distances scaled to an $_0$ of 75 $^{-1}$."
 Α histoer‘ain ofthe exlen of the HI distrioution to optical scale length for the dI sample is shown in Fietre Taa. Τοeternine the statistical correction to coivert [ron a stellar rotation width to a neutra gas rotation with. we measured the ratio oftle 1naximun 1'otation velocity to the slope of the rotalion curve.," A histogram of the extent of the HI distribution to optical scale length for the dI sample is shown in Figure \ref{fig:slope}a a. To determine the statistical correction to convert from a stellar rotation width to a neutral gas rotation width, we measured the ratio of the maximum rotation velocity to the slope of the rotation curve."
 A histogram of the Va /slope for dwarf irreguar galaxies is shown in Figure Tob. wiere the sloyye of he rotation curve is in units of per scale length.," A histogram of the $_{\rm max}$ /slope for dwarf irregular galaxies is shown in Figure \ref{fig:slope}b b, where the slope of the rotation curve is in units of per scale length."
 The nean value is 3.[5 c 0.58 scale lenetls. which shows remarkable (ard perliaps co-iucidental) agreement with the ise of he velocity at 2.2 scale lenelis as a fiducial measure of spiral galaxy rotation curves 1999).," The mean value is 2.45 $\pm$ 0.58 scale lengths, which shows remarkable (and perhaps co-incidental) agreement with the use of the velocity at 2.2 scale lengths as a fiducial measure of spiral galaxy rotation curves \citep[e.g.,][]{CR99}."
. Based on t1ese results. it is lisely that the stelar rotation curves obtained rere uucderestimate the maximum 1Xation velocity for the dwarf elliptical galaxies sitce most were raced out to only 1 - 1.5 scale lenehs.," Based on these results, it is likely that the stellar rotation curves obtained here underestimate the maximum rotation velocity for the dwarf elliptical galaxies since most were traced out to only 1 - 1.5 scale lengths."
 Arrows in Figure 6. indicate tie location of each galaxy if hestelar rotation curves were traced to 2.15 scale leneths aud the gaaxy dyjalules ollow similar elcs as those of the neutral gas it dL galaxies., Arrows in Figure \ref{fig:tf} indicate the location of each galaxy if the stellar rotation curves were traced to 2.45 scale lengths and the galaxy dynamics follow similar trends as those of the neutral gas in dI galaxies.
 Civen the uncertainties associaed with this velocity width correcion. it is premature to draw ar reacune couclusious from the revised velocity widtlis.," Given the uncertainties associated with this velocity width correction, it is premature to draw far reaching conclusions from the revised velocity widths."
 Noneheless. it is important to note that such ineasureiments could provide siguilicaut coislralis ο1 the uminosity evoution of dE galaxies.," Nonetheless, it is important to note that such measurements could provide significant constraints on the luminosity evolution of dE galaxies."
 In particular. these rough correcion [actors indicate that the progenitor galaxies were at tnost ouly 2 uaguitudes more luminous than the p'sent poptlatioi (Le.. the revised rotation widlis are comparable to those of galaxies 2 immagnittdes more Updaucous).," In particular, these rough correction factors indicate that the progenitor galaxies were at most only 2 magnitudes more luminous than the present population (i.e., the revised rotation widths are comparable to those of galaxies 2 magnitudes more luminous)."
 IHE these results are coudir by obse‘vatious that fully trace tle galaxy dynamics. the progeütor population of Virgo dEs uiIst be restricted to immoderate luminosity systems.," If these results are confirmed by observations that fully trace the galaxy dynamics, the progenitor population of Virgo dEs must be restricted to moderate luminosity systems."
 In particlar. i is unlikely that dEs evolve from significantly more luminous galaxien.," In particular, it is unlikely that dEs evolve from significantly more luminous galaxies."
 One of the perplexinge issues in egalaxy evolution is the remarkable commonality between dwarf elliptical galaxies aud dwarl irregular galaxies., One of the perplexing issues in galaxy evolution is the remarkable commonality between dwarf elliptical galaxies and dwarf irregular galaxies.
 These low iass systems have similar stellar, These low mass systems have similar stellar
Can a non-linear fitting process improve upon our optimal linear shear estimates of M200m?,Can a non-linear fitting process improve upon our optimal linear shear estimates of $M_{200m}$?
" For comparison, we note that for two-dimensional fitting of an NFW profile with Mo2oo& and c2oos as free parameters, a sample with halos of mass Mooo>4:1019 from the same simulation has c4/M=0.4 (0.27) for shape noise levels of 10 (40) aremin~? (?).."," For comparison, we note that for two-dimensional fitting of an NFW profile with $M_{200m}$ and $c_{200m}$ as free parameters, a sample with halos of mass $M_{200m}>4\cdot10^{14}\Msol$ from the same simulation has $\sigma_M/M=0.4$ $0.27$ ) for shape noise levels of 10 (40) $^{-2}$ \citep{2010arXiv1011.1681B}."
 We do not have results for the exact corresponding mass range and the methods differ in that we pre-sort halos into true mass bins., We do not have results for the exact corresponding mass range and the methods differ in that we pre-sort halos into true mass bins.
" However, the comparison of mass uncertainties suggests that the two-parameter non-linear fit does not yield significant improvements."," However, the comparison of mass uncertainties suggests that the two-parameter non-linear fit does not yield significant improvements."
 This is potentially because the contribution of concentration variation to the intrinsic variability of profiles is subdominant (cf., This is potentially because the contribution of concentration variation to the intrinsic variability of profiles is subdominant (cf.
 Section 3.1)) and a degeneracy between mass and concentration exists., Section \ref{sec:ipv}) ) and a degeneracy between mass and concentration exists.
 We briefly examine the optimal linear filters found by our procedure., We briefly examine the optimal linear filters found by our procedure.
 These take into account the covariance due to uncorrelated LSS along the line of sight and shape noise while minimizing the variance of the mass estimate empirically by using the simulated cluster shear profiles., These take into account the covariance due to uncorrelated LSS along the line of sight and shape noise while minimizing the variance of the mass estimate empirically by using the simulated cluster shear profiles.
 Figure 4 compares these S+U+C weights to the S and S+U filters optimized for NFW-profile clusters., Figure \ref{fig:weights} compares these $S+U+C$ weights to the $S$ and $S+U$ filters optimized for NFW-profile clusters.
" 'The optimized filters differ from the NFW-optimized filters in that they do not put as much weight to the innermost region, shifting the maximum of q-r to rz5' for the mass bin 1...2-10Mo."," The optimized filters differ from the NFW-optimized filters in that they do not put as much weight to the innermost region, shifting the maximum of $q\cdot r$ to $r\approx5'$ for the mass bin $1\ldots2\cdot10^{14}\Msol$."
" In terms of weights on convergence u, this puts more weight on projected density at intermediate distance from the core."," In terms of weights on convergence $u$, this puts more weight on projected density at intermediate distance from the core."
" Consequently, the convergence filter u compensates at larger radii."," Consequently, the convergence filter $u$ compensates at larger radii."
" All filters that take LSS into account, however, do put less weight on the shear signal outside r~10’, where the LSS signal becomes comparable to or larger than shape noise."," All filters that take LSS into account, however, do put less weight on the shear signal outside $r\approx10'$, where the LSS signal becomes comparable to or larger than shape noise."
" This suggests an explanation for why the S+U filter that includes uncorrelated LSS can perform worse than the S filter optimized only for shape noise: the S--U filter places higher weight on the intrinsically variable central region, generating noise that outweighs the gain from putting less weight to the outer regions where uncorrelated LSS dominates the errors. 7,"," This suggests an explanation for why the $S+U$ filter that includes uncorrelated LSS can perform worse than the $S$ filter optimized only for shape noise: the $S+U$ filter places higher weight on the intrinsically variable central region, generating noise that outweighs the gain from putting less weight to the outer regions where uncorrelated LSS dominates the errors. \citet{2007A&A...462..875S},"
 ? and ? discuss various reasons for the high uncertainty of shear measurements near the core and the benefits of downweighting the shear signal in that region., \citet{2010MNRAS.405.2078M} and \citet{2010arXiv1011.1084H} discuss various reasons for the high uncertainty of shear measurements near the core and the benefits of downweighting the shear signal in that region.
" Some of the effects mentioned are not present in our simulations, such as baryonic effects, signal dilution due to cluster member galaxies (which are most prominent near the center), and magnification-induced change and incomplete sampling of the redshift distribution of sources when no or"," Some of the effects mentioned are not present in our simulations, such as baryonic effects, signal dilution due to cluster member galaxies (which are most prominent near the center), and magnification-induced change and incomplete sampling of the redshift distribution of sources when no or"
Iu Fig.,In Fig.
" 1 owe plot AR, versus Ry. for Mj=100: the three shadowed regions represent the relation between R, aud BS for fixed P2C[O.02.0.01 and Y21.3.10: ProfR2=PuyWP=IORRoALG)."," \ref{fig:M100} we plot $\Rt$ versus $\Rs$ for $M_0=100$: the three shadowed regions represent the relation between $\Rs$ and $\Rt$ for fixed $P_{w2}\in [0.02,0.04]$ and $W=1,~3,~10$: $P_{w2}/\Rs^2 = P_{w1} = W P_{g1}
=W\left(\Rt/\Rs\right)^\gamma/(\gamma M_0^2)\,$."
 The three solid linesrepresent the/ relation RyΠ for the three given values of ΤΕ as even by Eq. 8:, The three solid linesrepresent the relation $\Rt-\Rs$ for the three given values of $W$ as given by Eq. \ref{rsrt};
" the dashed liue refers to HT=0. when p, is not iucluded."," the dashed line refers to $W=0$, when $p_w$ is not included."
 The compression factor lics at the intersection between the curve aud the shadowed region for a given value of WT., The compression factor lies at the intersection between the curve and the shadowed region for a given value of $W$.
 I£ JV«0.7 there are no intersections., If $W<0.7$ there are no intersections.
 This iuplies that the values of the magnetic pressure inferred from observations require substantial ME. amplification pstreann. and that the conservation equatious are affected by the dynamical reaction of the field.," This implies that the values of the magnetic pressure inferred from observations require substantial MF amplification upstream, and that the conservation equations are affected by the dynamical reaction of the field."
 Oulv values WO>3 are compatible with the whole rauge 02<P420xO.OL interred from. observations., Only values $W\geq 3$ are compatible with the whole range $0.02\leq P_{w2}\leq 0.04$ inferred from observations.
 This ueaus that in order to account for tle inferred values of By. the magnetic pressure nist be comparable to he eas pressure. and thus its dvuamical role caunot be welected.," This means that in order to account for the inferred values of $B_2$, the magnetic pressure must be comparable to the gas pressure, and thus its dynamical role cannot be neglected."
 From Fig., From Fig.
 1 one also sees that the magnetic reaction leads to values of Ry lower by roughly a factor ~2 compared with the case H=0., \ref{fig:M100} one also sees that the magnetic reaction leads to values of $\Rt$ lower by roughly a factor $\sim 2$ compared with the case $W=0$.
 We will comuunent ther on this point below., We will comment further on this point below.
 Up until this point we never used the plivsically crucial xut that the observed fields may be generated through a cosnuc rav induced SI upstream of the shock., Up until this point we never used the physically crucial point that the observed fields may be generated through a cosmic ray induced SI upstream of the shock.
 The instability may operate in the resonant (Bell (1978a))) and in the nou-resonant (Bell (2001))) regime., The instability may operate in the resonant \cite{bell78}) ) and in the non-resonant \cite{bell2004}) ) regime.
 The growth rates of these different modes eau be casily estimated only iu the context of quasilinear theory., The growth rates of these different modes can be easily estimated only in the context of quasi-linear theory.
 Given the difficulty in deriving this iuformation iu the general non linear case. here we assume the following general relation between the pressures of CRs aud wave pressure upstream of the subshock: where £60)=poGo)/porP isB the normalized+ CR pressure.," Given the difficulty in deriving this information in the general non linear case, here we assume the following general relation between the pressures of CRs and wave pressure upstream of the subshock: where $\xi(x) = p_{cr}(x)/\rho_0u_0^2$ is the normalized CR pressure."
 For resonant SL one has y2Mjαμ01. while for non-resonant 1iodoes. xLefty.," For resonant SI, one has $\chi\simeq M_A=u_0/v_A$, while for non-resonant modes, $\chi\sim 4c/u_0$."
 Tn both cases. for typical values of the parameters. oue obtains ο 500.," In both cases, for typical values of the parameters, one obtains $200\leq\chi\leq 500$ ."
 From Eq., From Eq.
 1 applied to the precursor. namely between upstream of the subshock Ge=0 ) and upstream infinity. we can write: The physical values of Ry and Ry for a given X are obtained by determuniusg the intersection of the corresponding curve with that obtained for a given value of WT at the subshock.," \ref{eq:massmomentum} applied to the precursor, namely between upstream of the subshock $x=0^-$ ) and upstream infinity, we can write: The physical values of $\Rs$ and $\Rt$ for a given $\chi$ are obtained by determining the intersection of the corresponding curve with that obtained for a given value of $W$ at the subshock."
 Whether the solution reproduces the estimated value of Py. depends on whether the intersection falls within or outside the shadowed region for the same WW iu Fie. l.., Whether the solution reproduces the estimated value of $P_{w2}$ depends on whether the intersection falls within or outside the shadowed region for the same $W$ in Fig. \ref{fig:M100}.
 The dash-dotted and the dotted line show the results for 4=200 aud 500 respectively: it is evident that the chosen values of \ allow for a consistent explanation of the dowustream magnetic pressures as inferred frou observations. and. equally iuportant. lead to compression factors which are much lower than those predicted by the standard NLT (Berezhko&Volk(1997). aud papers that followed).," The dash-dotted and the dotted line show the results for $\chi=200$ and $500$ respectively: it is evident that the chosen values of $\chi$ allow for a consistent explanation of the downstream magnetic pressures as inferred from observations, and, equally important, lead to compression factors which are much lower than those predicted by the standard NLT \cite{bv97} and papers that followed)."
" The strong shock modification predicted by NET when the magnetic pressure is ignored is usually assumed to be somewhat mitigated bv heating of the precursor as a gdesult of damping of Alfven waves (Volk&AlfeI&euzie(lost). hereafter VMISSIT. and MISV52) on the background eas,"," The strong shock modification predicted by NLT when the magnetic pressure is ignored is usually assumed to be somewhat mitigated by heating of the precursor as a result of damping of Alfven waves \cite{v-mck81}, ,hereafter VMK81, and MKV82) on the background gas."
 Other phenomena (for instance acoustic instability) may also lead to heating of the precursor., Other phenomena (for instance acoustic instability) may also lead to heating of the precursor.
 Tn the original description. that remained basically uuchaneed to the preseut time. VMEKSSI assiuned that the rate of damping (D) equals the rate of erowth (0) of Alfven waves.," In the original description, that remained basically unchanged to the present time, VMK81 assumed that the rate of damping $\Gamma$ ) equals the rate of growth $\sigma$ ) of Alfven waves."
 The main implication of this assmuption is that the erowth of the waves never reaches the nonu-linear regunue. which is in fact the very reason why the amechanisua was invoked in the ss.," The main implication of this assumption is that the growth of the waves never reaches the non-linear regime, which is in fact the very reason why the mechanism was invoked in the 80's."
 The recent observations prove that waves can erow to 6B/B»1., The recent observations prove that waves can grow to $\delta B/B\gg 1$.
 It is therefore at least not sclfcousistent to apply the standard treatuient for TII to situations iu which AIF auplification to the non-liuear regime takes place., It is therefore at least not self-consistent to apply the standard treatment for TH to situations in which MF amplification to the non-linear regime takes place.
 Iu a uuuimal attempt to include faster growth one may asstune that P— ασ. with a<1.," In a minimal attempt to include faster growth one may assume that $\Gamma=\alpha \sigma$ , with $\alpha<1$."
 Following \IyVs2 id Derezhko&Ellison(1999) one cau then obtain a eeneralized relation between Ry and Ry in the form where which becomes equivalent to the standard Eq., Following MKV82 and \cite{be99} one can then obtain a generalized relation between $\Rt$ and $\Rs$ in the form where which becomes equivalent to the standard Eq.
 50 of Berezhko&Ellison(1999) only for a=1., 50 of \cite{be99} only for $\alpha=1$.
 Now it is casy to check that for typical values of Ry aud Ry Ary>Ap iamA.," Now it is easy to check that for typical values of $\Rs$ and $\Rt$ $\Lambda_{TH}>\Lambda_B$ if $\alpha\gtrsim
3W\frac{M_A}{M_0^2}$."
 For iustauce for Ay~10° and My~100 one requires à to be of order unity.," For instance for $M_A\sim 10^3$ and $M_0\sim
100$ one requires $\alpha$ to be of order unity."
 In this case however it is not easv to amplify the MF to 6B2» By.," In this case however it is not easy to amplify the MF to $\delta B\gg
B_0$ ."
 Ifa is appreciably sinaller than unity. the main process for the sanoothening of the precursor is the dvuunical reaction of the sclbecnerated ME.," If $\alpha$ is appreciably smaller than unity, the main process for the smoothening of the precursor is the dynamical reaction of the self-generated MF."
 Iu both cases the role of TII can be seriously. questioned., In both cases the role of TH can be seriously questioned.
 A deeper lookat the plivsical processes that may result in the heating of the precursor make the role of TI, A deeper lookat the physical processes that may result in the heating of the precursor make the role of TH
 A deeper lookat the plivsical processes that may result in the heating of the precursor make the role of TII, A deeper lookat the physical processes that may result in the heating of the precursor make the role of TH
2b) 52 at.;,2b) 52 at.;
" derived from 2a by excluding the O-pentagon and the CH2-capped trio, which leaves us with 1 pyrene and 1 S-capped trio, linked by a short chain -O-CH»-; 2c) 49 at.;"," derived from 2a by excluding the O-pentagon and the $_{2}$ -capped trio, which leaves us with 1 pyrene and 1 S-capped trio, linked by a short chain $_{2}$ -; 2c) 49 at.;"
 derived from (2b) by suppression of the CH2 group in the short bridging chain; 2d) 43 at.;, derived from (2b) by suppression of the $_{2}$ group in the short bridging chain; 2d) 43 at.;
" in (2c), substitute the pyrene with a Chain CHs; 2e) 46 at.;"," in (2c), substitute the pyrene with a Chain $_{2}$; 2e) 46 at.;"
" in (2d), insert a CH» group between the O atom and the S-trio; 2f) 64 at.;"," in (2d), insert a $_{2}$ group between the O atom and the S-trio; 2f) 64 at.;"
" in (2e), hang on a second CH» chain to the bridge between the S-trio and the first CH2 chain."," in (2e), hang on a second $_{2}$ chain to the bridge between the S-trio and the first $_{2}$ chain."
 2g)63 at.;, 2g)63 at.;
" in (28), replace the second CH» chain by an O-capped pentagon."," in (2f), replace the second $_{2}$ chain by an O-capped pentagon."
 Concatenated structures This family differs from the two previous one by the presence of several OH groups attached at the periphery of the main structure., Concatenated structures This family differs from the two previous one by the presence of several OH groups attached at the periphery of the main structure.
 The leading member (3a) is drawn in Fig., The leading member (3a) is drawn in Fig.
 10; 98 at.;, 10; 98 at.;
 other members are 3b) 97 at.;, other members are 3b) 97 at.;
 derived from (3a) by suppression of the OH group attached to the pyrene; 3c) 95 at.;, derived from (3a) by suppression of the OH group attached to the pyrene; 3c) 95 at.;
 derived from (3a) by substituting an H atom to the CH3 group attached to the pyrene;, derived from (3a) by substituting an H atom to the $_{3}$ group attached to the pyrene;
overall atmospheric enerev budget. at least in the static To help us evaluate more quantitatively (he magnitude of bulk Doppler shift elfects. we now turn to models of line (ransiissivides and equivalent widths in dvnamic atmospheres.,"overall atmospheric energy budget, at least in the static To help us evaluate more quantitatively the magnitude of bulk Doppler shift effects, we now turn to models of line transmissivities and equivalent widths in dynamic atmospheres."
 As summarized in relS:dvuatin.. monochromatic Gransmissivitlies encapsulate the absorption aud emission properties of the atmospheric medium (eqs. [2- 3].," As summarized in \\ref{S:dynatm}, monochromatic transmissivities encapsulate the absorption and emission properties of the atmospheric medium (eqs. \ref{eq:two}- \ref{eq:three}] ])."
" Here. we isolate the effects of velocity gradients along an arbitrary optical path by modeling (he monochromatic transnmissivityv in a dynamic ablmosphere as where s' is the length along the unit optical the line integrated. opacity m is assumed to be constant along (he path and e, is the dimensionless Voiet line profile defined in Eq. (8))."," Here, we isolate the effects of velocity gradients along an arbitrary optical path by modeling the monochromatic transmissivity in a dynamic atmosphere as where $s'$ is the length along the unit optical the line integrated opacity $\tilde{k}_{\rm tot}$ is assumed to be constant along the path and $\Phi_V$ is the dimensionless Voigt line profile defined in Eq. \ref{eq:voigt}) )."
" The above expression for the bulk Doppler shift term in the line function assumes a constant. velocity gradient along the path.ie. a velocity offset that increases linearly with s'. from Oats’=0 to the maximum value lj4,; alos’=1."," The above expression for the bulk Doppler shift term in the line function assumes a constant velocity gradient along the path,i.e. a velocity offset that increases linearly with $s'$, from $0$ at $s'=0$ to the maximum value $V_{\rm proj}$ at $s'=1$."
 This simple model isolates the effects of bulk Doppler shifts by assuming that the path is otherwise homogeneous., This simple model isolates the effects of bulk Doppler shifts by assuming that the path is otherwise homogeneous.
 In a more realistic atmospheric model. optical paths would be inhomogeneous. with line strengtlis. Ait. generally varving with temperature and line shapes. $4. generally varying with both temperature and pressure along (he specilic path," In a more realistic atmospheric model, optical paths would be inhomogeneous, with line strengths, $\tilde{k}_{\rm tot}$, generally varying with temperature and line shapes, $\Phi_V $ generally varying with both temperature and pressure along the specific path"
Dallesteros-Paredes Mac Low 2002: Pineda οἱ al.,Ballesteros-Paredes Mac Low 2002; Pineda et al.
 2009: Federrath et al., 2009; Federrath et al.
 2010: Shetty οἱ al., 2010; Shetty et al.
 2010) our work further hiehlishts the importance of generating synthetic observations from (hree-climensional numerical simulations that can be compared to real observatio15., 2010) our work further highlights the importance of generating synthetic observations from three-dimensional numerical simulations that can be compared to real observations.
 We would like to (hank the referee for her/his constructive comments., We would like to thank the referee for her/his constructive comments.
 We woud also like to thank Anne-Ixhatarina Jappsen. Stella Olfner. and Chris Melxee for interesting discussions on issues related to the topic of this paper.," We would also like to thank Anne-Khatarina Jappsen, Stella Offner, and Chris McKee for interesting discussions on issues related to the topic of this paper."
 S. Dib acknowledges support rom ije. project MAGNET of the Agence Nationale de la Recherche (France) and is very grateful to Soren Larsen for his hospitality at the Astronomical Institute in Utrecht and to Andreas Burkert for his hospitality al the Excellence Cluster Universe in Garching and to the hospitality. of the Institute of Theory and Computation al Harvard. University., S. Dib acknowledges support from the project MAGNET of the Agence Nationale de la Recherche (France) and is very grateful to ren Larsen for his hospitality at the Astronomical Institute in Utrecht and to Andreas Burkert for his hospitality at the Excellence Cluster Universe in Garching and to the hospitality of the Institute of Theory and Computation at Harvard University.
 T. Csengeri acknowledges support from the FPG Marie-Curie Research Training Network Constellation: the origin of stellar masses (AIRTN-C'T-2006-035890)., T. Csengeri acknowledges support from the FP6 Marie-Curie Research Training Network Constellation: the origin of stellar masses (MRTN-CT-2006-035890).
 The numerical simulations were performed on 256 processors of the SG] ALTIX machine JADE at the Centre Informatique National de |Enseignement Supérrieur (CINES)., The numerical simulations were performed on 256 processors of the SGI ALTIX machine JADE at the Centre Informatique National de l'Enseignement Supérrieur (CINES).
The nature of dark matter remains one of the outstanding questions of modern astrophysics.,The nature of dark matter remains one of the outstanding questions of modern astrophysics.
" The success of the cold dark matter cosimologica model (albeit with ""dark energy now required: ACDM) argues strongly for a major componcn of the dark matter being iu the form of an elementary particle.", The success of the cold dark matter cosmological model (albeit with “dark energy” now required: $\Lambda$ CDM) argues strongly for a major component of the dark matter being in the form of an elementary particle.
 However. the inveutorv of barvous which we can observe locally falls fax short of the total inferred from observations of cosmic ∖⊳↴⋅⊳microwave background∢⊳↽∢⊾⋅ fluctuations⊳⊀⋅ and↴e Fukueita2001)..2Maak ∖ u∖thie possibility⋠ -Walker iav be a significant barvouicavingop coniponen tha of! dark inatter.," However, the inventory of baryons which we can observe locally falls far short of the total inferred from observations of the cosmic microwave background fluctuations \citep{Fuk04}, leaving open the possibility that there may be a significant baryonic component of dark matter."
 Furthermore. although ACD. is very successful iu deseribiug the growth of structure in the universe on large scales. we still lack a direct detection of anv of the caucdida5 dark matter particles.," Furthermore, although $\Lambda$ CDM is very successful in describing the growth of structure in the universe on large scales, we still lack a direct detection of any of the candidate dark matter particles."
 Lacking this decisive piece of observational evidence. some authors lave proposed models which include a large courponent of barvonic dark matter.," Lacking this decisive piece of observational evidence, some authors have proposed models which include a large component of baryonic dark matter."
 In particular there have been any papers dealing with the possibility that cold. sclberavitating molecular clouds constitu5 a 1najor compoucut of the dark matter (Pfenniger.1999:|e.Sciama2000a.)..:.," In particular there have been many papers dealing with the possibility that cold, self-gravitating molecular clouds constitute a major component of the dark matter \citep{Pfe94,DeP95,Hen95,Ger96, Com97, Wal99, Sci00a, Sci00b}."
 A variety of. there( different forms. iucludiug isolated. clustered. aud fractal. have been considered for the clouds. but all proposals involve deuse eas of hieh," A variety of different forms, including isolated, clustered, and fractal, have been considered for the clouds, but all proposals involve dense gas of high"
Figure 6 shows a imap of pixels inclucec in the smoothing for a single pixel in the mock galaxy ünage.,Figure \ref{fig:kernel} shows a map of pixels included in the smoothing for a single pixel in the mock galaxy image.
 The pixels with green crosses are included in the mediau average when smoothing for the central pixel., The pixels with green crosses are included in the median average when smoothing for the central pixel.
 The circle is the best-fit racial aperture of Radits=L pixels., The circle is the best-fit radial aperture of $Radius=4$ pixels.
 The pixels with green crosses all have similar locatious in PCA-space (left panel of Figure 2)) and SNR range (right panel ol Figure 2))., The pixels with green crosses all have similar locations in PCA-space (left panel of Figure \ref{fig:PCAanalysis}) ) and SNR range (right panel of Figure \ref{fig:PCAanalysis}) ).
 This figure shows that most of the pixels iucluded iu the inedian filter are HII-like region pixels., This figure shows that most of the pixels included in the median filter are HII-like region pixels.
 Figure 7 shows the cliauge in total SNR for pixels centered ou the HIT region., Figure \ref{fig:SNRchange} shows the change in total SNR for pixels centered on the HII region.
 The SNR per pixel after PCA smoothing increases by a [actor of 2-3 in the range of original signal-to-noise of 5-20., The SNR per pixel after PCA smoothing increases by a factor of 2-3 in the range of original signal-to-noise of 5-20.
 Above the SNRlimit there is uo change in the SNR., Above the SNRlimit there is no change in the SNR.
 This is slightly less than the expected chauge in the SNR., This is slightly less than the expected change in the SNR.
 In a simple circular average of radius-3 pixels. the SNR shoulcl increase by 5.3.," In a simple circular average of radius=3 pixels, the SNR should increase by 5.3."
 The SNR does not increase by a [actor of 5.3 because uot all pixels within the circular aperture are sed. as they are not iu the same location in PCA space as the pixel be being smoothled.," The SNR does not increase by a factor of 5.3 because not all pixels within the circular aperture are used, as they are not in the same location in PCA space as the pixel be being smoothed."
 If the smoothing is not done over a range of augular bins in PC'À-space (Figure 2)). or i SNRenhanced=BGr.y). then the FOAL always tucreases by 1.0.," If the smoothing is not done over a range of angular bins in PCA-space (Figure \ref{fig:PCAanalysis}) ), or if $SNRenhanced=SNR(x,y)$, then the $FOM$ always increases by 1.0."
 The FOAL increases jecause there are so few pixels with the PCA-space in the same bin aud within the same spatial 'eejon., The $FOM$ increases because there are so few pixels with the PCA-space in the same bin and within the same spatial region.
 If the regiou is not restricted by a certain aperture. then the POA increases ouly slightly.," If the region is not restricted by a certain aperture, then the $FOM$ increases only slightly."
 For exaimple. if the radius is set to a value larger than the image. essentially iucludiug all the pixels in the analysis. then the FOAL increases by ouly 0.5.," For example, if the radius is set to a value larger than the image, essentially including all the pixels in the analysis, then the $FOM$ increases by only 0.8."
 This is much better than the simple radial average. which increases by orders of mmaenitucde when the radius is the size of the image.," This is much better than the simple radial average, which increases by orders of magnitude when the radius is the size of the image."
 Changing he region over which the PCA eigenspectra are determined scatters the eigenvalues. reclucing the correlation between location in PCA-space aud color.," Changing the region over which the PCA eigenspectra are determined scatters the eigenvalues, reducing the correlation between location in PCA-space and color."
 Using a larger region includes pixels with such high noise values due to sky. so that PCA results are scattered throughout the PCA-space.," Using a larger region includes pixels with such high noise values due to sky, so that PCA results are scattered throughout the PCA-space."
 Using too sinall a region does not include a variation iu color., Using too small a region does not include a variation in color.
 For example. using the ceutral bulge half-light radius includes almost πο blue star formation colors.," For example, using the central bulge half-light radius includes almost no blue star formation colors."
 We compare PCA smoothing with other smoothing techniques: a simple circular siuoothing kernel ancl Acdaptsmooth (Zibetti.Charlot.Rix2009)., We compare PCA smoothing with other smoothing techniques: a simple circular smoothing kernel and Adaptsmooth \citep{zib09}.
. Adaptsmooth uses a circular aperture smoothing kernel. where the radius of the circle is set to achieve a SNR of 20.," Adaptsmooth uses a circular aperture smoothing kernel, where the radius of the circle is set to achieve a SNR of 20."
 Adaptsmooth (Zibetti.Charlot.Rix2009) is compared to the PCA-smoothiug techuique for an area on the edge of aun HII-like region of the mock [n]galaxy., Adaptsmooth \citep{zib09} is compared to the PCA-smoothing technique for an area on the edge of an HII-like region of the mock galaxy.
 Adaptsmooth is run in default mocle. where the racial aperture is determined by increasing the radius until the resulting SNR equals 20.," Adaptsmooth is run in default mode, where the radial aperture is determined by increasing the radius until the resulting SNR equals 20."
 Fixiug the radius for all bauds resembles the simple radial average results., Fixing the radius for all bands resembles the simple radial average results.
 Figures. Lo and show the FOAL for Adaptsimooth., Figures \ref{fig:IMSTATall} and \ref{fig:ANALYZEHII} show the $FOM$ for Adaptsmooth.
 In almost all cases the FOAL for Acdaptsinooth is larger thau the PCÀ-snoothing method presented here., In almost all cases the $FOM$ for Adaptsmooth is larger than the PCA-smoothing method presented here.
 When the FOAM is calculated for the HII-like region. the results in 5 shows that Adaptsimooth has a FOAL worse that no smoothing at all.," When the $FOM$ is calculated for the HII-like region, the results in \ref{fig:ANALYZEHII} shows that Adaptsmooth has a $FOM$ worse that no smoothing at all."
 This is due to Adaptsimooth mixing pixels with different colors. which will be demonstrated below.," This is due to Adaptsmooth mixing pixels with different colors, which will be demonstrated below."
to observe brown dwarls in the mid-infrared. will give new insights in the astrophysics οἱ the complex atmospheres of these cool. dim denizens of our neighborhood.,"to observe brown dwarfs in the mid-infrared will give new insights in the astrophysics of the complex atmospheres of these cool, dim denizens of our neighborhood."
 In thisLetter. we present mid-IR model spectra of brown cwarls and discuss (heir properties in teris of effective temperature. important molecular absorbers. (he role of silicate clouds. ancl anticipate potential discoveries wilh SIRTF.," In this, we present mid-IR model spectra of brown dwarfs and discuss their properties in terms of effective temperature, important molecular absorbers, the role of silicate clouds, and anticipate potential discoveries with SIRTF."
 The instruments onboard SIRTF cover the wavelength range from 3 to san. Two of these will target brown dwarls: the Infrared. Array Camera (LRAC') ancl the Infrared Spectrograph (RS).," The instruments onboard SIRTF cover the wavelength range from 3 to $\,\mu$ m. Two of these will target brown dwarfs: the Infrared Array Camera (IRAC) and the Infrared Spectrograph (IRS)."
 Brown dwarls will be imaged by URAC in four bandpasses centered al pim. yan. jam. and san. respectively (Fig.," Brown dwarfs will be imaged by IRAC in four bandpasses centered at $\,\mu$ m, $\,\mu$ m, $\,\mu$ m, and $\,\mu$ m, respectively (Fig."
"1).. Since brown dwarls become very dim and their spectra contain little information bevond yan. the most useful IRS observations will be in the ""Short wavelength. Low resolution” (SL) and the less sensitive ""Short wavelength. High resolution” (SII)modes."," Since brown dwarfs become very dim and their spectra contain little information beyond $\,\mu$ m, the most useful IRS observations will be in the “Short wavelength, Low resolution” (SL) and the less sensitive “Short wavelength, High resolution” (SH)."
. The SL and SII modes cover the 5.3 yan and the 10.0 pam spectral bands. respectively.," The SL and SH modes cover the 5.3 – $\,\mu$ m and the 10.0 – $\,\mu$ m spectral bands, respectively."
 To model the alinospheres and spectra of (he L- aud T-dwarls we emplov the equilibrium atmosphere model of Marley et al. (, To model the atmospheres and spectra of the L- and T-dwarfs we employ the radiative-convective equilibrium atmosphere model of Marley et al. (
1996: futher described in Burrows el al.,1996; further described in Burrows et al.
 1997 and Marley et al., 1997 and Marley et al.
 2002) which includes the precipitating cloud model of Ackerman Marley (2001)., 2002) which includes the precipitating cloud model of Ackerman Marley (2001).
 High resolution spectra are computed from the initial temperature prolile and cloud structure (Saumon et al., High resolution spectra are computed from the initial temperature profile and cloud structure (Saumon et al.
 2000: Geballe et al., 2000; Geballe et al.
 2001)., 2001).
 The chemistry is computed in the framework of the cloud condensation model (Lodders 1999a: Lodders Feeley 2002: Lodders 2002; Lewis 1969)., The chemistry is computed in the framework of the cloud condensation model (Lodders 1999a; Lodders Fegley 2002; Lodders 2002; Lewis 1969).
" The opacity includes the molecular lines of Π.Ο. Cll). CO. NII. HIS. PII4. TiO. VO. Cul. Fell. COs. HCN. Colle. Coll). Coll; complemented with (he atomic lines of the alkali metals (Li. Na. Ix. Rb and Cs) and continuum opacity sources from IH» CIA. Hs. HL and He Ravleigh scattering. bf and tf IL, (EF. ff and IL, bf and (E."," The opacity includes the molecular lines of $_2$ O, $_4$ , CO, $_3$, $_2$ S, $_3$, TiO, VO, CrH, FeH, $_2$, HCN, $_2$ $_2$, $_2$ $_4$, $_2$ $_6$ complemented with the atomic lines of the alkali metals (Li, Na, K, Rb and Cs) and continuum opacity sources from $_2$ CIA, $_2$, H and He Rayleigh scattering, $^-$ bf and ff, $_2^-$ ff, $^-$ ff, and $_2^+$ bf and ff."
" While the chemical equilibrium is computed with a large number of coucensates. only Fe. AleSiOs. AlSO4. H5O. and. NIL, are considered in the cloud model."," While the chemical equilibrium is computed with a large number of condensates, only Fe, $_3$ , $_2$ $_3$, $\rm H_2O$, and $\rm NH_3$ are considered in the cloud model."
 Condensed ουν is accounted for with MgSiO; and (he remaining condensates are nol appreciable sourcesof opacity., Condensed $\rm Mg_2SiO_4$ is accounted for with $_3$ and the remaining condensates are not appreciable sourcesof opacity.
 We consider spectra [rom Z;y=GOO to 2400Ix. which covers the full range ofL and T," We consider spectra from $\Teff=600$ to $\,$ K which covers the full range ofL and T"
 Ioassunme that the independent variable. £. is drawn from a probability distribution p(£|o). where ο denotes the paramcters for this distribution.,"I assume that the independent variable, $\xi$, is drawn from a probability distribution $p(\xi|\psi)$ , where $\psi$ denotes the parameters for this distribution."
 The depeudent variable is then drawn from the conditioua distribution of 4 given £. denoted as p(jl£.0): 0 denotes the parameters for this distribution.," The dependent variable is then drawn from the conditional distribution of $\eta$ given $\xi$, denoted as $p(\eta|\xi,\theta)$; $\theta$ denotes the parameters for this distribution."
 The joint distribution of£ and iis then p(s.ojo.0)=ρενε|o).," The joint distribution of $\xi$ and $\eta$ is then $p(\xi,\eta|\psi,\theta) = p(\eta|\xi,\theta) p(\xi|\psi)$."
" Tu this work Tassuime the uormal linear regression model given by Equation (1)). aud thus p(y[¢.@) is a normal density with mean à.|6 and variauce 97. iik =(a.Dhar), "," In this work I assume the normal linear regression model given by Equation \ref{eq-adderr}) ), and thus $p(\eta|\xi,\theta)$ is a normal density with mean $\alpha + \beta \xi$ and variance $\sigma^2$, and $\theta = (\alpha, \beta, \sigma^2)$."
Since the data are a randomly observed sample. we cau derive the likelihood fiction for the nieasurec data.," Since the data are a randomly observed sample, we can derive the likelihood function for the measured data."
 The likelihood function of the measured data. ptc.g|0.0). is obtained by integrating the complete data likelihood over the missing data. £ aud 5 (e.g..Little&Rubin2002:Celmanetal.2001): ere. plesg.£40.0) is the complete data likelihood fuuctiou.," The likelihood function of the measured data, $p(x,y|\theta,\psi)$ , is obtained by integrating the complete data likelihood over the missing data, $\xi$ and $\eta$ \citep[e.g.,][]{lit02,gelman04}: Here, $p(x,y,\xi,\eta|\theta, \psi)$ is the complete data likelihood function."
" Because of the hierarchical structure inherent in the measurement error model. it is helpful to decompose the complete data likelihood. iuto conditional probability densities: The density ple.g|£.0) describes the jotut distribution of the measured values e and. y at à given © aud η. aud depends on the assuned distribution ofthe measurement errors. e, aud ey."," Because of the hierarchical structure inherent in the measurement error model, it is helpful to decompose the complete data likelihood into conditional probability densities: The density $p(x,y|\xi,\eta)$ describes the joint distribution of the measured values $x$ and $y$ at a given $\xi$ and $\eta$, and depends on the assumed distribution ofthe measurement errors, $\epsilon_x$ and $\epsilon_y$."
" Iu this work I assiuue Gaussian 1neasureiment error. and thus poe;yi)6;.ye) is a multivariate uormaldensity with mean (£;.))5) and covariance matrix X; where “yy;=07,.Noo;02, and yo;=Try7"," In this work I assume Gaussian measurement error, and thus $p(x_i,y_i|\xi_i,\eta_i)$ is a multivariate normaldensity with mean $(\xi_i,\eta_i)$ and covariance matrix $\Sigma_i$, where $\Sigma_{11,i} = \sigma^2_{y,i},
 \Sigma_{22,i} = \sigma^2_{x,i},$ and $\Sigma_{12,i} =
 \sigma_{xy,i}$."
 The statistical τος) may then be convenieutlv expressed. hicrarchically as Note that ife; is measured without error. then ptr;|£;) is a Dirac delta function. aud ο).," The statistical model may then be conveniently expressed hierarchically as Note that if $x_i$ is measured without error, then $p(x_i|\xi_i)$ is a Dirac delta function, and $p(x_i,y_i|\xi_i,\eta_i) = p(y_i|\eta_i)
 \delta(x_i - \xi_i)$ ."
 Au equivaleut result holds if y; is measured without error., An equivalent result holds if $y_i$ is measured without error.
 Equation (11)) 1nav be used to obtain the observed data likelihood fiction for auy assumed distribution of £., Equation \ref{eq-obslik2}) ) may be used to obtain the observed data likelihood function for any assumed distribution of $\xi$ .
 In this work. T model p(£|o) as a mixture of A Gaussimus. $77 QjFN=1.," In this work, I model $p(\xi|\psi)$ as a mixture of $K$ Gaussians, where $\sum_{k=1}^{K} \pi_k = 1$."
4Note that.- zi maybe interpreted as: the probability of⋅⋅ drawing⋅ a. data point from. thewhere jh Gaussian.," Note that, $\pi_k$may be interpreted as the probability of drawing a data point from the $k^{\rm th}$ Gaussian."
 Twill use the convenieut notation $ =(m$...πο...fig).aud τὸ =(τῇ∙∙∙∙∙7$) note that c=(Gcpi. 77).,"I will use the convenient notation $\pi =
 (\pi_1,\ldots,\pi_K), \mu = (\mu_1,\ldots,\mu_K),$ and $\tau^2 =
 (\tau^2_1,\ldots,\tau^2_K)$ ; note that $\psi = (\pi,\mu,\tau^2)$ ."
 Tt is useful to model p(£[o) using this form becauseit is flexible enough to adapt, It is useful to model $p(\xi|\psi)$ using this form becauseit is flexible enough to adapt
present paper rests ultimately onstars.,present paper rests ultimately on.
 We compare in Fig., We compare in Fig.
" 2 the observed intrinsic spreads in Fe (defined as the rms scatter of all stars in each cluster), as given by GIRAFFE and UVES spectra (columns 5 and 8 in Tab.1))."," \ref{f:doss} the observed intrinsic spreads in Fe (defined as the $rms$ scatter of all stars in each cluster), as given by GIRAFFE and UVES spectra (columns 5 and 8 in \ref{t:ferms}) )."
 The error bars show the maximum and minimum spread allowed for each cluster taking into account the statistical errors., The error bars show the maximum and minimum spread allowed for each cluster taking into account the statistical errors.
" Looking at this figure, two features are immediately evident: first, on average, the rms scatter obtained from UVES spectra is larger than the one we derived from the analysis of GIRAFFE spectra."," Looking at this figure, two features are immediately evident: first, on average, the $rms$ scatter obtained from UVES spectra is larger than the one we derived from the analysis of GIRAFFE spectra."
" At first sight, this result is just the opposite one would expect, given the higher resolution and spectral coverage of the UVES spectra."," At first sight, this result is just the opposite one would expect, given the higher resolution and spectral coverage of the UVES spectra."
 Possible explanations for this effect will be examined in the next section., Possible explanations for this effect will be examined in the next section.
" Second, intrinsic scatters from GIRAFFE spectra show quite small associated error bars, owing to the much larger statistics; if we focus on these values, the first conclusion is thatsmall."," Second, intrinsic scatters from GIRAFFE spectra show quite small associated error bars, owing to the much larger statistics; if we focus on these values, the first conclusion is that."
" On average, we found a value of 0.048 dex (with o=0.018 dex) from 19 GCs; the iron abundance in each cluster is homogeneous within12%."," On average, we found a value of 0.048 dex (with $\sigma=0.018$ dex) from 19 GCs; the iron abundance in each cluster is homogeneous within."
". Furthermore, we note that these are strictly to the actual dispersion of [Fe/H] values in GCs."," Furthermore, we note that these are strictly to the actual dispersion of [Fe/H] values in GCs."
" The true intrinsic values should be estimated by subtracting (in quadrature) the scatter expected from errors in the analysis, namely in the derivation of the atmospheric parameters and in the measurement of EWs. These quantities were estimated with a thorough procedure amply described in previous papers and are reported in the Appendix of Paper VII and in Papers I to"," The true intrinsic values should be estimated by subtracting (in quadrature) the scatter expected from errors in the analysis, namely in the derivation of the atmospheric parameters and in the measurement of $EW$ s. These quantities were estimated with a thorough procedure amply described in previous papers and are reported in the Appendix of Paper VII and in Papers I to"
 (Fukuda1982:Tassoul2000).. (IHegeretal.2X00a:Irscehi2001:Limongi20003... (Wooslevetal.20ο). Ostrisor&Mark(1968," \citep{Fukuda:1982,Tassoul:2000}. \citep{Heger:2000ud,Hirschi:2004ks,
Limongi:2000km}. \citep{Woosley:2005gy}. \citet{Ostriker:1968},"
)... Tachisu(1986). 199la:Iiuchi&Yoshida2008):I&omiatsueta.1989:TomiunuraExriguchi2005).. (Coox.ctal.J99tb:Ἱνπιοή&I&otake20082:I&iuchiet2009).. (Tassoul90000.," \citet{Hachisu:1986} \citep{Bocquet:1995,Cook:1993qj,Kiuchi:2008ch,Komatsu:1989,Tomimura:2005}. \citep{Cook:1993qr,Kiuchi:2007pa,Kiuchi:2009zt}. \citep{Tassoul:2000}."
that the procedure based on spatial templates creates deviations comparable to the amplitude of the D09 residual.,that the procedure based on spatial templates creates deviations comparable to the amplitude of the D09 residual.
" Furthermore, we find that these deviations are morphologically similar to the Fermi haze."," Furthermore, we find that these deviations are morphologically similar to the Fermi haze."
 We thus conclude that the determination of an excessgamma-ray diffuse emission cannot reliably be assessed from the spatial template proxies used in the “Type 2” and “Type 3” fits of D09.," We thus conclude that the determination of an excessgamma-ray diffuse emission cannot reliably be assessed from the spatial template proxies used in the “Type 2"" and “Type 3"" fits of D09."
 We stress that our results do not claim that there is no “haze” in the Fermi data., We stress that our results do not claim that there is no “haze” in the Fermi data.
" In particular, the systematic effects we study here are not relavent to explain the puzzling excess emission in the “Type 1” fit of D09, which employes Fermi-LAT data in the 1-2 GeV range as a proxy for the morphology of the 7° component."," In particular, the systematic effects we study here are not relavent to explain the puzzling excess emission in the “Type 1” fit of D09, which employes Fermi-LAT data in the 1-2 GeV range as a proxy for the morphology of the $\pi^0$ component."
" We comment on this ""Type 1"" approach in Section 5..", We comment on this “Type 1” approach in Section \ref{sec:discussion}.
" Employing the cosmic ray propagation code 50.1p) (Strong&Moskalenko1998;StrongGalpropal.(v we compute the line-ofsight emission for galactic 2009),synchrotron, IC and 7° decay predicted by a model that is consistent with all cosmic ray and photon observations (seeStrongetal.2009,forfurther detail).."," Employing the cosmic ray propagation code (v 50.1p) \citep{Strong:1998pw, 2009arXiv0907.0559S}, we compute the line-of-sight emission for galactic synchrotron, IC and $\pi^0$ decay predicted by a model that is consistent with all cosmic ray and photon observations \citep[see][for further detail]{2009arXiv0907.0559S}."
" Except where noted, we employ standard parameters given by the GALDEF file throughout this work."," Except where noted, we employ standard parameters given by the GALDEF file throughout this work."
 A large uncertainty in the propagation of cosmic rays relates to the intensity and orientation of galactic magnetic fields (Broadbentetal.1990;Heiles1996;Vallee1996) as the intensity of synchrotron radiation varies with the square of the local magnetic field intensity.," A large uncertainty in the propagation of cosmic rays relates to the intensity and orientation of galactic magnetic fields \citep{1990ICRC....3..229B,1996ASPC...97..457H,1996A&A...308..433V} as the intensity of synchrotron radiation varies with the square of the local magnetic field intensity."
" In our default simulation we assume a magnetic field of random orientation and an intensity that exponentially decays in both r and z with scale radii of 10 kpc and 2 kpc respectively, normalized to 5 µία at the solar position (Strong&Moskalenko1998;Strongetal. 2009).."," In our default simulation we assume a magnetic field of random orientation and an intensity that exponentially decays in both $r$ and $z$ with scale radii of 10 kpc and 2 kpc respectively, normalized to 5 $\mu$ G at the solar position \citep{Strong:1998pw, 2009arXiv0907.0559S}. ."
" 'To determine the accuracy of the D09 spatial templates for astrophysical foreground emission, we generate line-of-sight skymaps for the input gas density, as well as the outputs of emission due to «? decay, synchrotron and IC."," To determine the accuracy of the D09 spatial templates for astrophysical foreground emission, we generate line-of-sight skymaps for the input gas density, as well as the outputs of emission due to $\pi^0$ decay, synchrotron and IC."
 Note that the gas density maps we employ here differ from the SFD map used in D09., Note that the gas density maps we employ here differ from the SFD map used in D09.
" Most notably, the SFD map traces dust, while our map traces galactic gas."," Most notably, the SFD map traces dust, while our map traces galactic gas."
" The difference between these approaches is expected to be small, but might introduce additional systematic deviations."," The difference between these approaches is expected to be small, but might introduce additional systematic deviations."
" By dividing, pixel by pixel, the line-of-sight map for 1? decay by the input gas map, and the map of IC emission by the synchrotron map, we can assess the size of any systematic effects produced by assumptions (1) and (2) of Section 1.."," By dividing, pixel by pixel, the line-of-sight map for $\pi^0$ decay by the input gas map, and the map of IC emission by the synchrotron map, we can assess the size of any systematic effects produced by assumptions (1) and (2) of Section \ref{sec:introduction}."
" We normalize each map over pixels of |b| > 5°, using equal area weighting to determine the normalization constant."," We normalize each map over pixels of $|$ $|$ $>$ $^\circ$, using equal area weighting to determine the normalization constant."
 This is equivalent to the masking procedure of D09 - though we do not mask out the galactic plane in our plots., This is equivalent to the masking procedure of D09 - though we do not mask out the galactic plane in our plots.
" We select several regions of the sky for which we provide numerical analyses of each map we present, with a background normalized as in D09."," We select several regions of the sky for which we provide numerical analyses of each map we present, with a background normalized as in D09."
" We first evaluate D09's claim of an excess emission in the southern galactic plane between -30? « b « -10° and |l| < 15°, indicated as thehaze."," We first evaluate D09's claim of an excess emission in the southern galactic plane between $^\circ$ $<$ b $<$ $^\circ$ and $|$ $|$ $<$ $^\circ$, indicated as the."
 We add the symmetric region « b < 30° and | <15)., We add the symmetric region $^\circ$ $<$ b $<$ $^\circ$ and $|$ $|<$ 15).
" D09 defines their haze (10°to begin at 10?, but only masked the region |b| « 5?."," D09 defines their haze to begin at $^\circ$, but only masked the region $|$ $|$ $<$ $^\circ$."
" In order to determine the importance of this choice, we include both northern and southern regions following 5? < |b| « 25? and |l| « 15°, which we denote as the region."," In order to determine the importance of this choice, we include both northern and southern regions following $^\circ$ $<$ $|$ $|$ $<$ $^\circ$ and $|$ $|$ $<$ $^\circ$, which we denote as the region."
" Since D09 models the morphology of the haze with a bivariate Gaussian that decays exponentially in both latitude and longitude, we further consider a map weighting the value at each unmasked pixel using a bivariate Gaussian of 25? in latitude and 15° in longitude, and dubbed theHaze."," Since D09 models the morphology of the haze with a bivariate Gaussian that decays exponentially in both latitude and longitude, we further consider a map weighting the value at each unmasked pixel using a bivariate Gaussian of $^\circ$ in latitude and $^\circ$ in longitude, and dubbed the."
" Finally, in order to ascertain the variation of each map, we consider the galactic anticenter region 5?« |b]« 25? and [I| > 170."," Finally, in order to ascertain the variation of each map, we consider the galactic anticenter region $^\circ<|$ $|<$ $^\circ$ and $|$ $|$ $>$ 170."
 In Figure 1 we show the normalized line-of-sight skymap for 7° decay divided by the normalized line-of-sight gas density input into our simulations., In Figure \ref{pi0divgas} we show the normalized line-of-sight skymap for $\pi^0$ decay divided by the normalized line-of-sight gas density input into our simulations.
" The results are shown on a linear scale (left) and a logarithmic scale (right), and both are smoothed using a Gaussian of 2? width."," The results are shown on a linear scale (left) and a logarithmic scale (right), and both are smoothed using a Gaussian of $^\circ$ width."
" We find that the resultant skymap displays significant deviations from unity, with factors of approximately two above and below the galactic center, to values of about 0.3 near the galactic anti-center."," We find that the resultant skymap displays significant deviations from unity, with factors of approximately two above and below the galactic center, to values of about 0.3 near the galactic anti-center."
" In Table 1 (top we provide both the average value in the D09 backgroundrow), region, as well as the numeric ratios in each of our defined regions."," In Table \ref{tab:regions} (top row), we provide both the average value in the D09 background region, as well as the numeric ratios in each of our defined regions."
" While this map for 7° decay is taken at a test energy of 1 GeV, the variation of the ratio across four decades in energy (0.1 GeV - 1 TeV) is less than 2%.."," While this map for $\pi^0$ decay is taken at a test energy of 1 GeV, the variation of the ratio across four decades in energy (0.1 GeV - 1 TeV) is less than ."
 While wefind a deviation between the D09 haze region and the D09, While wefind a deviation between the D09 haze region and the D09
The evolution of the zero point. 5. wilh redshift is calculated using (he measurements of Fundamental Plane parameters al different recshilts bv Jorgensenefa£.(1999).. vieldine 5-023132:—1.31x10...,"The evolution of the zero point, $\gamma$, with redshift is calculated using the measurements of Fundamental Plane parameters at different redshifts by \citet{Jorgensen2}, , yielding $\gamma = 0.2132 z - 1.31 \times 10^{-3}$."
 The velocity dispersions derived were used (o caleulate black hole masses using the relation: The value of the exponent is somewhat uncertain. with conflicting measurements in the literature.," The velocity dispersions derived were used to calculate black hole masses using the relation: The value of the exponent is somewhat uncertain, with conflicting measurements in the literature."
 Kormencdy&Gebhardt(2001) measure an a=3.65. while (2001) measure a=4.72.," \citet{KormendyG} measure an $\alpha=3.65$, while \citet{Merritt} measure $\alpha=4.72$."
 To reflect this uncertainty. we adopt a mean value of a=4.2 with an uncertaintv equal to the standard deviation of the two values: £0.75.," To reflect this uncertainty, we adopt a mean value of $\alpha=4.2$ with an uncertainty equal to the standard deviation of the two values: $\pm 0.75$."
" The median black hole masses derived using this method are. for thelow-power sample: Al,=1.1x1O°AL. (mean: L3x10?M. ): and for the high-power sample: M,=4.6x105M. (mean: 2.0x109. )."," The median black hole masses derived using this method are, for thelow-power sample: $M_{\bullet}=1.1 \times 10^9 M_{\odot}$ (mean: $1.8 \times 10^9 M_{\odot}$ ); and for the high-power sample: $M_{\bullet}=4.6 \times 10^8 M_{\odot}$ (mean: $2.0 \times 10^9 M_{\odot}$ )."
" Black hole masses derived with this method show a greater spread than those derived using the M, Liu, relation. with standard deviations 2.3xLO?AL. and 3.0xI0?M. respectively."," Black hole masses derived with this method show a greater spread than those derived using the $M_{\bullet}$ $L_{bulge}$ relation, with standard deviations $2.3 \times 10^9 M_{\odot}$ and $3.0 \times 10^9 M_{\odot}$ respectively."
" The median [or the entire sample is M,=1.0x10?M. (mean: 8.9x107AM. ). with standard deviation 2.5x109M."," The median for the entire sample is $M_{\bullet}=1.0 \times 10^9
M_{\odot}$ (mean: $8.9 \times 10^8 M_{\odot}$ ), with standard deviation $2.5
\times 10^9 M_{\odot}$."
 The lower part of Figure 4. shows black hole mass versus the magnitude of the nucleus for the masses derived in this section., The lower part of Figure \ref{fig4} shows black hole mass versus the magnitude of the nucleus for the masses derived in this section.
" The errors in the black hole massesare dominated by the scatter in the Fundamental Plane relation. which is around in o, for a given 44 and ον."," The errors in the black hole massesare dominated by the scatter in the Fundamental Plane relation, which is around in $\sigma_e$ for a given $\mu_e$ and $r_e$."
" The uncertainty in yy, and 7. affect the errors to a lesser extent. and the errors in the actual Fundamental Plane fit parameters are small in comparison."," The uncertainty in $\mu_e$ and $r_e$ affect the errors to a lesser extent, and the errors in the actual Fundamental Plane fit parameters are small in comparison."
" The assumed error in o. although leading to dilferences of only ~415% in black hole mass. compounds with the error in g,."," The assumed error in $\alpha$, although leading to differences of only $\sim \pm15\%$ in black hole mass, compounds with the error in $\sigma_e$."
" As a result. although the scatter in the M, σ, relation is small. the final errors in the black hole masses caleulated by this method are of similar order to those calculated from the M, Li, relation."," As a result, although the scatter in the $M_{\bullet}$ $\sigma_e$ relation is small, the final errors in the black hole masses calculated by this method are of similar order to those calculated from the $M_{\bullet}$ $L_{bulge}$ relation."
 Again. taking these errors into account. there is no statistically significant. trend. between black hole masses derived in Chis section and nuclear Iuminositv. beaming corrected or otherwise.," Again, taking these errors into account, there is no statistically significant trend between black hole masses derived in this section and nuclear luminosity, beaming corrected or otherwise."
 The median Eddington ratio lint for the eight BL Lacswith measured Doppler factor limits is Lu< 0.0L. while the median for the entire low-power subsample is Bz3x10 !.," The median Eddington ratio limit for the eight BL Lacswith measured Doppler factor limits is $\frac{L_{bol.}}{L_{Edd}} \lesssim 0.01$ , while the median for the entire low-power subsample is $\frac{L_{bol.}}{L_{Edd}} \lesssim 3\times10^{-4}$ ."
 Again. these Exldington ratios are a great deal smaller than the median for the high-power," Again, these Eddington ratios are a great deal smaller than the median for the high-power"
magnetic field between 20 Gauss and 30 Gauss.,magnetic field between 20 Gauss and 30 Gauss.
 The differences between FALC and FALX results are not meaningful with regard to the accuracy of the polarization measurements., The differences between FALC and FALX results are not meaningful with regard to the accuracy of the polarization measurements.
 We now take into account the effect of neglecting alignment transfer with the metastable *D3)25;2 levels.," We now take into account the effect of neglecting alignment transfer with the metastable $^2D_{3/2,5/2}$ levels."
 Table | gives the correction factor f. that we have to apply to the value of the turbulent magnetic field strength derived from our equivalent two-level model., Table 1 gives the correction factor $f_c$ that we have to apply to the value of the turbulent magnetic field strength derived from our equivalent two-level model.
 It is obtained as explained in Derouich (2008) by solving the statistical equilibrium equations for the density matrix elements of the 5-level model of and of the two-level model. in the presence of depolarizing collision. a radiation. field and the Hanle effect and comparing the alignment of the P; level in both models.," It is obtained as explained in Derouich (2008) by solving the statistical equilibrium equations for the density matrix elements of the 5-level model of and of the two-level model, in the presence of depolarizing collision, a radiation field and the Hanle effect and comparing the alignment of the $^2P_{3/2}$ level in both models."
 The line profiles observed close to the solar limb. are formed at altitudes z> 900 km. where the hydrogen density is lower than 510? em~ and the correction factor is between 0.60 and 0.51.," The line profiles observed close to the solar limb, are formed at altitudes $z \ge$ 900 km, where the hydrogen density is lower than $5\,10^{13}$ $^{-3}$ and the correction factor is between 0.60 and 0.51."
 Let us stress that the correction factor depends in a non-linear way on the magnetic field strength implemented in the density matrix statistical rates: here 1t was computed for a magnetic field of the order of 15 G. Applying this correction to our previous estimate we find that the turbulent magnetic field strength is between 10 G and 18 G. The chromosphere ts à highly inhomogeneous medium where temperature. velocity and magnetic fields have complex structures that are still poorly investigated.," Let us stress that the correction factor depends in a non-linear way on the magnetic field strength implemented in the density matrix statistical rates; here it was computed for a magnetic field of the order of 15 G. Applying this correction to our previous estimate we find that the turbulent magnetic field strength is between 10 G and 18 G. The chromosphere is a highly inhomogeneous medium where temperature, velocity and magnetic fields have complex structures that are still poorly investigated."
 As the magnetic strength decreases with height in the solar atmosphere. the Hanle effect in resonance lines offers a valuable complement to Zeeman diagnostics.," As the magnetic strength decreases with height in the solar atmosphere, the Hanle effect in resonance lines offers a valuable complement to Zeeman diagnostics."
 We have tested the sensitivity of the linear resonance polarization of the Ball 455.4. nm line to partial frequency redistribution (PFR). temperature variations in the atmospheric model. elastic collisions and weak unresolved magnetic fields.," We have tested the sensitivity of the linear resonance polarization of the BaII 455.4 nm line to partial frequency redistribution (PFR), temperature variations in the atmospheric model, elastic collisions and weak unresolved magnetic fields."
 These investigations show that the line polarization is strongly affected by PFR. but that it ts weakly sensitive to temperature variations.," These investigations show that the line polarization is strongly affected by PFR, but that it is weakly sensitive to temperature variations."
 Recent studies on the depolarizing effects of elastic collisions with hydrogen atoms by Derouich (2008) showed that the line polarization is affected by alignment transfer with the metastable D levels which are not included in the equivalent two-level atom model that we use for modeling the non-LTE polarized line formation., Recent studies on the depolarizing effects of elastic collisions with hydrogen atoms by Derouich (2008) showed that the line polarization is affected by alignment transfer with the metastable $^2D$ levels which are not included in the equivalent two-level atom model that we use for modeling the non-LTE polarized line formation.
 We propose to take this depolarizing mechanism into account by introducing a correction factor on the turbulent magnetic field strength obtained with the equivalent two-level atom model., We propose to take this depolarizing mechanism into account by introducing a correction factor on the turbulent magnetic field strength obtained with the equivalent two-level atom model.
 We estimate this correction factor by solving the statistical equilibrium equations for the density matrix of the 5-levels atomie model including collisions. radiation and magnetic field effects. with a single scattering approximation as in Derouich (2008).," We estimate this correction factor by solving the statistical equilibrium equations for the density matrix of the 5-levels atomic model including collisions, radiation and magnetic field effects, with a single scattering approximation as in Derouich (2008)."
 This procedure is a first step toward a complete treatment of non-LTE polarized transfer including partial frequency redistribution and full multi-level coupling., This procedure is a first step toward a complete treatment of non-LTE polarized transfer including partial frequency redistribution and full multi-level coupling.
 This paper shows that the solar D2 line is very well suited for the diagnosis of weak magnetic fields of the order of afew tens of Gauss in the low chromosphere. typically between 900 km and 1300 km above the basis of the photosphere.," This paper shows that the solar D2 line is very well suited for the diagnosis of weak magnetic fields of the order of a few tens of Gauss in the low chromosphere, typically between 900 km and 1300 km above the basis of the photosphere."
 Our observations are well recovered with a turbulent magnetic field between 10 G and 18 G. These values are significantly lower than those which are derived from the linear limb polarization observed 11 the Srl line at 406.7 nm or in molecular lines of MH. which range between 20 G and 50 G (see Faurobert et al 2001. Bommier et al.," Our observations are well recovered with a turbulent magnetic field between 10 G and 18 G. These values are significantly lower than those which are derived from the linear limb polarization observed in the SrI line at 406.7 nm or in molecular lines of MgH, which range between 20 G and 50 G (see Faurobert et al 2001, Bommier et al."
 2005. Bommier et al.," 2005, Bommier et al."
 2006)., 2006).
 But those lines are formed in the upper photosphere. typically between 200 km and 400 km above the basis of the photosphere. where the turbulent magnetic field may very well be stronger than," But those lines are formed in the upper photosphere, typically between 200 km and 400 km above the basis of the photosphere, where the turbulent magnetic field may very well be stronger than"
and ring-like structures.,and ring-like structures.
" From this modified Jeans mass, we obtained the filtering mass and the baryonic gas fraction of a dark matter halo."," From this modified Jeans mass, we obtained the filtering mass and the baryonic gas fraction of a dark matter halo."
" We showed that, depending on the magnetogenesis model, which determines Bo and Lo, both the Jeans mass and the baryonic gas fraction can change by orders of magnitude."," We showed that, depending on the magnetogenesis model, which determines $B_0$ and $L_0$, both the Jeans mass and the baryonic gas fraction can change by orders of magnitude."
" We found, for example, for a comoving Bo=0.1μα, and a reionization epoch that starts at z,=11 and ends at z.= 8, for Lo=100pc at z=12, the f, becomes severely depressed for M<10’Mo, whereas for Bo=0 the f, becomes severely depressed only for much smaller masses, M<10°Mo."," We found, for example, for a comoving $B_0=0.1\muG$, and a reionization epoch that starts at $z_s=11$ and ends at $z_e=8$ , for $L_0=100\,\text{pc}$ at $z=12$, the $f_g$ becomes severely depressed for $M<10^7\msun$, whereas for $B_0=0$ the $f_g$ becomes severely depressed only for much smaller masses, $M<10^5\msun$."
" Since it is very difficult to make observations of intergalactic magnetic fields at high redshifts, and the constraints imposed by CMB measurements are not very restrictive, we suggest the possibility to add new constraints on a family of models for the primordial magnetic field, by following the redshift evolution of the filtering mass of galaxies."," Since it is very difficult to make observations of intergalactic magnetic fields at high redshifts, and the constraints imposed by CMB measurements are not very restrictive, we suggest the possibility to add new constraints on a family of models for the primordial magnetic field, by following the redshift evolution of the filtering mass of galaxies."
 We also calculated the modified baryonic gas fraction that can also be used as an indirect observable to help us to understand the origin and structure of cosmic magnetic fields., We also calculated the modified baryonic gas fraction that can also be used as an indirect observable to help us to understand the origin and structure of cosmic magnetic fields.
 R.S.S. thanks the Brazilian agency FAPESP for financial support (2009/06770-2)., R.S.S. thanks the Brazilian agency FAPESP for financial support (2009/06770-2).
 L.F.S.R. thanks the Brazilian agency CNPq for financial support (142394/2006-8)., L.F.S.R. thanks the Brazilian agency CNPq for financial support (142394/2006-8).
 R.O. thanks the Brazilianagencies FAPESP (06/56213-9) and, R.O. thanks the Brazilianagencies FAPESP (06/56213-9) and
"20-22/, Large Put?2 £2» £D 2].","$^{th}$ $^{1,2}$ $H_2$ $HD$ \cite{puy1}."
 CO {ο HD CO 3].., $CO$ $H_2$ $HD$ $CO$ \cite{puy2}.
 z , $\tau$ 
"objectively define MS outliers, hence starburst galaxies.","objectively define MS outliers, hence starburst galaxies."
" To this purpose, Gaussians functions are fitted to the BzK distributions in the four mass bins, resulting in a nearly constant σ=0.24 dex, slightly lower than reported in Daddi et al. ("," To this purpose, Gaussians functions are fitted to the BzK distributions in the four mass bins, resulting in a nearly constant $\sigma=0.24$ dex, slightly lower than reported in Daddi et al. ("
2007).,2007).
 Deviations from the Gaussian distributions start to be clearly detected at SSFRs 0.6 dex above the average (Fig. 2;;, Deviations from the Gaussian distributions start to be clearly detected at SSFRs 0.6 dex above the average (Fig. \ref{histo};
" or some 2.50), and we adopt this threshold to define on-sequence and off-sequence galaxies."," or some $\sigma$ ), and we adopt this threshold to define on-sequence and off-sequence galaxies."
 Such deviations are less obvious in the highest mass bin., Such deviations are less obvious in the highest mass bin.
" We also note that the peak positions of the Gaussians shift as a function of the bin central mass, with a slope of 0.79+0.04 in the shallower than the 0.9 slope log(reportedM.) by Daddi et al."," We also note that the peak positions of the Gaussians shift as a function of the bin central mass, with a slope of $0.79\pm0.04$ in the $M_*$ ) (slightly shallower than the 0.9 slope reported by Daddi et al."
 (slightly2007)., 2007).
" It is worth emphasizing the good agreement of the four independent samples in the common SSFR bins, in particular for M,>10!'Mo, where PACS-GOODS fully samples the MS distribution around its peak."," It is worth emphasizing the good agreement of the four independent samples in the common SSFR bins, in particular for $M_*>10^{11}M_{\odot}$, where PACS-GOODS fully samples the MS distribution around its peak."
 In this case the UV and IR SFR tracers define exactly the same Gaussian distribution., In this case the UV and IR SFR tracers define exactly the same Gaussian distribution.
 From the histograms in Fig., From the histograms in Fig.
" 2 we have estimated the relative contribution of on-sequence and off-sequence galaxies to the total comoving number density and SFR density, in absolute (Fig. 3))"," \ref{histo} we have estimated the relative contribution of on-sequence and off-sequence galaxies to the total comoving number density and SFR density, in absolute (Fig. \ref{density}) )"
 as well as relative (Fig. 4)), as well as relative (Fig. \ref{dist}) )
 terms., terms.
" The space density of galaxies in the highest mass bin is getting lower, as we are entering the exponentially decaying part of the mass function."," The space density of galaxies in the highest mass bin is getting lower, as we are entering the exponentially decaying part of the mass function."
" The MS population dominates the SFR density at all masses, whereas off-sequence starburst galaxies contribute almost constantly ~10% of the total, or even less since some outliers may actually be MS objects with exceptionally large errors (in either SFR or Μ.)."," The MS population dominates the SFR density at all masses, whereas off-sequence starburst galaxies contribute almost constantly $\sim 10\%$ of the total, or even less since some outliers may actually be MS objects with exceptionally large errors (in either SFR or $_*$ )."
" If a top-heavy IMF were really to apply to starbursts, then this fraction would even be largely reduced."," If a top-heavy IMF were really to apply to starbursts, then this fraction would even be largely reduced."
" The number density of off-sequence sources is also very small, varying between 2 and 3% as a function of the stellar mass."," The number density of off-sequence sources is also very small, varying between 2 and $\%$ as a function of the stellar mass."
 Only in SFR-limited samples (Fig. ," Only in SFR-limited samples (Fig. \ref{dist}) ),"
"off-sequence galaxies become important representing 4)),46+20% of the galaxies with SFR»1000 Mo yr-! and 2044% of those with SFR» Mo ντ.", off-sequence galaxies become important representing $46\pm20$ of the galaxies with $>1000$ $M_\odot$ $^{-1}$ and $\pm4$ of those with $>100~$ $_\odot$ $^{-1}$.
 This suggests that even among SMGs (or luminous Herschel selected populations) only a fraction of the galaxies are strong MS outliers., This suggests that even among SMGs (or luminous Herschel selected populations) only a fraction of the galaxies are strong MS outliers.
 An important aspect of this work concerns the combination of UV-based and IR-based SFR indicators for the sources for which both data are available., An important aspect of this work concerns the combination of UV-based and IR-based SFR indicators for the sources for which both data are available.
" Indeed, about 70%((80%)) of the COSMOS(GOODS) PACS sources have a BzK counterpart."," Indeed, about ) of the COSMOS(GOODS) PACS sources have a BzK counterpart."
 For ~30% of these, For $\sim 30\%$ of these
galaxies can successfully be used to estimate photometric redshifts for the N-rav. harder sources (see also Barger οἱ al.,galaxies can successfully be used to estimate photometric redshifts for the X-ray harder sources (see also Barger et al.
 2002. 2003: Mobasher ct al.," 2002, 2003; Mobasher et al."
 2004: Gandhi et al., 2004; Gandhi et al.
 2004)., 2004).
 This method. provides photometric redshift estimates for 3 sources that have no spectroscopic redshift measurement., This method provides photometric redshift estimates for 3 sources that have no spectroscopic redshift measurement.
 X-ray sources with soft. N-rav. spectral properties are most likely dominated by light from the central AGN (see section 7?7)). although we caution the reader that there is increasing evidence for broad line AGNs that do not behave this way and show Lat (hard) X-ray spectra (Risaliti ct al.," X-ray sources with soft X-ray spectral properties are most likely dominated by light from the central AGN (see section \ref{results}) ), although we caution the reader that there is increasing evidence for broad line AGNs that do not behave this way and show flat (hard) X-ray spectra (Risaliti et al."
 2001: ltisalitiet al., 2001; Risaliti et al.
 2003)., 2003).
 Unlike galaxies. estimating photonietric redshifts for ΑΝ dominated. svstems is challenging ancl despite recent progress the results are significantly less accurate (Richards et al.," Unlike galaxies, estimating photometric redshifts for AGN dominated systems is challenging and despite recent progress the results are significantly less accurate (Richards et al."
 2001: Witsionas et al., 2001; Kitsionas et al.
 2004: Jabbodge et al., 2004; Babbedge et al.
 2004)., 2004).
 In the present. study. we cdo not estimate photometric redshifts for sources with soft. N-rav spectral properties likely to be Sevfert ls or QSOs., In the present study we do not estimate photometric redshifts for sources with soft X-ray spectral properties likely to be Seyfert 1s or QSOs.
 One of the hard. X-ray. selected sources 25 in Table 1l below) has à verv bright. 7!& 13mmag. optically unresolved. counterpart ancl very low X-raytooptical Lux ratio (logfxfij;&— 3).," One of the hard X-ray selected sources 25 in Table \ref{tbl1}
 below) has a very bright, $R\approx13$ mag, optically unresolved counterpart and very low X-ray–to–optical flux ratio $\log f_X/f_{opt}\approx-3$ )."
 Also. as discussed in Appendix the N-ray spectrum of this object is best fit by a Itavmond-Smith hot gas model (ltàvmond Smith 1977) with temperature KI=0.7keV.," Also, as discussed in Appendix \ref{app1} the X-ray spectrum of this object is best fit by a Raymond-Smith hot gas model (Raymond Smith 1977) with temperature $\rm kT=0.7\,keV$."
 Although optical spectroscopy is not available the evidence above indicates that this X-ray source is associated with a Galactic star., Although optical spectroscopy is not available the evidence above indicates that this X-ray source is associated with a Galactic star.
 In the rest of this paper we will not consider this source in our analysis., In the rest of this paper we will not consider this source in our analysis.
 The hard X-ray selected: sample used in this paper is presented in Table 1 which has the following format: Identification number., The hard X-ray selected sample used in this paper is presented in Table \ref{tbl1} which has the following format: Identification number.
 Right ascension and declination of the X-ray centroid position in J2000.4-7 U. V.," Right ascension and declination of the X-ray centroid position in J2000. $U$, $V$,"
 HR and A-band magnitudes. (Vega: based svsteni) respectively of the optical counterpart if available., $R$ and $K$ -band magnitudes (Vega based system) respectively of the optical counterpart if available.
 Probability. P. the optical counterpart is a chance coincidence.," Probability, $P$, the optical counterpart is a chance coincidence."
 Olfset in arcseconds between the X-ray. and optical source positions., Offset in arcseconds between the X-ray and optical source positions.
 Spectroscopic or photometric redshift., Spectroscopic or photometric redshift.
 Quality. éQ. of the redshift estimate.," Quality, $Q$, of the redshift estimate."
 A value Q= corresponds to three or more identified spectral features indicating a reliable redshift., A value $Q=3$ corresponds to three or more identified spectral features indicating a reliable redshift.
 A value Q=1.2 corresponds to 1 and 2 identified spectral features respectively.," A value $Q=1, 2$ corresponds to 1 and 2 identified spectral features respectively."
 Classification on the basis of the observed optical spectral features: absorption lines only: narrow emission lines: broad emission lines., Classification on the basis of the observed optical spectral features: absorption lines only; narrow emission lines; broad emission lines.
 Htadio tus density.Sy. of the radio counterpart of the N-rayv source. if available.," Radio flux density,$S_{1.4}$, of the radio counterpart of the X-ray source if available."
 Radio sources that Die below the formal limit Sy)SOfjjvy. of the radio catalogue corresponding to about Sa are marked., Radio sources that lie below the formal limit $S_{1.4}\approx\rm 80\mu Jy$ of the radio catalogue corresponding to about $5\sigma$ are marked.
 Although the peak lux density of these sources is below the So level their integrated [ux density is. in some cases. brighter than μον.," Although the peak flux density of these sources is below the $5\sigma$ level their integrated flux density is, in some cases, brighter than $\rm 80\mu Jy$."
 Ollset in arescconds between the radio and X-ray source positions., Offset in arcseconds between the radio and X-ray source positions.
 We further explore the X-ray spectral properties of the present sample using the v11.2 package., We further explore the X-ray spectral properties of the present sample using the v11.2 package.
 For sources with small number of net counts we use the C-statistic echnique (Cash 1979) specifically developed: to extract information from low signal-to-noise ratio spectra., For sources with small number of net counts we use the C-statistic technique (Cash 1979) specifically developed to extract information from low signal-to-noise ratio spectra.
 The data are grouped to have at least one count per bin., The data are grouped to have at least one count per bin.
 We note jowever. that higher binning factors or no binning does not ange our results.," We note however, that higher binning factors or no binning does not change our results."
 Firstly. we attempt to constrain the Ny w fitting an absorbed. (Wisconsin cross-sections: Morrison and AleCammon 1983) power-law model (wabs*pow) fixing 10 power-Iaw index to E—1.7.," Firstly, we attempt to constrain the $\rm
N_H$ by fitting an absorbed (Wisconsin cross-sections; Morrison and McCammon 1983) power-law model (wabs*pow) fixing the power-law index to $\Gamma=1.7$ ."
 This value of Pis selected o be inbetween the mean spectral index of radio Loud (P=1.6: Reeves Turner 2000: Cambill 2003) and racio uiet ACGNs (EPzL9: Laor et al., This value of $\Gamma$ is selected to be inbetween the mean spectral index of radio loud $\Gamma=1.6$; Reeves Turner 2000; Gambill 2003) and radio quiet AGNs $\Gamma\approx1.9$; Laor et al.
 1997: Reeves Turner 2000)., 1997; Reeves Turner 2000).
 We then use the same model (wabs*pow) to estimate re power law index E keeping the column density. fixed to 1 Galactic value (Ng=2«107em.7).," We then use the same model (wabs*pow) to estimate the power law index $\Gamma$ keeping the column density fixed to the Galactic value $\rm
N_H=2\times10^{20}\,cm^{-2}$ )."
 For sources with sullicient. counts we perform standard: X7 spectral fitting., For sources with sufficient counts we perform standard $\chi^{2}$ spectral fitting.
 The data were >grouped to have a minimum of 15 counts ver bin to ensure that Gaussian statistics apply., The data were grouped to have a minimum of 15 counts per bin to ensure that Gaussian statistics apply.
 For the X7 analysis we require that the source spectrum has at least 15 spectral bins., For the $\chi^{2}$ analysis we require that the source spectrum has at least 15 spectral bins.
 An absorbed. power-law (wabs*pow) is fit to he data vielding the intrinsic absorbing column density (i.c. after subtracting the Galactic absorption) and the power-aw photon index E., An absorbed power-law (wabs*pow) is fit to the data yielding the intrinsic absorbing column density (i.e. after subtracting the Galactic absorption) and the power-law photon index $\Gamma$.
 Fhis model provides acceptable fits (i.e. reduced. 472 1) for all sources., This model provides acceptable fits (i.e. reduced $\chi^{2}\approx1$ ) for all sources.
 The parameters estimated rom the C-statistic and the x72 analysis are consistent within he errors., The parameters estimated from the C-statistic and the $\chi^{2}$ analysis are consistent within the errors.
 For both the 47 and the Cestatistie analysis the it was performed. in the kkeV. energy. range where he sensitivity. of the is the highest., For both the $\chi^{2}$ and the C-statistic analysis the fit was performed in the keV energy range where the sensitivity of the is the highest.
 The estimated errors correspond to the 90 per cent. confidence evel., The estimated errors correspond to the 90 per cent confidence level.
 Phe results of the above N-ray spectral analysis along with the X-rav properties of the sample are presented. in ‘Table 2. which has the following format: Identification number., The results of the above X-ray spectral analysis along with the X-ray properties of the sample are presented in Table \ref{tbl2} which has the following format: Identification number.
" 2-SkkeV X-ray “ux in eresten"""," keV X-ray flux in $\rm erg\,s^{-1}\,cm^{-2}$."
 Llardness ratio. Hi. defined as ∖∖⋎↓↥⋖⊾↓⋅∢⋅∐⇀∖↾↓∖∣⊲⇀⊲↿∖∪⋅↱≻⇉∪⊐⋜⋯∠⇂∐⇀∖↾↓∖∣⊲⇀⊲↿∖⇉∪↖∖⋯⋜⊔⋅⋖⋅↿↓∐⋅≼∼∪⊔⊔∣ rates in the 0.5-2 anc 2-SkkeV spectral bands respectively.," Hardness ratio, $\rm HR$, defined as where $\rm RATE(0520)$ and $\rm RATE(2080)$ are the count rates in the 0.5-2 and keV spectral bands respectively."
 For sources with less than 5 net counts in either the hard or the soft bands a lower or an upper limit (30) respectively is estimated for the hardness ratio assuming Poissonstatistics., For sources with less than 5 net counts in either the hard or the soft bands a lower or an upper limit $3\sigma$ ) respectively is estimated for the hardness ratio assuming Poissonstatistics.
 The hardness ratios are estimated using the PN data except [or sources that lie close to PN CCD eaps or hot. pixels where we use MOS data (see section 2.1)., The hardness ratios are estimated using the PN data except for sources that lie close to PN CCD gaps or hot pixels where we use MOS data (see section 2.1).
 These sources are markecl in Table 2.., These sources are marked in Table \ref{tbl2}.
 Column density Ng estimated by either the C-statistic method. assuming P.—1.7 or the standard. 7 spectral fitting in the case of sources with sullicient counts (see discussion above)., Column density $\rm N_H$ estimated by either the C-statistic method assuming $\Gamma=1.7$ or the standard $\chi^{2}$ spectral fitting in the case of sources with sufficient counts (see discussion above).
 Power law spectral index E estimated by eitherthe C-statistic for a fixed Galactic column density Ng=2 or the standard. y 7ospectral fitting in the case of sources with sullicient counts (see discussion above)," Power law spectral index $\rm \Gamma$ estimated by eitherthe C-statistic for a fixed Galactic column density $\rm
N_H=2\times10^{20}\,cm^{-2}$ or the standard $\chi^{2}$ spectral fitting in the case of sources with sufficient counts (see discussion above)."
 2-SkkeV. N-rav. luminosity if. ài spectroscopic or, keV X-ray luminosity if a spectroscopic or
For many years the X-ray emission of active galactic nuclei (AGN) has been known to be strongly variable (seee.g.Gaskelletal.2006:Uttley2007.for reviews).,"For many years the X-ray emission of active galactic nuclei (AGN) has been known to be strongly variable \citep[see e.g.][for
reviews]{gaskell06,uttley07}."
. However. the nature of this variability remains unknown.," However, the nature of this variability remains unknown."
 Most proposed models have been based on a natural assumption that the emission originates close to the accreting supermassive black hole and fluctuates on the dynamical timescale., Most proposed models have been based on a natural assumption that the emission originates close to the accreting supermassive black hole and fluctuates on the dynamical timescale.
 Rapid variability is among the arguments in favor of this interpretation (Krolik1999)., Rapid variability is among the arguments in favor of this interpretation \citep{krolik99}.
. The effects of general relativity are expected to play an important role in shaping the observed signal (Katoetal.1905)., The effects of general relativity are expected to play an important role in shaping the observed signal \citep{kato98}.
 As the innermost part of aceretion flow likely proceeds through some form of a disk. characterized by a (roughly) Keplerian profile of rotational velocity. the relativistic effects are expected to depend on the inclination angle of the observer with respect to the disk plane.," As the innermost part of accretion flow likely proceeds through some form of a disk, characterized by a (roughly) Keplerian profile of rotational velocity, the relativistic effects are expected to depend on the inclination angle of the observer with respect to the disk plane."
 These effects are only weakly seen in the stationary continuum models if the emission is due to Comptonization. but they are very profound in the observed shapes of spectral features such as the tron Ka line (e.g. Fabianetal. 1995)).," These effects are only weakly seen in the stationary continuum models if the emission is due to Comptonization, but they are very profound in the observed shapes of spectral features such as the iron $\alpha$ line (e.g. \citeauthor{fabian95} \citeyear{fabian95}) )."
 hi addition. earlier studies predict that non-stationary continuum models can display relativistic effects also through the dependence of the level of variability on the inclination angle of an observer (Zhang&Bao1991;al. 2004).," In addition, earlier studies predict that non-stationary continuum models can display relativistic effects also through the dependence of the level of variability on the inclination angle of an observer \citep{zhang91,abramowicz91,karas98,fukue03,czerny04}."
. Therefore. the application of a specific model to both low and high inclination sources opens an additional possibility of model testing.," Therefore, the application of a specific model to both low and high inclination sources opens an additional possibility of model testing."
" In the present paper. we apply the flare model developed originally for the case of Seyfert galaxy MCG-6-30-15. which is à source at a moderate inclination (@,~30 deg) with respect to the observer's line of sight (Fabianetal. 1995. 2002). to the galaxy viewed from the almost edge-on direction."," In the present paper, we apply the flare model developed originally for the case of Seyfert galaxy MCG–6-30-15, which is a source at a moderate inclination $\incli\sim30$ deg) with respect to the observer's line of sight \citeauthor{fabian95} \citeyear{fabian95}, \citeyear{fabian02}) ), to the galaxy viewed from the almost edge-on direction."
" This active galaxy is unique in several aspects: well-resolved maser emission from the nucleus allows an accurate mass determination of the black hole: the source Is Compton thin (despite the high inclination). which allows us to measure the X-ray variability; rotation studies also show that the mner accretion disk follows Keplerian orbital motion very accurately,"," This active galaxy is unique in several aspects: well-resolved maser emission from the nucleus allows an accurate mass determination of the black hole; the source is Compton thin (despite the high inclination), which allows us to measure the X-ray variability; rotation studies also show that the inner accretion disk follows Keplerian orbital motion very accurately."
 The paper is organized as follows., The paper is organized as follows.
 In Sect. 2..," In Sect. \ref{sec:application},"
 we summarize the general scenario of the flare model. introduce a convenient parameterization. and adapt this scheme to the case of NGC 4258.," we summarize the general scenario of the flare model, introduce a convenient parameterization, and adapt this scheme to the case of NGC 4258."
 We discuss the main differences in the model set-up caused by our concentration in previous papers on low to moderate inclinations for the application to unobscured Seyfert | AGN. whereas now we wish to apply the model to a highly-inclined source.," We discuss the main differences in the model set-up caused by our concentration in previous papers on low to moderate inclinations for the application to unobscured Seyfert 1 AGN, whereas now we wish to apply the model to a highly-inclined source."
 In Sect. 3..," In Sect. \ref{sec:results},"
 we present our showing in particular the inclination dependence of the variability variance., we present our showing in particular the inclination dependence of the variability variance.
 We consider the role of the avalanche prescription. where the flares are mutually interconnected às they occur in families.," We consider the role of the avalanche prescription, where the flares are mutually interconnected as they occur in families."
 Finally we summarize the results in Sect., Finally we summarize the results in Sect.
 4 and present our conclusions., \ref{sec:discussion} and present our conclusions.
 The idea of X-ray emission coming from multiple locations within/above accretion disks around a black hole is motivated by the important role of magnetic fields in the process of aceretion., The idea of X-ray emission coming from multiple locations within/above accretion disks around a black hole is motivated by the important role of magnetic fields in the process of accretion.
 The original formulation of the flare model by Galeevetal.(1979) was followed by numerous papers (e.g.Fabian2001:Collinetal.2003:Goosmann 2007b).," The original formulation of the flare model by \citet{galeev79} was followed by numerous papers \citep[e.g.][]{dimatteo98,nayakshin01,merloni01,collin03,goosmann07b}."
. A common theme to these models is an underlying assumptior of a standard-type accretion flow driving the magnetic field., A common theme to these models is an underlying assumption of a standard-type accretion flow driving the magnetic field.
 A similar picture can also be developed in the absence of a cold disk since in that case multiple shocks are expected to form in the hot aceretion flow (e.g.Boettcher&Liang1999:Zycki 2003).," A similar picture can also be developed in the absence of a cold disk since in that case multiple shocks are expected to form in the hot accretion flow \citep[e.g.][]{boettcher99,zycki03}."
. The attractiveness of the flare model is also supported by the close correlation between the radio and X-ray emissitor in radio quiet AGN. which ts a phenomenon typical of active stellar coronae (Laor&Behar2005).," The attractiveness of the flare model is also supported by the close correlation between the radio and X-ray emission in radio quiet AGN, which is a phenomenon typical of active stellar coronae \citep{laor08}."
 In the present work. we generalize the model developec by Czemyetal.(2004) and Goosmanietal.(2006)..," In the present work, we generalize the model developed by \citet{czerny04} and \citet{goosmann06}."
 We parameterize the distribution of the flares across the disk and the flare properties., We parameterize the distribution of the flares across the disk and the flare properties.
 We assume that the luminosity of a single flare following the initial onset decreases gradually with time., We assume that the luminosity of a single flare following the initial onset decreases gradually with time.
 This differs from the previous paper where we adopted a rectangular profile for the flare light curve., This differs from the previous paper where we adopted a rectangular profile for the flare light curve.
 The most important, The most important
sensitive to the macro-model flux ratio.,sensitive to the macro-model flux ratio.
 As a result. we have parameterisecl the macro-mocels available from. the literature by their precictec [ux-atio., As a result we have parameterised the macro-models available from the literature by their predicted flux-ratio.
 The strongest limits are found. from the Dux ratios between images B anc A. This is due in part to the dillerences between the relative Vebanel and. micl-L fluxes. as well as the more consistent niacro-mocel predictions for these images.," The strongest limits are found from the flux ratios between images B and A. This is due in part to the differences between the relative V-band and mid-IR fluxes, as well as the more consistent macro-model predictions for these images."
" We find that the micd-LIt. source size Syyp2lp, with z90% confidence. and 0.55, with 95% confidence."," We find that the mid-IR source size $S_{IR}>1\eta_o$ with $>90\%$ confidence, and $>0.5\eta_o$ with $>95\%$ confidence."
 The Hi-emission scale is arger than the optical emission with a confidence z994., The IR-emission scale is larger than the optical emission with a confidence $>99\%$.
 The limit on the infrared source size derived. here for he Einstein Cross may be converted to a limit on the rightness temperature., The limit on the infrared source size derived here for the Einstein Cross may be converted to a limit on the brightness temperature.
 Assuming microlensing by. stars. Sip2gecLO em. and the brightness temperature at 10 yam (rest frame 3.7 pam) is about 75£z;1900A for a uminosity distance of 1077E cm. magnification of 15. and flux of 20 mJv.," Assuming microlensing by stars, $S_{IR} \ga \eta_o \sim 10^{17}$ cm, and the brightness temperature at 10 $\mu$ m (rest frame 3.7 $\mu$ m) is about $T_b \la 7900 K$ for a luminosity distance of $10^{28} $ cm, magnification of 15, and flux of 20 mJy."
 This upper limit on the source brightness rules, This upper limit on the source brightness rules
introduce afurther gener,where we used spherical symmetry and where $C^{ab}_{\phantom{ab}cd}$ is the Weyl tensor.
"al lineare-correction yh -Ly e£a(r)) (no summation) where (Ag.A3) 0 constants with eitherft4? 4? otherwise onlyDas4 4 0.and We use ( 5aaa) require[e£(7)| «1for all £-functions forr>0.In addition weset the boundary. conditions: lim,ως£(r)"," The magnetic parts of the field strengths are obtained from Bianchi identities, which for our static spherically symmetric metric \ref{metric}) ) give: For our choice of charges, and the complex-valued form of the prepotential \ref{prep}) ) and the ansatz \ref{r2sol}) ) we get For the $U(1)$ and $SU(2)$ connections we assume The equation of motion for the $SU(2)$ connection is always satisfied by the vanishing $SU(2)$ connection, for a bosonic background and with either the $V$ -gauge for the nonlinear multiplet \ref{gauge}) ) or covariantly constant hypermultiplet scalars."
 — 0. This givesan asvinplolically flat solution. Let introduce thedual fieldstre," This is because the $SU(2)$ connection and its derivatives, appear then in the Lagrangian \ref{lag}) ) always in at least a quadratic The vanishing of the $SU(2)$ connection implies also $Y_{ij}^I=0$ \cite{yeom}."
"ngth: Gau e FuES/ +n FN, wherewe have considered ouly bosoni"," When using the nonlinear multiplet, the auxiliary field $D$ may be determined by the constraint on the nonlinear multiplet \ref{nl}) )."
cterms., We assume
"temperature (Ho&Townes1983),, however, the analytical expression of Tafallaetal.(2004,pg.211) has been used to estimate from.","temperature \citep{hotownes1983}, however, the analytical expression of \citet[pg.\,211]{tafalla} has been used to estimate from."
. This is believed to be accurate to within of the real value of for temperatures in the 5-20KK range., This is believed to be accurate to within of the real value of for temperatures in the K range.
" Importantly, this method for obtaining temperatures is only considered valid for up to ~40 KK. To obtain the column density for the NHa emission, we use the (1,1) transition and follow Equation 9 of Goldsmith&Langer (1999)."," Importantly, this method for obtaining temperatures is only considered valid for up to $\sim$ K. To obtain the column density for the $_3$ emission, we use the (1,1) transition and follow Equation 9 of \citet{goldsmith_langer}."
". Since the (1,1) represents only a fraction of the NHs gas, the total NH3 column density Nxu, can be obtained from the (1,1) column density and the partition function Q(T)."," Since the (1,1) represents only a fraction of the $_3$ gas, the total $_3$ column density $N_{\textrm{\tiny{NH}}_{3}}$ can be obtained from the (1,1) column density and the partition function $Q(T)$ ."
 In this work we assume contributions up to the 513 term in the series expansion., In this work we assume contributions up to the $5^{\rm th}$ term in the series expansion.
" 'To determine the total mass M and molecular hydrogen number density ng, (hereafter referred as just density) of the various cores we need to assume the core intrinsic radius R and the abundance ratio Xxu4 of NH3 to Ho.", To determine the total mass $M$ and molecular hydrogen number density $n_{\rm H_2}$ (hereafter referred as just density) of the various cores we need to assume the core intrinsic radius $R$ and the abundance ratio $\chi_{\textrm{\tiny{NH}}_{3}}$ of $_{3}$ to $_{2}$.
 We note that theabundance ratio is known to depend on the gas temperature T'., We note that theabundance ratio is known to depend on the gas temperature $T$.
" Ratios quoted in literature extend from 71077, few x10? (Walmsley&Schilke1983;Ottetal. 2005), down to ~10-!? Ottetal.(2010) in the Large Magellanic Cloud."," Ratios quoted in literature extend from $\sim$ $^{-7}$, few $\times 10^{-8}$ \citep{walmsley1983,ott2005}, down to $\sim 10^{-10}$ \cite{ott2010} in the Large Magellanic Cloud."
 For typical infrared dark clouds (IRDCs) with T«20 K an average value of ~4x10? is found (Pillaietal. 2006)., For typical infrared dark clouds (IRDCs) with $T<20$ K an average value of $\sim4\times10^{-8}$ is found \citep{pillai}. .
". However with the exception of Core 2 and Core 6, all NH3 cores in the W28 field are identified with star formation IR sources asindicated in Figure 7 and Table 3.."," However with the exception of Core 2 and Core 6, all $_3$ cores in the W28 field are identified with star formation IR sources asindicated in Figure \ref{fig:IRdata} and Table \ref{tab:coreID}. ."
" In hot cores, with (T'>100 K), abundance ratios of 10or even as high as 10~° have been suggested"," In hot cores, with $T>100$ K), abundance ratios of $^{-6}$or even as high as $^{-5}$ have been suggested"
parameters are listed in Table 2..,parameters are listed in Table \ref{tab-model}.
 The gas kinetic temperature distribution is shown in Fig. 3.1.., The gas kinetic temperature distribution is shown in Fig. \ref{fig-temp}.
" We assume a distance of 150 pc (?),, and the resulting mass- rate is 7x1077 Μο νι”! using an adopted CO abundance of 6x10~4 (relative to Hy, see Table 2)), which provide the best fits to both the line profile and line intensities."," We assume a distance of 150 pc \citep{knapp03}, and the resulting mass-loss rate is $\times 10^{-7}$ $_{\odot}$ $^{-1}$ using an adopted CO abundance of $\times 10^{-4}$ (relative to $_{2}$, see Table \ref{tab-model}) ), which provide the best fits to both the line profile and line intensities."
 The uncertainty in the mass-loss rate is of the order50%., The uncertainty in the mass-loss rate is of the order.
. This mass-loss rate agrees well with the dynamical mass-loss rate (certainly to within the errors in the input parameters)., This mass-loss rate agrees well with the dynamical mass-loss rate (certainly to within the errors in the input parameters).
 A comparison of the model fits and the HIFI observations can be seen in Fig 2.., A comparison of the model fits and the HIFI observations can be seen in Fig \ref{COfits}.
 The models have been scaled to match the line intensities and the scaling factor (given in each panel of the figure) is a measure of the goodness of fit., The models have been scaled to match the line intensities and the scaling factor (given in each panel of the figure) is a measure of the goodness of fit.
" The high rotational line at J 116— is noticeably narrower than the lower-level lines observed with HIFI and ground-based instruments (e.g., ?)), indicating that this line originates in a region where the gas is still being accelerated."," The high rotational line at $J$ 16--15 is noticeably narrower than the lower-level lines observed with HIFI and ground-based instruments (e.g., \citealt{knapp98}) ), indicating that this line originates in a region where the gas is still being accelerated."
 The estimated outer CO radius is 4x10!° cm., The estimated outer CO radius is $\times 10^{16}$ cm.
" To calculate the strength and shape of the circumstellar Η2Ο lines, we apply the parameters derived from our CO linemodelling (mass-loss rate, gas temperature and density structure, and gas velocity law) to the radiative transfer model for H2O based on an accelerated lambda iteration (ALI) code (22?).."," To calculate the strength and shape of the circumstellar $_{2}$ O lines, we apply the parameters derived from our CO linemodelling (mass-loss rate, gas temperature and density structure, and gas velocity law) to the radiative transfer model for $_{2}$ O based on an accelerated lambda iteration (ALI) code \citep{just05, maercker08, maercker09}. ."
 We used the molecular data from ? and the collisional cross-sections from ? for the lowest 45 levels of ortho- and para-H5O. The radiative excitation due to the absorption in the yz bending and v5 stretching modes is included., We used the molecular data from \citet{rothman09} and the collisional cross-sections from \citet{faure07} for the lowest 45 levels of ortho- and $_{2}$ O. The radiative excitation due to the absorption in the $\nu_{2}$ bending and $\nu_{3}$ stretching modes is included.
 The latter has been found to have a non-negligible effect in the low rate case (?).., The latter has been found to have a non-negligible effect in the low mass-loss-rate case \citep{maercker09}.
" The outer radius of the H5O shell was derived using the model results of ?,, i.e., 3.6Χ1015 cm."," The outer radius of the $_{2}$ O shell was derived using the model results of \citet{netzer87}, i.e., $\times 10^{15}$ cm."
" Since the ortho- and para-species are expected to be independent, we model the two species separately, using the same circumstellar input values and estimate the two abundances independently."," Since the ortho- and para-species are expected to be independent, we model the two species separately, using the same circumstellar input values and estimate the two abundances independently."
" Using the temperature and velocity structure from the CO modelling (Fig 3.1)), we calculate the best-fit model to the H5O lines."," Using the temperature and velocity structure from the CO modelling (Fig \ref{fig-temp}) ), we calculate the best-fit model to the $_{2}$ O lines."
 All the lines are found to be sub-thermally excited., All the lines are found to be sub-thermally excited.
" As mentioned above, both CO and H20 line cooling is taken into account."," As mentioned above, both CO and $_{2}$ O line cooling is taken into account."
 We present the fits to four lines of ortho-H2O and three lines of para-H2O observed with HIFI in Fig. 3.., We present the fits to four lines of $_{2}$ O and three lines of $_{2}$ O observed with HIFI in Fig. \ref{H2Ofits}.
 These lines span upper energies from 60 to KK so the lines probe the cool part of the CSE as well as the warmer inner part., These lines span upper energies from 60 to K so the lines probe the cool part of the CSE as well as the warmer inner part.
 From Figs., From Figs.
" 3.1 and 4,, it can be seen that H2O lines originate well within the acceleration zone."," \ref{fig-temp} and \ref{cool}, it can be seen that $_{2}$ O lines originate well within the acceleration zone."
" All lines are of reasonably high signal-to-noise ratio, including the 393—21? line, the highest frequency line, where the spectrum is affected by standing waves inside HIFI."," All lines are of reasonably high signal-to-noise ratio, including the $_{03} - 2_{12}$ line, the highest frequency line, where the spectrum is affected by standing waves inside HIFI."
" For this line, we used a higher order Chebyshev polynomial for the baseline subtraction (bottom right panel of Fig 3))."," For this line, we used a higher order Chebyshev polynomial for the baseline subtraction (bottom right panel of Fig \ref{H2Ofits}) )."
 Our results are consistent with the velocity structure of a dust-driven wind as can be seen in good fits to both the CO and H350 line profiles (Figs., Our results are consistent with the velocity structure of a dust-driven wind as can be seen in good fits to both the CO and $_{2}$ O line profiles (Figs.
" 2 and 3,, respectively)."," \ref{COfits} and \ref{H2Ofits}, respectively)."
" Unlike the case for IK Tau (??),, no modification to the dynamical calculation is required."," Unlike the case for IK Tau \citep{decin10, decin10h}, no modification to the dynamical calculation is required."
 The observed HIFI lines are reliable probes of the inner CSE as the high-energy lines probe the wind in the acceleration zone., The observed HIFI lines are reliable probes of the inner CSE as the high-energy lines probe the wind in the acceleration zone.
 Both the velocity and density structures are tightly constrained using the HIFI lines., Both the velocity and density structures are tightly constrained using the HIFI lines.
"The abundance of CO used is 6x10~, intermediate to those usually adopted for O- and C-rich CSEs.","The abundance of CO used is $\times 10^{-4}$, intermediate to those usually adopted for O- and C-rich CSEs."
" The derived ortho- and para-H2O abundances are significantly lower, (7.5+1.4)x107 and (3.6+0.5)x1075, respectively (Table 2))."," The derived ortho- and $_{2}$ O abundances are significantly lower, $\pm1.4)\times 10^{-6}$ and $\pm0.5)\times 10^{-6}$, respectively (Table \ref{tab-model}) )."
 These values are well below the limits for O-rich AGB stars of > 1107* (222) consistent with y Cyg being an S- of C/O very close to unity.," These values are well below the limits for O-rich AGB stars of $>$ $^{-4}$ \citep{just05, maercker08, maercker09} consistent with $\chi$ Cyg being an S-star of C/O very close to unity."
" From our modelling, assuming that all carbon is locked up in CO (i.e., Ο/Η = 3x107) and the oxygen is locked up in both CO and H50 (i.e., O/H = 3x107* + 5.5x10~°), our derived C/O is < 0.98, given that a small fractional abundance of the oxygen is in dust grains."," From our modelling, assuming that all carbon is locked up in CO (i.e., C/H = $\times 10^{-4}$ ) and the oxygen is locked up in both CO and $_{2}$ O (i.e., O/H = $\times 10^{-4}$ + $\times 10^{-6}$ ), our derived C/O is $\leq$ 0.98, given that a small fractional abundance of the oxygen is in dust grains."
" This value is slightly higher than that of 0.95, assumed by ?.."," This value is slightly higher than that of 0.95, assumed by \citet{duari00}."
" A non-thermal equilibrium chemistry model for S-stars 00.98) predicts an H2O abundance of 107 at the stellar photosphere, falling off to a few 1076 at 5 R, (?),, anorder of magnitude lower than our value."," A non-thermal equilibrium chemistry model for S-stars 0.98) predicts an $_{2}$ O abundance of $^{-4}$ at the stellar photosphere, falling off to a few $^{-6}$ at 5 $_{*}$ \citep{cherchneff06}, , anorder of magnitude lower than our value."
" In the thermal equilibrium (TE) limit at high temperature, the expected ortho-to-para ratio is 3."," In the thermal equilibrium (TE) limit at high temperature, the expected ortho-to-para ratio is 3."
" Our derived ortho-to-para ratio is 2.1+0.6, close to the high-temperature TE value."," Our derived ortho-to-para ratio is $\pm$ 0.6, close to the high-temperature TE value."
 The reported ortho-to-para ratio in CSEs of O-rich stars vary from 1 in W Hya with a large uncertainty (?) to 3 in IK Tau (?).., The reported ortho-to-para ratio in CSEs of O-rich stars vary from 1 in W Hya with a large uncertainty \citep{barlow96} to 3 in IK Tau \citep{decin10h}.
 Our, Our
"withs,=e,=h, —0forn κ and wy,—0for n«1.",with$u_n=v_n=h_n=0$ for $n<0$ and $w_n=0$ for $n<1$.
 Jowring in mind that Z7 depends on r. we have The projected equations are then (cf.Tanakactal.2002:Zhang&Lai2006)..," Bearing in mind that $H$ depends on $r$, we have The projected equations are then \citep[cf.][]{2002ApJ...565.1257T,2006MNRAS.368..917Z}."
 This approach corresponds to a (Galerkin) spectral treatment of the partial differential equations governing the lincarizecl dynamics. which is much preferable to a finite-dillerence treatment.," This approach corresponds to a (Galerkin) spectral treatment of the partial differential equations governing the linearized dynamics, which is much preferable to a finite-difference treatment."
" In. practice this system of equations must be truncated. by setting πμ, etc."," In practice this system of equations must be truncated by setting $u_n$, etc.,"
 to zero for mo»ΑΝ for some integer IN., to zero for $n>N$ for some integer $N$.
 The 2DO theory is obtained. in fact. by considering a radical truncation. IN=0. of the equations.," The 2DO theory is obtained, in fact, by considering a radical truncation, $N=0$, of the equations."
 Vo include viscosity. a terni should be added to the right-hand side of the equation of motion (32)). where is the viscous stress tensor.," To include viscosity, a term should be added to the right-hand side of the equation of motion \ref{motion}) ), where is the viscous stress tensor."
" 1n the context of an isothermal dise it is reasonable to assume that the kinematic shear and bulk viscosities 7 and f, depend only on r.", In the context of an isothermal disc it is reasonable to assume that the kinematic shear and bulk viscosities $\nu$ and $\nu_\rmb$ depend only on $r$.
 We parametrize them as AC full treatment of the cllects οἱ viscosity is complicated. not only because the above expression for the viscous force must be evaluated in. evlindrical polar coordinates and then projected on to the basis of Hermite polynomials. but. also because the basic state is mocified to include a meridional low. ἄνίνοι by viscous stresses. which should be considered in the lincarized equations.," We parametrize them as A full treatment of the effects of viscosity is complicated, not only because the above expression for the viscous force must be evaluated in cylindrical polar coordinates and then projected on to the basis of Hermite polynomials, but also because the basic state is modified to include a meridional flow driven by viscous stresses, which should be considered in the linearized equations."
 Εις problem is therefore deferred to a future investigation., This problem is therefore deferred to a future investigation.
 In the present. paper we adopt a simpler approach in which only selected viscous elfects are incbuced., In the present paper we adopt a simpler approach in which only selected viscous effects are included.
 We consider what might be assumed to be the dominant. viscous ternis. tthose involving two derivatives with respect to z.," We consider what might be assumed to be the dominant viscous terms, those involving two derivatives with respect to $z$ ."
 Since the inviscicl perturbation equations (48)) (50)) are moclified by the addition of the viscous terms while equation (51)) is unchanged., Since the inviscid perturbation equations \ref{un}) \ref{wn}) ) are modified by the addition of the viscous terms while equation \ref{hn}) ) is unchanged.
 These terms act to damp the mode. but have most cect on components of large n.," These terms act to damp the mode, but have most effect on components of large $n$."
 They have no effect on 4o and eo. which represent horizontal. motions independent of z.," They have no effect on $u_0$ and $v_0$, which represent horizontal motions independent of $z$."
 These viscous terms can also be thought of as providing a coupling between different lavers of the disc ancl thereby encouraging it to acdopt a horizontal motion independent of z., These viscous terms can also be thought of as providing a coupling between different layers of the disc and thereby encouraging it to adopt a horizontal motion independent of $z$.
 We show below that this effect is of considerable importance., We show below that this effect is of considerable importance.
 We solve the system. of ordinary. dilferential equations in r for modes with m=1 using a Chebyshev collocation ppseudospectral) method., We solve the system of ordinary differential equations in $r$ for modes with $m=1$ using a Chebyshev collocation pseudospectral) method.
 This approach converts the differential equations and. boundary conditions into an algebraic generalized. eigenvalue problem for the frequency w. which we solve using a standard. direct method.," This approach converts the differential equations and boundary conditions into an algebraic generalized eigenvalue problem for the frequency $\omega$, which we solve using a standard direct method."
 Specifically. equations. (48)) (51)). supplemented. by the viscous terms (56)) (58)). are solved for »=0.2.4.....N with μι etc.," Specifically, equations \ref{un}) \ref{hn}) ), supplemented by the viscous terms \ref{unviscous}) \ref{wnviscous}) ), are solved for $n=0,2,4,\dots,N$ with $u_n$, etc.,"
 set to zero for ncUN., set to zero for $n>N$.
" Rigid boundary conditions 4/,=O are adopted at both inner and outer boundaries. but it is ensured that the modes obtained. are completely insensitive to the value of the outer radius and therefore to the choice of outer boundary condition."," Rigid boundary conditions $u_n=0$ are adopted at both inner and outer boundaries, but it is ensured that the modes obtained are completely insensitive to the value of the outer radius and therefore to the choice of outer boundary condition."
" For comparison with the results in Section 3. consider a cise with a midplane density profile py,xr7 777, "," For comparison with the results in Section \ref{s:powerlaw}, we consider a disc with a midplane density profile $\rho_\rmm\propto
r^{-\sigma-3/2}$ ."
We also include a shear viscosity. corresponding to à constant @ parameter. but no bulk viscosity.," We also include a shear viscosity corresponding to a constant $\alpha$ parameter, but no bulk viscosity."
 Sample results are shown in Table 1.., Sample results are shown in Table \ref{t:ot}.
 Phe convergence of the eigenfrequeney. with increasing truncation order JN of the Llermite polynomial basis is remarkable., The convergence of the eigenfrequency with increasing truncation order $N$ of the Hermite polynomial basis is remarkable.
 The case N=0 corresponds exactly to the two-dimensional theory considered. by Okazaki(1991)... and. therefore. agrees well with the 2DO secular approximation.," The case $N=0$ corresponds exactly to the two-dimensional theory considered by \citet{1991PASJ...43...75O}, and therefore agrees well with the 2DO secular approximation."
 Llere Q=20 Is large cnough to support a confined. progracde mode., Here $\tilde Q=20$ is large enough to support a confined prograde mode.
 The precession rate is much larger in the case No=2 and hardly varies as further Hermite polynomials are included., The precession rate is much larger in the case $N=2$ and hardly varies as further Hermite polynomials are included.
 lt agrees reasonably well with the 3D secular theory for an inviscid disc., It agrees reasonably well with the 3D secular theory for an inviscid disc.
 The slight ollset of the precession frequency. is attributable partly to errors in the secular approximation. which is valid only to leacling order in c. and partly to the elfects of viscosity.," The slight offset of the precession frequency is attributable partly to errors in the secular approximation, which is valid only to leading order in $\epsilon$, and partly to the effects of viscosity."
" As described in Appendix A.. the viscous damping of vertical motions considered in the full model can be represented within the 3D secular theory by multiplying the coellicient 9/4 in the three-dimensional expression. (S)) for f bv (CL.12)/(11i7). where 3=ay,|ia."," As described in Appendix \ref{s:appendix}, , the viscous damping of vertical motions considered in the full model can be represented within the 3D secular theory by multiplying the coefficient $9/4$ in the three-dimensional expression \ref{f3d}) ) for $f$ by $(1-\rmi\beta)/(1+\rmi\beta)$, where $\beta=\alpha_\rmb+{\textstyle\f{4}{3}}\alpha$."
 Table 1. shows that this viscous secular theory gives good agreement with the full mocel for a=0.1.," Table \ref{t:ot}
 shows that this viscous secular theory gives good agreement with the full model for $\alpha=0.1$."
 The viscous damping rate of the modes is considerable., The viscous damping rate of the modes is considerable.
 Although the dominant motion is horizontal and independent of z. and therefore does not incur any Viscous forces in our approximation. the accompanying vertical motion is damped.," Although the dominant motion is horizontal and independent of $z$ , and therefore does not incur any viscous forces in our approximation, the accompanying vertical motion is damped."
 To excite eccentric modes in a three-dimensional disc. this damping must be overcome.," To excite eccentric modes in a three-dimensional disc, this damping must be overcome."
 Viscous overstability may be able todo this. but. detailed calculationsare required and there is uncertainty in the applicability of a NavierStokes. viscosity. to. turbulent," Viscous overstability may be able todo this, but detailed calculationsare required and there is uncertainty in the applicability of a Navier–Stokes viscosity to turbulent"
"where B and d are the rms magnetic field strength and transverse correlation length of filaments, respectively.","where $B$ and $d$ are the rms magnetic field strength and transverse correlation length of filaments, respectively."
" The relevant argument focusing on the specified case of the nearby M87 jet has been given (Honda&Honda2007),, although the value of d remained unsolved."," The relevant argument focusing on the specified case of the nearby M87 jet has been given \citep{hh07}, although the value of $d$ remained unsolved."
" Its determination is necessary not only to estimate equation (2)) but also complete the filamentary jet model, which could involve various radiation channels (Honda2008)."," Its determination is necessary not only to estimate equation \ref{eq:2}) ) but also complete the filamentary jet model, which could involve various radiation channels \citep{honda08}."
". This paper has been prepared to spell out explicitly the scalings of the cut-off and break for the dominant synchrotron spectrum established via normal (non-diffuse) processes in filamentary jets, and to revise equation (1)), including relativistic beaming effects."," This paper has been prepared to spell out explicitly the scalings of the cut-off and break for the dominant synchrotron spectrum established via normal (non-diffuse) processes in filamentary jets, and to revise equation \ref{eq:1}) ), including relativistic beaming effects."
" Making use of the results, we attempt to extract the scaling of the lower limit of the filament correlation length, dmin, from observational data for sample extragalactic jets."," Making use of the results, we attempt to extract the scaling of the lower limit of the filament correlation length, $d_{\rm min}$, from observational data for sample extragalactic jets."
 We find the property that the dmin value increases as the size of emission regions increases., We find the property that the $d_{\rm min}$ value increases as the size of emission regions increases.
 A corollary derived from this is that the allowable maximum number (capacity) of filaments with the outer scale (~ d) increases as the propagation distance of the jet increases., A corollary derived from this is that the allowable maximum number (capacity) of filaments with the outer scale $\sim d$ ) increases as the propagation distance of the jet increases.
" For the situation in which AGN jets carry huge currents driven by the central engines of black holes (Appl&Camenzind 1992),, we take the current filamentation into consideration in order to calculate the number of filaments (N)."," For the situation in which AGN jets carry huge currents driven by the central engines of black holes \citep{appl92}, we take the current filamentation into consideration in order to calculate the number of filaments $N$ )."
" From comparing N with the capacity of the outer-scale filaments, we infer the population of fine filaments inside the jets."," From comparing $N$ with the capacity of the outer-scale filaments, we infer the population of fine filaments inside the jets."
" As a result, it is demonstrated that compact LLac objects such as 4421 and 501 would possess typically ~10!! filaments with various transverse size scales that are smaller than the entire emission-region size."," As a result, it is demonstrated that compact Lac objects such as 421 and 501 would possess typically $\sim 10^{11}$ filaments with various transverse size scales that are smaller than the entire emission-region size."
" According to the original idea in Honda&(2004),, we rely on the hypothesis that a jet consists of many magnetized filaments, accommodated by some radio observations (e.g.Owenetal. 1989)."," According to the original idea in \citet{hh04}, we rely on the hypothesis that a jet consists of many magnetized filaments, accommodated by some radio observations \citep[e.g.][]{owen89}."
" For information, the circumstance concerned is illustrated in Fig. 1.."," For information, the circumstance concerned is illustrated in Fig. \ref{fig:1}."
" The quasi-stationary magnetic fields are considered to be generated by leptonic currents, and retain an energy-density level comparable to that of the random component of lepton motion (Honda 2007)."," The quasi-stationary magnetic fields are considered to be generated by leptonic currents, and retain an energy-density level comparable to that of the random component of lepton motion \citep{honda07}."
". It is then expected that the Poynting flux level is less than (or, at most, comparable to) the lepton energy flux."," It is then expected that the Poynting flux level is less than (or, at most, comparable to) the lepton energy flux."
" In respect of the global energy budget, the small portion that takes part in controlling the transverse dynamics (Section 5)) is loaded from the energy reservoir of the jet bulk."," In respect of the global energy budget, the small portion that takes part in controlling the transverse dynamics (Section \ref{sec:5}) ) is loaded from the energy reservoir of the jet bulk."
" If the dominant kinetic energy is carried by hadronic components then an excess of lepton energy departing from the mass ratio (say, 0.05 per cent for a simple electron-proton plasma with no pairs) is entailed in order to generate the currents and magnetic fields, in accord with arguments concering the power of blazar jets (e.g.Celotti&Ghisellini 2008)."," If the dominant kinetic energy is carried by hadronic components then an excess of lepton energy departing from the mass ratio (say, $0.05$ per cent for a simple electron--proton plasma with no pairs) is entailed in order to generate the currents and magnetic fields, in accord with arguments concering the power of blazar jets \citep[e.g.][]{celotti08}."
. The merging of current filaments can be associated with the inverse cascade of turbulent magnetic energy., The merging of current filaments can be associated with the inverse cascade of turbulent magnetic energy.
" For the inertial range of the turbulence, we invoke the phenomenological expression for local magnetic intensity [B|=B4(A/d)-9/?, where A (X d) is the transverse size of a filament (Fig. 1))"," For the inertial range of the turbulence, we invoke the phenomenological expression for local magnetic intensity $|{\bf B}|=B_{m}(\lambda/d)^{(\beta-1)/2}$, where $\lambda$ $\leq d$ ) is the transverse size of a filament (Fig. \ref{fig:1}) )"
 and 8 corresponds to the turbulent spectral index., and $\beta$ corresponds to the turbulent spectral index.
" As seems plausible, this (zeroth order) magnetic field, trapping lower-energy electrons, is disturbed by Alfvénnic waves to allow resonant scattering diffusion."," As seems plausible, this (zeroth order) magnetic field, trapping lower-energy electrons, is disturbed by Alfvénnic waves to allow resonant scattering diffusion."
" Also, in analogy to the knot and hotspot features, it is reasonable to suppose a relativistic (non-relativistic) shock overtaking the relativistic (non-relativistic) flow with the Lorentz factor D;=(1—7, such that the shock viewed in the upstream rest frame82) likely has a non-/weakly relativistic speed."," Also, in analogy to the knot and hotspot features, it is reasonable to suppose a relativistic (non-relativistic) shock overtaking the relativistic (non-relativistic) flow with the Lorentz factor $\Gamma_{j}=(1-\beta_{j}^{2})^{-1/2}$, such that the shock viewed in the upstream rest frame likely has a non-/weakly relativistic speed."
" Providing the fields defined upstream, we consider the standard diffusive acceleration of bound electrons due to the Fermi-I mechanism (Honda&Honda 2007),, which yields a power-law energydistribution (cx? for y€ Υ”)."," Providing the fields defined upstream, we consider the standard diffusive acceleration of bound electrons due to the Fermi-I mechanism \citep{hh07}, which yields a power-law energydistribution $\propto\gamma^{-p}$ for $\gamma\leq\gamma^{\ast}$ )."
 The acceleration time-scale tacc is of the order of the cycle time for one back-and-forth divided by the energy gain per encounter with the shock (e.g.Gaisser1990)., The acceleration time-scale $t_{\rm acc}$ is of the order of the cycle time for one back-and-forth divided by the energy gain per encounter with the shock \citep[e.g.][]{gaisser90}.
 We here adopt a standard expression for tacc that involves a negligible contribution from particle escape downstream to the cycle time and gain (Ostrowski1988;Honda& 2005b).," We here adopt a standard expression for $t_{\rm acc}$ that involves a negligible contribution from particle escape downstream to the cycle time and gain \citep{ostrowski88,hh05b}."
". What we deal with below is, therefore, the non- (or flaring) regime around the working surface (a related issue is revisited in Section 3.1))."," What we deal with below is, therefore, the non-ageing (or flaring) regime around the working surface (a related issue is revisited in Section \ref{sec:3.1}) )."
" Compatible with this, it is reasonable to suppose that, for major electrons bound to the outer-scale filament with maximum field strength Bm, the acceleration is degraded by strong synchrotron cooling rather than escape losses (Honda2008)."," Compatible with this, it is reasonable to suppose that, for major electrons bound to the outer-scale filament with maximum field strength $\sim B_{m}$, the acceleration is degraded by strong synchrotron cooling rather than escape losses \citep{honda08}."
". 'The synchrotron emission, largely polarized, appears to constitute the dominant radio continuum with a power index of a=(p—1)/2 in the flux-density spectrum , provided the electron density is uniform, e.g. Longair 1994))."," The synchrotron emission, largely polarized, appears to constitute the dominant radio continuum with a power index of $\alpha=(p-1)/2$ in the flux-density spectrum $S_{\nu }\propto\nu^{-\alpha}$ , provided the electron density is uniform, e.g. \citealt{longair94}) )."
" The spectral break reflects the highest energy of an accelerated electron (7*|,~amc”) at which tacc is comparable to radiative time-scale.", The spectral break reflects the highest energy of an accelerated electron $\gamma^{\ast}|_{\lambda\sim d}mc^{2}$ ) at which $t_{\rm acc}$ is comparable to radiative time-scale.
" From balancing these time-scales,"," From balancing these time-scales,"
"=p where AE,z6,Mec? ix the total radiative energy output of the accretion process,","= , where $\Delta E_\bullet\simeq\epsilon_\ditto{rad}M_\bullet c^2$ is the total radiative energy output of the accretion process."
" Since €, depouds ouly on black hole spin. the quasar lifetime Af,~ should be iudepeudeut of black hole mass."," Since $\epsilon_\ditto{rad}$ depends only on black hole spin, the quasar lifetime $\Delta t_\ditto{QS}\sim t_\ditto{Salp}$ should be independent of black hole mass."
" ‘Tt followsf. from that. iu order for a system to lie on the M,— relation. the coupling cfitcicucy εν ta the Imuinous quasar phase must depeud ou the stellar velocity dispersiou σι such that SIE"," It follows from that, in order for a system to lie on the $M_\bullet-M_\star$ relation, the coupling efficiency $\epsilon_\ditto{QP}$ in the luminous quasar phase must depend on the stellar velocity dispersion $\sigma_\star$ such that ^2."
NA This nuplies that. if the quasar phase were to selt-regulate the black hole and galaxy evolution. the feedback mechiauisui at work would be aροκ. or process.," This implies that, if the quasar phase were to self-regulate the black hole and galaxy evolution, the feedback mechanism at work would be a, or process."
" Wo stress again that this follows from Af,~ or equivalently from the fact that the total fo.enerev output AtL is observationally pinned cstobe close to the maximum amount of energy AESreleased in the formation of theblack hole. given by There is no apparent reason why the coupling efficiency May not depend on the stellar velocity dispersion o, or €,,,the black hole mass M,."," We stress again that this follows from $\Delta t_\ditto{QP}\sim t_\ditto{Salp}$, or equivalently from the fact that the total quasar energy output $\Delta t_\ditto{QP}L_\ditto{acc}$ is observationally pinned to be close to the maximum amount of energy released in the formation of the black hole, given by $\Delta E_\bullet$ There is no apparent reason why the coupling efficiency $\epsilon_\ditto{QP}$ may not depend on the stellar velocity dispersion $\sigma_\star$ or the black hole mass $M_\bullet$."
" However. it «hould depeud upon c, and Af, in such a wav that makes the ratio AlfAL, a coustaut across nearly four decades iu black hole nass"," However, it should depend upon $\sigma_{\star}$ and $M_\bullet$ in such a way that makes the ratio $M_\bullet/M_{\star}$ a constant across nearly four decades in black hole mass."
" This is. of course. not iupossible. but it would have to involve a cosmic couspiracy with respect to the eas dynamics of black hole ποποσαπο,"," This is, of course, not impossible, but it would have to involve a cosmic conspiracy with respect to the gas dynamics of black hole self-regulation."
 We now show how our jet-powered cosmic ray feedback scenario provides a satisfactory solution for this appareut contradiction., We now show how our jet-powered cosmic ray feedback scenario provides a satisfactory solution for this apparent contradiction.
" For a generic feedback mechanisia operating during epochs of ACN radio-loud activity. the total energv AE, injected into the interstellar mediuu is (110) where zAf,L, is the tincutegrated. kinetic output ofAE, the radio jet. Af, is the duration of the radio phase aud ealacticἐμι. is the efficiency for coupling the jet power L, to the gas."," For a generic feedback mechanism operating during epochs of AGN radio-loud activity, the total energy $\Delta E_\ditto{RP}$ injected into the interstellar medium is , where $\Delta E_\ditto{J}\simeq\Delta t_{\ditto{RP}} L_\ditto{J}$ is the time-integrated kinetic output of the radio jet, $\Delta t_{\ditto{RP}}$ is the duration of the radio-loud phase and $\epsilon_\ditto{RP}$ is the efficiency for coupling the jet power $L_\ditto{J}$ to the galactic gas."
" The energybalance in requires that E,.(111) where Ay,=£,/£,,,,."," The energy balance $\Delta E_{\ditto{RP}}\sim E_g$ in requires that E_g, where $\Lambda_\ditto{Edd}=L_\ditto{J}/L_{\ditto{Edd,\bullet}}$."
" This cau be rewritten asdm from which it is hueapparent that the product pAAya, for radio-loud phases replaces ερ.Ato.Me d quasar epochs (cf. (223))."," This can be rewritten as, from which it is apparent that the product $\epsilon_\ditto{RP}\,\Delta t_\ditto{RP}\,\Lambda_\ditto{Edd}$ for radio-loud phases replaces $\epsilon_\ditto{QP}\,\Delta t_\ditto{QP}$ in quasar epochs (cf. )."
" For a black hole svsteni that lies ou the Af,AZ, relation. this iuplies SQM"," For a black hole – galaxy system that lies on the $M_\bullet-M_\star$ relation, this implies ^2."
 As opposite to the quasar feedback scenario discussed. in refsec:qp.. does not inunediately constrain the coupling effidencey ἐμι to depend upon the stellar velocity dispersion.," As opposite to the quasar feedback scenario discussed in \\ref{sec:qp}, does not immediately constrain the coupling efficiency $\epsilon_\ditto{RP}$ to depend upon the stellar velocity dispersion."
" The possibility that the feedback efficiency 15 independent of M, aud 0, would then require that €i,AtXu, duereases with the stellar velocitydispersion. or that the timiuteerated jet kinetic output per uuit of black hole mass should scale as XD 07."," The possibility that the feedback efficiency $\epsilon_{_{\rm RP}}$ is independent of $M_\bullet$ and $\sigma_\star$ would then require that $\Delta t_{_{\rm RP}}\,\Lambda_{_{\rm Edd}}$ increases with the stellar velocitydispersion, or that the time-integrated jet kinetic output per unit of black hole mass should scale as $\propto\sigma_\star^2$ ."
The extended atmospheres of Iate-tvpe. evolved stars on the asvimplotic eiant. branch (AGB) are host to complex underlving astroplivsical processes of vital importance.,"The extended atmospheres of late-type, evolved stars on the asymptotic giant branch (AGB) are host to complex underlying astrophysical processes of vital importance."
 Mass-loss from these stars originates in this region and is an important enrichment mechanism for the interstellar medium., Mass-loss from these stars originates in this region and is an important enrichment mechanism for the interstellar medium.
 The large-amplitude. long-period variables (LALPV) span a range of variability sub-classes. including the Mira variables. with a median pulsation period of several hundred days (Habing.1996).," The large-amplitude, long-period variables (LALPV) span a range of variability sub-classes, including the Mira variables, with a median pulsation period of several hundred days \citep{habing96}."
. Their near-circumstellar environments (NCSE) are permeated by pulsation shocks from the central star (linkle.Hall.&Ricdeway1982:Winkle.Lebzelter.&Scharlach1997:Alvarezetal.2000) and complex convective motions in the outer envelope (Porter.Anderson.&Woodward1997:Frevtag.Steffen.Dorch2002).," Their near-circumstellar environments (NCSE) are permeated by pulsation shocks from the central star \citep{hinkle82,
hinkle97, alvarez00} and complex convective motions in the outer envelope \citep{porter97,freytag02}."
. These stars have significant mass-loss rates and are often. obseured in visible optical bands., These stars have significant mass-loss rates and are often obscured in visible optical bands.
 SiO masers al 43 Gllz are however ubiquitous in the extended atmospheres of these objects., SiO masers at 43 GHz are however ubiquitous in the extended atmospheres of these objects.
 As compact hieh-brishtness components that are significantly polarized. (μον act as important. probes of the astrophysics in the close circumstellar environment. including the morphology. ancl relative dynamical influence of magnetic fields.," As compact high-brightness components that are significantly polarized, they act as important probes of the astrophysics in the close circumstellar environment, including the morphology and relative dynamical influence of magnetic fields."
 Spectralline polarization VLBI techniques allow direct imaging of this region in Stokes (/.Q.C.V) at à spatial resolution of µας. unmatched at other wave-bands.," Spectral-line polarization VLBI techniques allow direct imaging of this region in Stokes $(I,Q,U,V)$ at a spatial resolution of $\mu$ as, unmatched at other wave-bands."
 The power of this technique is significantly enhanced if svnoplic monitoring is conducted over a range of stellar pulsation phase. so that the kev dvnamical drivers can be studied in this region.," The power of this technique is significantly enhanced if synoptic monitoring is conducted over a range of stellar pulsation phase, so that the key dynamical drivers can be studied in this region."
 There remain sienilicant uncertainties in integrated astrophyvsical models of the NCSE., There remain significant uncertainties in integrated astrophysical models of the NCSE.
 Stellar pulsation hyclodvuamiucal models are either semi-analvtic (Dertshinger 1985).. or confined to spherical or axi-ssvannietric numerical studies," Stellar pulsation hydrodynamical models are either semi-analytic \citep{bertshinger85}, or confined to spherical or axi-symmetric numerical studies"
Alfvénn mode to small scales as can be seen in the insert of Fig.,Alfvénn mode to small scales as can be seen in the insert of Fig.
 3 result was also found in Fig., \ref{whamp1} (this result was also found in Fig.
 1 of Krauss-et(thisal.(1994) although not discussed in detail in that paper)., 1 of \cite{krauss94} although not discussed in detail in that paper).
 The mode becomes dispersive at scales kp;1 and develops frequencies larger (resp., The mode becomes dispersive at scales $k\rho_i\gtrsim 1$ and develops frequencies larger (resp.
 smaller) than 2we; for ka<88° (resp., smaller) than $\omega_{ci}$ for $\theta_{\bf kB}<88^\circ$ (resp.
 > 88?) up to the scale kp;<10., $\geq 88^\circ$ ) up to the scale $k\rho_i\leq10$.
 We refer to the branches w«w.; and wZwe; respectively as the KAW and the whistler modes., We refer to the branches $\omega<\omega_{ci}$ and $\omega \gtrsim \omega_{ci}$ respectively as the KAW and the whistler modes.
" Note that the limit w=w,; is reached at different spatial scales depending on the value of the angle 0p.", Note that the limit $\omega=\omega_{ci}$ is reached at different spatial scales depending on the value of the angle $\theta_{\bf kB}$.
" Figure 4 shows that in contrast to the fast magnetosonic mode, the Alfvénn-whistler mode has a right hand polarization at all scales and does not undergo significant change near e»1. kpi"," Figure \ref{polar} shows that in contrast to the fast magnetosonic mode, the Alfvénn-whistler mode has a right hand polarization at all scales and does not undergo significant change near $k\rho_i \sim 1$."
"Nevertheless, the Alfvénn-whistler modes show features related to wave-particle resonances near the harmonics of ions they are not strictly circularly polarized)."," Nevertheless, the Alfvénn-whistler modes show features related to wave-particle resonances near the harmonics of ions (because they are not strictly circularly polarized)."
 This can be (becauseseen in Fig., This can be seen in Fig.
 5 which shows the enhancement of the damping of the Alfvénn-whistler modes near the harmonics wy=Νωα— (a similar observation can be made on Fig., \ref{damping_kaw87} which shows the enhancement of the damping of the Alfvénn-whistler modes near the harmonics $\omega_N=N\omega_{ci}-k_\parallel V_{th_i}$ (a similar observation can be made on Fig.
" 9 at kyVin,other angles of propagation).", \ref{whamp4} at other angles of propagation).
 Fig., Fig.
 6 shows the Alfvénn-whistler solutions extended to high frequencies and small scales., \ref{whamp2} shows the Alfvénn-whistler solutions extended to high frequencies and small scales.
 We observe that the damping of the Alfvénn-whistler mode becomes more important when departing from Okpg~90? toward less oblique angles., We observe that the damping of the Alfvénn-whistler mode becomes more important when departing from $\theta_{\bf kB}\sim 90^\circ$ toward less oblique angles.
" For kg=89.99? the solution extends down to the electron gyroscale p. where the damping rate remainssmall!,, y/w,~0.4."," For $\theta_{\bf kB}=89.99^\circ$ the solution extends down to the electron gyroscale $\rho_e$ where the damping rate remains, $\gamma/\omega_r\sim 0.4$."
 For less oblique angles the Alfvénn-whistler mode develops frequencies higher than we; but they are subject to stronger damping., For less oblique angles the Alfvénn-whistler mode develops frequencies higher than $\omega_{ci}$ but they are subject to stronger damping.
" This can be seen clearly in Fig. 7,,"," This can be seen clearly in Fig. \ref{damping}, ,"
 which shows the damping rate in one period of each wave mode., which shows the damping rate in one period of each wave mode.
 Figure 7 shows that the Alfvénn-whistler modes are abruptly(top panel)damped at kp;~1., Figure \ref{damping} (top panel) shows that the Alfvénn-whistler modes are abruptly damped at $k\rho_i\sim 1$.
 At smaller scales the most oblique modes are the least damped., At smaller scales the most oblique modes are the least damped.
 The linear damping rate may thus play a role of a “filter that lets pass” only very oblique modes at small scales., The linear damping rate may thus play a role of a “filter that lets pass” only very oblique modes at small scales.
 Thismay explain the high oblique modes frequently observed in the SW, Thismay explain the high oblique modes frequently observed in the SW
L.,.
". Tu Naselskv&Novikov(2005).. itf is reported that a major part of the CF produces a specific correlation in spherical harmonic unitipole domain at Af—I: between nodes ay, aud ay) 1,5."," In \citet{4n}, it is reported that a major part of the GF produces a specific correlation in spherical harmonic multipole domain at $\dl=4$: between modes $a_{\l,m}$ and $a_{\l+4,m}$ ."
 The series of bn-correlation frou the CGF requires more investigation., The series of $4n$ -correlation from the GF requires more investigation.
 This paper is thus devoted to further analysis of the statistical properties of the phases of the foreerounds for such correlation., This paper is thus devoted to further analysis of the statistical properties of the phases of the foregrounds for such correlation.
" We concentrate on the question as to what the reason is for the ly correlation in the data. and can such correlation help us to determine the properties of the foregrounds. in order to separate them from the CAIB ausotropies,"," We concentrate on the question as to what the reason is for the $4n$ correlation in the data, and can such correlation help us to determine the properties of the foregrounds, in order to separate them from the CMB anisotropies."
 Iu this paper we develop the idea proposed by Nasolskv&Novisov(2005) and demonstrate the pronounced svuuuetrv of the CF (in Calactic svstem of coordinates) is the main cause of the [o correlation., In this paper we develop the idea proposed by \citet{4n} and demonstrate the pronounced symmetry of the GF (in Galactic system of coordinates) is the main cause of the $4n$ correlation.
 The estimator designed in Naselskv&Novilsov(2005) to illustrate and tackle such correlation can help us unudoerstaud CF manifestation in the harmonic domain. leading to the development of “blind” method for foreeround cleaning.," The estimator designed in \citet{4n} to illustrate and tackle such correlation can help us understand GF manifestation in the harmonic domain, leading to the development of “blind” method for foreground cleaning."
 Iu combination with multi-frequency technique propose in Teemark&Efstathiou(1996):Teemark.deOliveira-Costa&Tamiultou (2003).. the removal of La correlation of phases can be easilv used as au effective ολοι of determination of the CAIB power spectrum without Galactic mask and disjoint regions for the data.," In combination with multi-frequency technique proposed in \citet{te96,toh}, the removal of $4n$ correlation of phases can be easily used as an effective method of determination of the CMB power spectrum without Galactic mask and disjoint regions for the data."
 Tt cau serve as a complementary iuethod to the Interna Linear Combination method (Bennettetal.2003¢:Exik-senoetal.2001) aud to the TOIL method as well. in order to decrease the coutamination of the GF in the derive maps.," It can serve as a complementary method to the Internal Linear Combination method \citep{wmapfg,eilc} and to the TOH method as well, in order to decrease the contamination of the GF in the derived maps."
 Such kind of correlation should be observed bv the nüssion and will help us to uuderstaud the properties of the CGF in details. as if can play a role as an additional test for the foreground models for the mission.," Such kind of correlation should be observed by the mission and will help us to understand the properties of the GF in details, as it can play a role as an additional test for the foreground models for the mission."
 This paper is organized as follows., This paper is organized as follows.
" Iu Section 2 we describe. the d estimator for la-correlation in the coefficients a,j, aud its manifestation in the observed sienals.", In Section 2 we describe the $\ddeltalm$ estimator for $4n$ -correlation in the coefficients $\alm$ and its manifestation in the observed signals.
 Iu Section 3 we apply the estimator on 23 tov models which mimics Calactic foreerounds to investigate the cause of such correlation., In Section 3 we apply the estimator on 3 toy models which mimics Galactic foregrounds to investigate the cause of such correlation.
 Iu Section { we discuss the connection between the la correlation aud the forceround svuuuetry., In Section 4 we discuss the connection between the $4n$ correlation and the foreground symmetry.
 We also examine the power spectrin of the estimator and the correlations of dA estimator in Section 5., We also examine the power spectrum of the estimator and the correlations of $\ddeltalm$ estimator in Section 5.
 The couclusion is in Section 6., The conclusion is in Section 6.
" As is shown in Naselskv&Novikov(2005) to illustrate the Lu-correlation. we recap the estimator taken from the colmbination of the spherical harionic coefficieuts ay). where ποxἐν aud the coefficients ανω are defined by the staudard wav: AJTT(O.0) is the whole-sky auisotropies at cach frequency anc. 0.0 are the polar and azimuthal augles of the polar coordinate xvsteui. τν0ω) are the spherical harmonics. 01,4,| and $,,, are the amplitudes (Quoduli) and phases of (077 harmonics."," As is shown in \citet{4n} to illustrate the $4n$ -correlation, we recap the estimator taken from the combination of the spherical harmonic coefficients $\alm$, where $|m| \le \l$, and the coefficients $\alm=|\alm| \exp(i\Phi_{\l,m})$ are defined by the standard way: $\Delta T(\theta,\phi)$ is the whole-sky anisotropies at each frequency band, $\theta,\phi$ are the polar and azimuthal angles of the polar coordinate system, $\ylm(\theta,\phi)$ are the spherical harmonics, $|\alm|$ and $\Phi_{\lm}$ are the amplitudes (moduli) and phases of ${\l,m}$ harmonics."
" The superscript A iu d characterizes he shift of the (-1nodo iu dA, aud. following Nasclsky& we concentrate on the series of correlation or A=In. n=1.2.3...."," The superscript $\Delta$ in $\ddeltalm$ characterizes the shift of the $\l$ -mode in $d^{\Delta}_{\l,m}$ and, following \citet{4n}, we concentrate on the series of correlation for $\Delta=4n$, $n=1,2,3\ldots$."
 Note that the singal of Galaxy mostly lies close to 0=z/2-plauc., Note that the singal of Galaxy mostly lies close to $\theta=\pi/2$ -plane.
 The estimator έn in form Eq.(1)) is closely related with phases of the uultipoles of the AT(0.0) signal.," The estimator $\ddeltalm$ in form \ref{eq1}) ) is closely related with phases of the multipoles of the $\Delta T(\theta,\phi)$ signal."
" Taking Eq.(2)) into account. we ect From Eq.(3)) one can sce that. if the phase difference ενωDou>O then If d,|NonQuεςπο the map svuthesized frou theQJ dT, estimator is suuplv a iuap from the τω with phases rotated by au anele 47/2 aud the amplitudes lessened by a factor ΟΕΕ while for non- phases Φ,|Avaebm,, we have specific (but known) inodulation of the£e,,, cocficients (see the Appendix)."," Taking \ref{eq2}) ) into account, we get From \ref{eq3}) ) one can see that, if the phase difference $\Phi_{\l+\Delta,m}-\Phi_{\l,m}\rightarrow 0$, then If $\Phi_{\l+\Delta,m}-\Phi_{\l,m}\ll \pi/2$, the map synthesized from the $d^{\Delta}_{\l,m}$ estimator is simply a map from the $\alm$ with phases rotated by an angle $\pm \pi/2$ and the amplitudes lessened by a factor $|\sin(\Phi_{\l+\Delta,m}-\Phi_{\l,m})|$, while for non-correlated phases $\Phi_{\l+\Delta,m},\Phi_{\lm}$ we have specific (but known) modulation of the$\alm$ coefficients (see the Appendix)."
" A uou-trivial aspect of dO, estimator ds that dt sienificantly decrease the brightest part of the Galaxy image in the K-W iaps."," A non-trivial aspect of $d^{\Delta}_{\l,m}$ estimator is that it significantly decrease the brightest part of the Galaxy image in the K-W maps."
 In the following analvsis we use a particular case s=1 so that A=1. although it can be clemonstrated that for 5)=2.3... the results of analvsis do not change siguificautlv as lone as Ax(uu. where (uuu Is the multipole nuuber iu the spectrum where the iustruucutal noise starts dominating over the CF sienal.," In the following analysis we use a particular case $n=1$ so that $\Delta=4$, although it can be demonstrated that for $n=2,3\ldots$ the results of analysis do not change significantly as long as $\Delta \le \l_{\rm noise}$, where $\l_{\rm noise}$ is the multipole number in the spectrum where the instrumental noise starts dominating over the GF signal."
 Tn this section we show low the d estimator transforms the GF image in the ΤΝ maps. taking from the NASA LAMBDA archive (?)..," In this section we show how the $d^{\Delta}_{\lm}$ estimator transforms the GF image in the K-W maps, taking from the NASA LAMBDA archive \citep{lambda}. ."
 In Fie.1 we plot the maps svuthesized from the dA estimator for I-W baud (for A= Laud (444;= 512) Note that the amplitudes are significantly reduced in cach map., In \ref{fig1} we plot the maps synthesized from the $\ddeltalm$ estimator for K-W band (for $\Delta=4$ and $\lmax=512$ ) Note that the amplitudes are significantly reduced in each map.
 It should be euphliasized that the D(0.0) map is not temperature anisotropy map. as the phases are altered.," It should be emphasized that the $D(\theta,\phi)$ map is not temperature anisotropy map, as the phases are altered."
 Let us discuss some of the properties of the d estimator.which determine the morphology of the D(0.ο) maps.," Let us discuss some of the properties of the $d^{\Delta}_{\lm}$ estimator,which determine the morphology of the $D(\theta,\phi)$ maps."
" First of all. from Eq.(1)) one cau find that for all ο=0 modes. the estimator is equivalent to zero if sigu(a;=sigu(o,|xy) aud it is nou-zero (aud doubled) ifsgu(ang)9)οp x.y)."," First of all, from \ref{eq1}) ) one can find that for all $m=0$ modes, the estimator is equivalent to zero if ${\rm sign} (a_{\l,0})={\rm sign} (a_{\l+\Delta,0})$ and it is non-zero (and doubled) if ${\rm sign} (a_{\l,0})=-{\rm sign} (a_{\l+\Delta,0})$ ."
 In terms of pliase difference in Eq.(1)) this means that for a7=0 modes dA estimator removes those whichhave the same phases. while doubles the amplitudes of others whose phases differiug by 4 iu the D(0.0) maps.," In terms of phase difference in \ref{eq4}) ) this means that for $m=0$ modes $d^{\Delta}_{\lm}$ estimator removes those whichhave the same phases, while doubles the amplitudes of others whose phases differing by $\pi$ in the $D(\theta,\phi)$ maps."
shell. become transparent during the planar phase as well.,"shell, become transparent during the planar phase as well."
 Shells (hat are deeper (and more massive and slower) than the shell remain opaque during the planar phase and become transparent onlv during the spherical phase., Shells that are deeper (and more massive and slower) than the shell remain opaque during the planar phase and become transparent only during the spherical phase.
" Since slower moving shells carry signilicantlv more energy. £;x5;H°°"". the breakout emission is dominated by the energy confined to the shell at ἐν. when its local frame temperature is 77,: where we use 7,2Apiig/(4rR2)=1 to find The observed temperature of this emission is and it is smeared by light travel time effects over a duration that is comparable to (2: where /* is (he time of transition [rom the planar to the spherical phase as seen by the observer."," Since slower moving shells carry significantly more energy, $E_i
\propto \g_i^{-3.75}$, the breakout emission is dominated by the energy confined to the shell at $t_{th,0}$, when its local frame temperature is $T'_{th}$: where we use $\tau_0 \approx \kappa_T m_0/(4\pi R_*^2)=1$ to find The observed temperature of this emission is and it is smeared by light travel time effects over a duration that is comparable to $t_s^{obs}$: where $t_s^{obs}$ is the time of transition from the planar to the spherical phase as seen by the observer."
 Clearly. equations 15-17 are general and are applicable to any gas densityv. profile.," Clearly, equations \ref{eq
m0}- \ref{eq tbo} are general and are applicable to any gas density profile."
 In fact also equation 14 is applicable to any. sharply decreasing density. gradient. even if il is nol a power-law.," In fact also equation \ref{eq Ebo} is applicable to any sharply decreasing density gradient, even if it is not a power-law."
" The reason is that my does not depend on this profile and so does the relation between >) and 5,4 (equation 2)). as long as acceleration ends during the planar phase and there is a large energy. reservoir behind (he shell."," The reason is that $m_0$ does not depend on this profile and so does the relation between $\g_0$ and $\g_{f,0}$ (equation \ref{eq
gf}) ), as long as acceleration ends during the planar phase and there is a large energy reservoir behind the shell."
 Together. equations 14-17 provide three generic observables that depend on only two parameters ερ and 72 ," Together, equations \ref{eq Ebo}- \ref{eq tbo} provide three generic observables that depend on only two parameters $\g_{f,0}$ and $R_*$ ."
"Thus. the energy. temperature ancl time scale of the breakout flare are enough to determine R, and 5,55. and they also must satisfv if the source of the flave is a relativistic shock breakout."," Thus, the energy, temperature and time scale of the breakout flare are enough to determine $R_*$ and $\g_{f,0}$, and they also must satisfy if the source of the flare is a relativistic shock breakout."
 This relativistic breakout relation can be used to testthe origin of observed gamuna-rav [lares., This relativistic breakout relation can be used to testthe origin of observed gamma-ray flares.
Populating the far end of the halo mass function. galaxy clusters are in. principle highly sensitive. indicators of the cosmological parameters and non-linear structure. growth.,"Populating the far end of the halo mass function, galaxy clusters are in principle highly sensitive indicators of the cosmological parameters and non-linear structure growth."
 Combining. Gaussian random density fields with linear structure growth anc spherical collapse. the Press-Schechter mass function and its variants turn out to reproduce the halo mass function in fully non-linear cosmological simulations extremely well.," Combining Gaussian random density fields with linear structure growth and spherical collapse, the Press-Schechter mass function and its variants turn out to reproduce the halo mass function in fully non-linear cosmological simulations extremely well."
 If measurable. the abundance of halos in the exponential tail of the mass function. and its evolution on cosmic time scales allow precise constraints on both the density-fluctuation amplitude today and duri£ the second half of the cosmic age and on the matter-density parameter.," If measurable, the abundance of halos in the exponential tail of the mass function and its evolution on cosmic time scales allow precise constraints on both the density-fluctuation amplitude today and during the second half of the cosmic age and on the matter-density parameter."
 The exponential dependence of the abundance of massive halos on cosmological assumptions promises tight constraints., The exponential dependence of the abundance of massive halos on cosmological assumptions promises tight constraints.
 A direct comparison between the theoretically predicted mass function of massive halos and the observed distributions of galaxy clusters in various observable quantities. such as the flux and the temperature of their X-ray emission or the velocity dispersion of their member galaxies requires observables to be translated into mass.," A direct comparison between the theoretically predicted mass function of massive halos and the observed distributions of galaxy clusters in various observable quantities, such as the flux and the temperature of their X-ray emission or the velocity dispersion of their member galaxies requires observables to be translated into mass."
 While this conversior appears straightforward under the idealised assumptions of spherical symmetry. thermal. and hydrostatic equilibrium. the cluster population as a whole shows all signs of being dynamically active.," While this conversion appears straightforward under the idealised assumptions of spherical symmetry, thermal, and hydrostatic equilibrium, the cluster population as a whole shows all signs of being dynamically active."
 [t i5 doubtful whether precise cosmological conclusions can be drawn based on symmetry assumptions., It is doubtful whether precise cosmological conclusions can be drawn based on symmetry assumptions.
 Even if clusters satisfied the idealising assumptions typically underlying their cosmological interpretation. their mass Is not an observable.," Even if clusters satisfied the idealising assumptions typically underlying their cosmological interpretation, their mass is not an observable."
 In fact. the mass of a dark-matter halo is a poorly defined. derived quantity to which hardly any precise meaning can be given.," In fact, the mass of a dark-matter halo is a poorly defined, derived quantity to which hardly any precise meaning can be given."
 It is common to operationally define halo masses as enclosed by spheres containing an average fixed overdensity., It is common to operationally define halo masses as enclosed by spheres containing an average fixed overdensity.
 However. the many different choices of apparently appropriate overdensity values in the literature demonstrate that there is no uniquely defendable choice.," However, the many different choices of apparently appropriate overdensity values in the literature demonstrate that there is no uniquely defendable choice."
 If the overdensity is chosen very high. the masses obtained are core masses rather than halo masses. and if it i5 chosen low. density profiles constrained near the core need to be extrapolated into regions where they are typically poorly measured or not at all.," If the overdensity is chosen very high, the masses obtained are core masses rather than halo masses, and if it is chosen low, density profiles constrained near the core need to be extrapolated into regions where they are typically poorly measured or not at all."
 Halo definitions in numerical simulations illustrate the same problem in a different way., Halo definitions in numerical simulations illustrate the same problem in a different way.
 There. halos are typically identified by group finders connecting particles with neighbours closer than a certam linking length.," There, halos are typically identified by group finders connecting particles with neighbours closer than a certain linking length."
 Recipes exist for how the linking length should be chosen. but there is no objective criterion.," Recipes exist for how the linking length should be chosen, but there is no objective criterion."
 The dependence on the linking length may be less relevant in. practice. because halo masses can again be defined as the masses of all particles in. spheres containing a fixed overdensity., The dependence on the linking length may be less relevant in practice because halo masses can again be defined as the masses of all particles in spheres containing a fixed overdensity.
 However. this refers back to the largely arbitrary overdensity threshold and creates the additional problem that several different plausible definitions of halo centres exist that often yield discrepant results.," However, this refers back to the largely arbitrary overdensity threshold and creates the additional problem that several different plausible definitions of halo centres exist that often yield discrepant results."
 Three main classes of observation are used to constrain cluster masses: gravitational lensing. X-ray flux and temperature. and galaxy kinematics.," Three main classes of observation are used to constrain cluster masses: gravitational lensing, X-ray flux and temperature, and galaxy kinematics."
 None of them measures cluster masses., None of them measures cluster masses.
 Gravitational lensing measures the curvature of the projected gravitational potential., Gravitational lensing measures the curvature of the projected gravitational potential.
 X-ray observables are primarily determined by the gas density and temperature. which respond to the depth of the gravitational potential and its gradient. as do galaxy kinematics.," X-ray observables are primarily determined by the gas density and temperature, which respond to the depth of the gravitational potential and its gradient, as do galaxy kinematics."
 Thus. cluster observables constrain the gravitational potential rather than any kind of mass.," Thus, cluster observables constrain the gravitational potential rather than any kind of mass."
 The conversion of the potential into a mass is hampered by the fact that mass 1s a non-local quantity. requiring an ntegration over potential derivatives.," The conversion of the potential into a mass is hampered by the fact that mass is a non-local quantity, requiring an integration over potential derivatives."
 We raise the question whether cosmological conclusions can be drawn directly from cluster observables without the detour through problematic definitions of cluster masses., We raise the question whether cosmological conclusions can be drawn directly from cluster observables without the detour through problematic definitions of cluster masses.
 As one step towards a possible answer. we derive here the X-ray temperature function from a locally defined quantity. amely the gravitational. potential.," As one step towards a possible answer, we derive here the X-ray temperature function from a locally defined quantity, namely the gravitational potential."
 To this purpose. we first derive a function. predicting the number density of potential minima having a certain depth.," To this purpose, we first derive a function predicting the number density of potential minima having a certain depth."
 We include the non-linear evolution of the potential by considering the collapse of a spherical and homogeneous overdensity. and locally relate the non-linear potential depth to a temperature using the virial theorem.," We include the non-linear evolution of the potential by considering the collapse of a spherical and homogeneous overdensity, and locally relate the non-linear potential depth to a temperature using the virial theorem."
 This direct relation of the temperature to the gravitational potential allows us to avoid introducing a global quantity such as the mass and the ambiguities in its definition., This direct relation of the temperature to the gravitational potential allows us to avoid introducing a global quantity such as the mass and the ambiguities in its definition.
 The formalism proposed in this work may thus contribute to reducing the systematic uncertainty in comparisons between theory and observation by avoiding empirical relations between cluster masses and observables., The formalism proposed in this work may thus contribute to reducing the systematic uncertainty in comparisons between theory and observation by avoiding empirical relations between cluster masses and observables.
 Unless declared otherwise. we shall use the following cosmological models and parameters: Einstein-de Sitter (EdS):," Unless declared otherwise, we shall use the following cosmological models and parameters: Einstein-de Sitter (EdS):"
have absolute value equal to one. the minima possible noise contributions to the visibilitics is achieved when all columns of A are orthogonal: or equivalently for ANA proportional to the ideutitv matrix.,"have absolute value equal to one, the minimum possible noise contributions to the visibilities is achieved when all columns of $A$ are orthogonal: _t or equivalently for ${\cal A}^\dag {\cal A}$ proportional to the identity matrix."
 A proof of his statement is provided iu Appendix AppendixA:., A proof of this statement is provided in Appendix \ref{sec:appendix}.
. Iituitivelv. it savs that the visibilities are recovered with muni noise when they are maximally independent of cach other. that is. when they coutribute orthosonallv to he time series of signals at the detector.," Intuitively, it says that the visibilities are recovered with minimum noise when they are maximally independent of each other, that is, when they contribute orthogonally to the time series of signals at the detector."
 Let us sunuuarize., Let us summarize.
 For aay pair of lorus yj.&. define an AM-dimenusional vectorcoal Ny," For any pair of horns $j,k$, define an $M$ -dimensional vector, )."
 Our goal is to choose the set of phase shifts 0j; such that the vectors $; aud ®jj. are orthogonal whenever (jh)+ GEM)., Our goal is to choose the set of phase shifts $\phi_{jt}$ such that the vectors $\vec \Phi_{jk}$ and $\vec \Phi_{j'k'}$ are orthogonal whenever $(jk)\ne(j'k')$ .
" Whe this coucition is satisfied. each visibility is recovered simply by taking the dot product of the detector sienal with the corresponding vector 9: the estimator of Vip ds ο.». ondery We will call the vector Pj, the “mask” for the baseline jh."," When this condition is satisfied, each visibility is recovered simply by taking the dot product of the detector signal with the corresponding vector $\vec\Phi$: the estimator of $V_{jk}$ is S= S_t We will call the vector $\vec\Phi_{jk}$ the “mask” for the baseline $jk$."
 Note that $;; aud Ῥ are coniplex. conjugates. of cach other., Note that $\vec\Phi_{jk}$ and $\vec\Phi_{kj}$ are complex conjugates of each other.
" The requirement that these be orthogonal. which means roughly that the elements of δη, muiformiyv saluple directions in the complex plaue. is necessary for both the real aud tuaginary parts of Vj, to be recovered with minii noise."," The requirement that these be orthogonal, which means roughly that the elements of $\Phi_{jk}$ uniformly sample directions in the complex plane, is necessary for both the real and imaginary parts of $V_{jk}$ to be recovered with minimum noise."
 It nav be iustructive to compare the phase shift schemes for the bolometric interferometer with tLOSC applied iu a traditional muultiphius interferometer., It may be instructive to compare the phase shift schemes for the bolometric interferometer with those applied in a traditional multiplying interferometer.
 Iu traditional iiterferoiietiy. orthogonal paterus of sqlare-wave phase shifts (e.g. Wash functions) are applied to each of the iiput antennas in order to recice the response of the instrument to spurious signals (6.8.7).," In traditional interferometry, orthogonal patterns of square-wave phase shifts (e.g., Walsh functions) are applied to each of the input antennas in order to reduce the response of the instrument to spurious signals \citep[e.g.,][]{thompson}."
 The p1ase shift patteris we require in the adding interferometer niust obey a more strngeu orthogouality requirement: rather than merely demanding orthogoinitv of all of the input pase shifts (0... demanding hat the $j bo orthosonal). we require tha the phase shifts associated with all (1.6.. all Pj.) be orthogonal.," The phase shift patterns we require in the adding interferometer must obey a more stringent orthogonality requirement: rather than merely demanding orthogonality of all of the input phase shifts (i.e., demanding that the $\vec\phi_j$ be orthogonal), we require that the phase shifts associated with all (i.e., all $\vec\Phi_{jk}$ ) be orthogonal."
 Let us suppose that the ummber No of horus is fixed. as is the wmuber P of possible phase shift values;," Let us suppose that the number $N$ of horns is fixed, as is the number $P$ of possible phase shift values."
 We wish to fud the shortest sequence of time steps (that is. the minimi AZ) that satisfies our orthogonality criterion.," We wish to find the shortest sequence of time steps (that is, the minimum $M$ ) that satisfies our orthogonality criterion."
 Alternatively. given ALP. we can ask for the maxinuun ΠΙΟ of horns that can be accommodated.," Alternatively, given $M,P$, we can ask for the maximum number of horns that can be accommodated."
 We will introduce the following shorthand notation for the possible phase actors: p—0.1., We will introduce the following shorthand notation for the possible phase factors: P-1.
"2....P1. For purposes of illustration. we will cousicer the case lin this section. so that the four possible phase shift values arePl. a, steps through the 2? values as slowly as possible aud each subsequent α evcles P times faster."," For purposes of illustration, we will consider the case $P=4$ in this section, so that the four possible phase shift values are, $\vec\alpha_{1}$ steps through the $P$ values as slowly as possible and each subsequent $\vec\alpha_{j}$ cycles $P$ times faster."
 We now define for integers2 jy...jog between O and 30," We now define for integers $j_\mu,\ldots j_2,j_1$ between 0 and 3."
 Ποσο multiplication aud exponcutiation are performed clemcntwise in cach vector., Here multiplication and exponentiation are performed elementwise in each vector.
 Since |p| is shorthand . mn ↕∪↥⋅↙∣∣↗⊓−∙⋯↿∏↑∏≻∐↸⊳⋜↧⊓∪∐↸⊳∪↥⋅↥⋅↸∖↴∖↴↻∪⋯↧↴∖↴↑∪⋜⊔∐↕⊓∪∐⋯∪≼↧∏↕∪⋅⋅⋅ ⋅⋅ lon the values m square| brackets.," Since $[p]$ is shorthand for $e^{ip\pi/2}$, multiplication corresponds to addition modulo 4 on the values in square brackets."
 For istance. in the Case ff=2. It is straightorwiud το check that the vectors ο...4o.a) are all mutuaIv orthogonal.," For instance, in the case $\mu=2$, It is straightforward to check that the vectors $\langle
j_\mu,\ldots,j_2,j_1\rangle$ are all mutually orthogonal."
 Since there are 1 distinct vectors. they are a maximal set of orthogonal vectors.," Since there are $4^\mu$ distinct vectors, they are a maximal set of orthogonal vectors."
 We can therefore search amoug this set for f1C optimal set of Npinse shift xitferus to apply to our iuput OTL., We can therefore search among this set for the optimal set of $N$ phase shift patterns to apply to our input horns.
 As an example. consider the case ji—2. that is. let the ΠΠνο of fastime steps be AM=[D—↽⋅16.," As an example, consider the case $\mu=2$, that is, let the number of time steps be $M=4^2=16$."
 We- willH determine- he maxima value of N that can be accomodated., We will determine the maximum value of $N$ that can be accommodated.
 We xoceed by assiguine phase shift sequences to the horIs oue at a time., We proceed by assigning phase shift sequences to the horns one at a time.
 Without loss of eeneralitv. we can assume hat the first hori has no phase shift at all (ince uy plase," Without loss of generality, we can assume that the first horn has no phase shift at all (since any phase"
sources (Source 2) is only detected in the soft baud of this still relatively shallow N-rav inage. the three sources appear to be representative of the optically faint lard X-rav source population.,"sources (Source 2) is only detected in the soft band of this still relatively shallow X-ray image, the three sources appear to be representative of the optically faint hard X-ray source population."
 The coordinates and properties of the three N-rav sources behind A2390 are sumunarized in Table P. and in the caption of Fig., The coordinates and properties of the three X-ray sources behind A2390 are summarized in Table \ref{tab1} and in the caption of Fig.
 1., 1.
" Magnuitudes are measured in 2"" diameter apertures.", Magnitudes are measured in $2''$ diameter apertures.
 We have applied a small differcutial correction relative to the A’ imaenitudes to allow for differences in the image quality between the bands: O.O2CIT ). 0.0107). 0.03). O.OSCR). 0.15}. and 0.1765).," We have applied a small differential correction relative to the $K'$ magnitudes to allow for differences in the image quality between the bands: $-0.02 (H)$ $-0.04 (J)$ , $0.03 (I)$, $-0.08 (R)$, $-0.18
(V)$, and $-0.17 (B)$."
 Iu the fitting procedures we have also allowed for a 0.2 magnitude systematic uncertaintv over the statistical errors in Table 1., In the fitting procedures we have also allowed for a 0.2 magnitude systematic uncertainty over the statistical errors in Table 1.
 Where total magnitudes are required. the offsets to the isophotal magnitudes of the final column of the table should be used.," Where total magnitudes are required, the offsets to the isophotal magnitudes of the final column of the table should be used."
 The X-aw coordinates have been offset to match the optical data., The X-ray coordinates have been offset to match the optical data.
 The Source 2 X-ray position has also been updated frou that eiven in FFabian et ((2000) aud now has a clear optical counterpart., The Source 2 X-ray position has also been updated from that given in \markcite{fabian00}F Fabian et (2000) and now has a clear optical counterpart.
 We used the new Cooled Iufrared Spectrograph: aud Camera for OIIS (CISCO. MMotoliara. ct 11998) on the Subaru nun telescope UT 2000 June 158.19. July 1516. September LO12. and November 7 to obtain extremely deep J. IT. aud A’ nuages of the clusters A2390 and À370.," We used the new Cooled Infrared Spectrograph and Camera for OHS (CISCO, \markcite{moto98}M Motohara et 1998) on the Subaru m telescope UT 2000 June $18-19$, July $15-16$, September $10-12$, and November 7 to obtain extremely deep $J$, $H$, and $K'$ images of the clusters A2390 and A370."
" The detector used was a 10211051 TeCdTe ILAWATII array with a pixel scale of 0.111"" for the June. July. aud November runs and a pixel scale of 0.105” for the September run."," The detector used was a $1024\times 1024$ HgCdTe HAWAII array with a pixel scale of $0.111''$ for the June, July, and November runs and a pixel scale of $0.105''$ for the September run."
 This provides a field-of-view ~2/«2’., This provides a field-of-view $\sim 2'\times 2'$.
 The data were taken in unguided mode aud therefore relied ou he superb telescope tracking to maintain nuage quality., The data were taken in unguided mode and therefore relied on the superb telescope tracking to maintain image quality.
" To nüunmuze the iuage degradation. a number of sub-exposures were taken at each position iu au ciglt-poiut »'utaeon pattern (5"" step size)."," To minimize the image degradation, a number of sub-exposures were taken at each position in an eight-point pentagon pattern $5''$ step size)."
 The weather conditions were photometric. aud the seeing was typically 0.370.57 during the first three observing ruus. which was also he resolution for nearly all the final reduced. images.," The weather conditions were photometric, and the seeing was typically $0.3''-0.5''$ during the first three observing runs, which was also the resolution for nearly all the final reduced images."
 Conditions were clear but with variable seeiug during he November run. with characteristic nage FWIIM of ~QN for the A8TO Z7 inuaee takeu ou this night.," Conditions were clear but with variable seeing during the November run, with characteristic image FWHM of $\sim0.8''$ for the A370 $H$ image taken on this night."
 The data were processed using median sky flats generated roni the dithered tuages., The data were processed using median sky flats generated from the dithered images.
 The data were calibrated from observations of the UKIRT. faint standards (CCasali Tlawarden 1992) FS27. FS29. FSG. aud FSLO.," The data were calibrated from observations of the UKIRT faint standards \markcite{irstds}C Casali Hawarden 1992) FS27, FS29, FS6, and FS10."
 The total exposure times for A2390 were ss (7). ss (IF). and ss CA). and those for A370 were ss (.7). ss (IT). and ss (K).," The total exposure times for A2390 were s $J$ ), s $H$ ), and s $K'$ ), and those for A370 were s $J$ ), s $H$ ), and s $K'$ )."
" The A"" image of A2390 is shown in Fie.", The $K'$ image of A2390 is shown in Fig.
 1 with the three A-vay sources marked., \ref{figimage} with the three X-ray sources marked.
 Deep inulticolor images of A370 were obtained using LRIS ou the Ikeck nuu telescopes on UT 1999 August 11. September 910. and 2000 August 25.," Deep multicolor images of A370 were obtained using LRIS on the Keck m telescopes on UT 1999 August 11, September 9–10, and 2000 August 25."
 The data were taken as a sequence of dithered exposures with uct inteeration times of 1200 s in V. ss in Z7. and ss in 7.," The data were taken as a sequence of dithered exposures with net integration times of 4200 s in $V\/$, s in $R\/$ , and s in $I\/$."
 The data were processed using imecian skv flats eenerated from the exposures., The data were processed using median sky flats generated from the exposures.
 Conditions were photometric during the observations., Conditions were photometric during the observations.
 The V. R. aud 7 data were calibrated using the photometric and spectrophotometric standard Zt CT Turushek ct 11990: OOke 1990) and faint Landolt standard stars iu the SA 95-12 field (LLandolt 1992).," The $V$, $R$, and $I$ data were calibrated using the photometric and spectrophotometric standard HZ4 \markcite{turnshek90}T Turnshek et 1990; \markcite{oke90}O Oke 1990) and faint Landolt standard stars in the SA 95-42 field \markcite{landolt92}L Landolt 1992)."
 Deep B (3780 s) aud R (20105) images of A370 were obtained with ESI on Neck. TT on UT 2000 September 2930., Deep $B$ (3780 s) and $R$ (2940s) images of A370 were obtained with ESI on Keck II on UT 2000 September 29–30.
 For A390. B ss}. R ss). and £ ss) Huages were obtained using ESI on the Keck II telescope ou UT 2000 November 2930.," For A2390, $B$ s), $R$ s), and $I$ s) images were obtained using ESI on the Keck II telescope on UT 2000 November 29–30."
 The V ss) nuage was obtained on UT 2000 September 29., The $V$ s) image was obtained on UT 2000 September 29.
 The data were calibrated with faint Laudolt staucdards in the fields of SA 113-337 and SA 95-12 (LLandolt 1992)., The data were calibrated with faint Landolt standards in the fields of SA 113-337 and SA 95-42 \markcite{landolt92}L Landolt 1992).
 We used CISCO on UT 2000 November 7 with the LJ erating to obtain NIR spectra of two of tlhe A2390 sources (Sources 1 and 2)., We used CISCO on UT 2000 November 7 with the $zJ$ grating to obtain NIR spectra of two of the A2390 sources (Sources 1 and 2).
 The iJ erating setup provides waveleugth coverage over the range AASI50.11100À.. with a steep decline iu seusitivitv below ~8750A.," The $zJ$ grating setup provides wavelength coverage over the range $\lambda\lambda$ 8450–14100, with a steep decline in sensitivity below $\sim8750$."
". We used a 1"" wide slit for the observatious. which provides a resolution of about R=2s0 over this wavelength rauge. as nieasiured from the PWITM of the neon calibration lines aud spectral cnussion features in the targets."," We used a $1''$ wide slit for the observations, which provides a resolution of about R=280 over this wavelength range, as measured from the FWHM of the neon calibration lines and spectral emission features in the targets."
" We took ss exposures using a 2-point dither with 5"" separation alone the slit at cight positions for Source 1. for a total of ss.aud at ten positious for Source 2. for a total of. ss. A second order polvuonmial fit for the waveleneth was obtained from nieht «Ev lines and Paschen series lines in A type spectral teiiplate stars. and the zero-point was adjusted to the position of OIIsky lines in the target observatious."," We took s exposures using a 2-point dither with $5''$ separation along the slit at eight positions for Source 1, for a total of s,and at ten positions for Source 2, for a total of s. A second order polynomial fit for the wavelength was obtained from night sky lines and Paschen series lines in A type spectral template stars, and the zero-point was adjusted to the position of OHsky lines in the target observations."
sensitivity to extended radio structures. but the high surface density of possible optical counterparts (over 4000 per square degree at high Galactic latitudes in the Palomar Observatory Sky Survey) limits the reliability of the optical matching.,"sensitivity to extended radio structures, but the high surface density of possible optical counterparts (over 4000 per square degree at high Galactic latitudes in the Palomar Observatory Sky Survey) limits the reliability of the optical matching."
 The first radio sky surveys were carried out at very low angular resolution and detected only the brightest radio sources., The first radio sky surveys were carried out at very low angular resolution and detected only the brightest radio sources.
 The resolution of these surveys was too low to allow identification of the host galaxies without detailed radio follow-up observations of the detected sources: this was time-consuming and meant that only small samples of galaxies could be studied (see discussion in MeMahon The VSS was the first radio survey of sufticiently high angular resolution (45 arcsec) to permit automated correlation with optical surveys.," The resolution of these surveys was too low to allow identification of the host galaxies without detailed radio follow-up observations of the detected sources; this was time-consuming and meant that only small samples of galaxies could be studied (see discussion in McMahon \nocite{mcm02}
 The NVSS was the first radio survey of sufficiently high angular resolution (45 arcsec) to permit automated cross--correlation with optical surveys."
 Machalski Condon (2?) cross—correlated the NVSS with the Las Campanas Redshift Survey (LCRS: Shectman 11996).. identifying 1157 radio-emitting galaxies.," Machalski Condon \shortcite{mac99} cross--correlated the NVSS with the Las Campanas Redshift Survey (LCRS; Shectman \nocite{she96}, , identifying 1157 radio–emitting galaxies."
 Machalski Godlowski (2?) used this sample to derive the local radio luminosity function., Machalski Godlowski \shortcite{mac00} used this sample to derive the local radio luminosity function.
 Using far-infrared data available for the LCRS they were also able to separate the luminosity function into a radio—loud active galactic nuclei (AGN) component. which dominates at high radio luminosities. and a lower-luminosity component due to starforming galaxies that emit in the radio predominantly due to the synchrotron emission from supernova remnants.," Using far–infrared data available for the LCRS they were also able to separate the luminosity function into a radio–loud active galactic nuclei (AGN) component, which dominates at high radio luminosities, and a lower-luminosity component due to star--forming galaxies that emit in the radio predominantly due to the synchrotron emission from supernova remnants."
 Similarly. Sadler shorteitesadO02. eross-correlated the NVSS with galaxies from the first data release of the 2dFGRS. defining a sample of 912 radio sources Which form a basis for further detailed studies (e.g. Bes The 45 aresee resolution of the NVSS has the advantage of being sufficiently large that 99% of radio sources are contained within a single NVSS component.," Similarly, Sadler \\shortcite{sad02} cross-correlated the NVSS with galaxies from the first data release of the 2dFGRS, defining a sample of 912 radio sources which form a basis for further detailed studies (e.g. Best \nocite{bes04a}
 The 45 arcsec resolution of the NVSS has the advantage of being sufficiently large that $\sim 99$ of radio sources are contained within a single NVSS component."
 With the exception of a few very large sources. the NVSS is also able to detect the entirety of the radio emission.," With the exception of a few very large sources, the NVSS is also able to detect the entirety of the radio emission."
 However. the poor angular resolution. of the NVSS leads to signiticant uncertainties in cross-identifying the radio sources with their optical host galaxies and there is a trade-off between the reliability of the matched sample and its completeness.," However, the poor angular resolution of the NVSS leads to significant uncertainties in cross-identifying the radio sources with their optical host galaxies and there is a trade-off between the reliability of the matched sample and its completeness."
 Sadler shortcitesadQ2 accepted radio sources within a matching radius of IO areseconds from an optical galaxy. leading to a catalogue that was ~90% complete. but in which of the matches are expected to be false identifications.," Sadler \\shortcite{sad02} accepted radio sources within a matching radius of 10 arcseconds from an optical galaxy, leading to a catalogue that was $\sim
90$ complete, but in which of the matches are expected to be false identifications."
 Samples with much higher reliability can be derived using the FIRST catalogue. due to its superior angular resolution (5 aresec).," Samples with much higher reliability can be derived using the FIRST catalogue, due to its superior angular resolution $\sim 5$ arcsec)."
 Ivezié shorteiteive02. eross-correlated the FIRST survey with the SDSS imaging sample., Ivezić \\shortcite{ive02} cross–correlated the FIRST survey with the SDSS imaging sample.
 Under the assumption that all true identifications of point radio sources would have radio—optical positional offsets of less than 3 aresec. they concluded that the optimal matching radius for cross—correlation was [.5 aresec. for which they derived a completeness for radio point sources of and a contamination rate of only3%.," Under the assumption that all true identifications of point radio sources would have radio–optical positional offsets of less than 3 arcsec, they concluded that the optimal matching radius for cross–correlation was 1.5 arcsec, for which they derived a completeness for radio point sources of and a contamination rate of only."
. However. at the high angular resolution of FIRST. new problems arise.," However, at the high angular resolution of FIRST, new problems arise."
 FIRST is not sensitive to extended radio structures because of a lack of short antennae baselines. and resolves out the extended emission of radio sources.," FIRST is not sensitive to extended radio structures because of a lack of short antennae baselines, and resolves out the extended emission of radio sources."
 As a result. the total radio luminosity of sources that are larger than a few arcseconds will be systematically low (cf.," As a result, the total radio luminosity of sources that are larger than a few arcseconds will be systematically low (cf."
 Becker In extreme cases. some larger radio sources are missed.," Becker \nocite{bec95} In extreme cases, some larger radio sources are missed."
 These effects introduce systematic biases into the derived radio source sample., These effects introduce systematic biases into the derived radio source sample.
 In addition. many extended radio sources are split into multiple components by FIRST.," In addition, many extended radio sources are split into multiple components by FIRST."
 Matching routines therefore need to be developed to account for the possible multi-component nature of radio sources., Matching routines therefore need to be developed to account for the possible multi-component nature of radio sources.
 The first attempt to automate such a routine was. by Magliocchetti shorteitemag98b.. who used a ‘collapsing algorithm! to identify multi-component FIRST sources.," The first attempt to automate such a routine was by Magliocchetti \\shortcite{mag98b}, who used a `collapsing algorithm' to identify multi–component FIRST sources."
 They considered all pairs of sources with separations below 3 aremins. and merged into a single combined source all pairs with separations below 100(4100m) arcsec and flux densities within a factor of four of each other.," They considered all pairs of sources with separations below 3 arcmins, and merged into a single combined source all pairs with separations below $100 \left( S_{\rm tot} / 100{\rm mJy}
\right)^{0.5}$ arcsec and flux densities within a factor of four of each other."
 This method is simple and works well for classical double-lobed radio sources. but accounts poorly for jet sources or sources with large asymmetries.," This method is simple and works well for classical double–lobed radio sources, but accounts poorly for core--jet sources or sources with large asymmetries."
 Ivezié shorteiteive02. improved on this by first eross-correlating all FIRST sources with the SDSS (thereby picking up all sources with a core component) and then adding candidate double-lobed radio sources to this sample., Ivezić \\shortcite{ive02} improved on this by first cross-correlating all FIRST sources with the SDSS (thereby picking up all sources with a core component) and then adding candidate double–lobed radio sources to this sample.
 These were identified by comparing the mid-points of all FIRST pairs with separations below 90 aresec. with the galaxies in the optical catalogue. and accepting all matches with offsets below 3 aresec.," These were identified by comparing the mid-points of all FIRST pairs with separations below 90 arcsec with the galaxies in the optical catalogue, and accepting all matches with offsets below 3 arcsec."
 They estimated that such double sources contribute less than of all radio sources., They estimated that such double sources contribute less than of all radio sources.
 McMahon shorteitememO2 carried out a detailed study of the properties of multi-component FIRST sources by comparing isolated pairs of FIRST sources with optieal Automated Plate Measuring Machine (APM) scans of the Palomar Observatory Sky Survey (POSS) dates., McMahon \\shortcite{mcm02} carried out a detailed study of the properties of multi–component FIRST sources by comparing isolated pairs of FIRST sources with optical Automated Plate Measuring Machine (APM) scans of the Palomar Observatory Sky Survey (POSS) plates.
 For core-jet type sources. where the optical counterpart is associated with one of the radio components. they found that he radio components usually have very different flux densities and that the component with the optical counterpart is usually brighter and is frequently unresolved in the radio.," For core–jet type sources, where the optical counterpart is associated with one of the radio components, they found that the radio components usually have very different flux densities and that the component with the optical counterpart is usually brighter and is frequently unresolved in the radio."
 In contrast. if the optical counterpart 1s located between the two radio components. he two radio components usually have comparable flux densities and similar radio sizes Ge.," In contrast, if the optical counterpart is located between the two radio components, the two radio components usually have comparable flux densities and similar radio sizes (ie."
 both are consistent with being radio obes. not one unresolved core and an extended radio lobe).," both are consistent with being radio lobes, not one unresolved core and an extended radio lobe)."
 In this case. the optically identified galaxy is typically located fairly close o the flux-weighted mean position of the two radio components.," In this case, the optically identified galaxy is typically located fairly close to the flux-weighted mean position of the two radio components."
 This information is extremely useful in the identification of component FIRST sources., This information is extremely useful in the identification of multi--component FIRST sources.
 Because the main spectroscopic galaxy sample of the SDSS has rather low median redshift ἐς~ 0.1). the problems described above associated with identifying extended radio sources will be more severe.," Because the main spectroscopic galaxy sample of the SDSS has rather low median redshift $z \sim 0.1$ ), the problems described above associated with identifying extended radio sources will be more severe."
 This paper thus presents a hybrid method. using information from both NVSS and FIRST in order to take advantage of thestrong points of both surveys and avoid the systematic errors that arise in using only one of them.," This paper thus presents a hybrid method, using information from both NVSS and FIRST in order to take advantage of thestrong points of both surveys and avoid the systematic errors that arise in using only one of them."
 The lavout of the paper is, The layout of the paper is
Iu the case of the svuchrotron photons being scattered (SSC process) the ceutral IC. surface brightuess of the source IS: where mg=Uy(i.p) for brevity.,"In the case of the synchrotron photons being scattered (SSC process) the central IC surface brightness of the source is: where $\nu_0 = \nu_0(\nu,p)$ for brevity."
" The ecometric factor g(7Q7)) is just the normalized. ceutral-line-ofsight integrated nuuber density of svuchrotron photons: This factor is approximated to better than accuracy by the asviuptotically exact expression (fort, > and τι, »ox) with gy=ποδια —2.and ij=5j[."," The geometric factor $g(\tau(\nu))$ is just the normalized central-line-of-sight integrated number density of synchrotron photons: This factor is approximated to better than $4\%$ accuracy by the asymptotically exact expression (for $\tau_\nu \rightarrow 0$ and $\tau_\nu \rightarrow \infty$ ) with $g_0 = (4 + \pi^2)/{8}$, $g_\infty
= 2$, and $\beta = 5/4$."
 If the spectra are power-laws. if the optical depth is sanall over the whole svuchrotron spectral ranges. and if all IC scattering electrons are ultra-relativistic (p29 1) Eqs.," If the spectra are power-laws, if the optical depth is small over the whole synchrotron spectral ranges, and if all IC scattering electrons are ultra-relativistic $p \gg 1$ ) Eqs."
 Cl and C8 cau be iutegrated analvtically: where This foxiuula Ooeives |quite accurateY. results well above the svuchrotrou sel-absorptiou break in the SSC spectra Tt shoukd lx| noted. that a inore exact treatment of the SSC process would require aking the anisotropy of the svuchrotron radiation ficld iuto account in the IC calculations.," \ref{eq:Lic} and \ref{eq:Bssc}
 can be integrated analytically: where This formula gives quite accurate results well above the synchrotron self-absorption break in the SSC spectrum It should be noted, that a more exact treatment of the SSC process would require taking the anisotropy of the synchrotron radiation field into account in the IC calculations."
 This could i principle be done within the formalism. described by Diunetti (2000).., This could in principle be done within the formalism described by Brunetti \cite*{2000APh....13..107B}.
 But it turus out that the difference beWECLL ISOropic aud anisotropic IC scattering for the line-ofsight integrated IC fiux ina spherical problem is too suall to be of importance for our rough estimates (Enfilineal..1999).., But it turns out that the difference between isotropic and anisotropic IC scattering for the line-of-sight integrated IC flux in a spherical problem is too small to be of importance for our rough estimates \cite{1999AA...344..409E}.
 A second note: we do rot correct for svuchrotron selt-absorption of the iverse €‘ommpton scattered radiation for he followingC» reasous., A second note: we do not correct for synchrotron self-absorption of the inverse Compton scattered radiation for the following reasons.
 Svuchrotron self-absorptiou occurs ouly at frequencies at wYeh also svuchrotrou cussion is produced., Synchrotron self-absorption occurs only at frequencies at which also synchrotron emission is produced.
 At lieher (than svuchrotrou cussion) requencies we therefore cο not need to correct for it., At higher (than synchrotron emission) frequencies we therefore do not need to correct for it.
 At ower frequencies the spectrin is dominated by orders of uaeuitude bv the svuchrotrou flux in all our examples and therefore the SSC’ cussion is uuobservable at these requenucies., At lower frequencies the spectrum is dominated by orders of magnitude by the synchrotron flux in all our examples and therefore the SSC emission is unobservable at these frequencies.
 This justifies our optical thin treatment of the IC oXoton escape., This justifies our optical thin treatment of the IC photon escape.
band (Delplancke2008)..,band \citep{2008NewAR..52..199D}.
 There is a bright star = 10.28) in he vicinity of MACHO-97-SMC-I (separated at 30.4 arcsec}. so heoretically it would be possible to obtain 30-jas accuracy in astrometric Measurements within one hour with the UTs (130 m baseline).," There is a bright star = 10.28) in the vicinity of MACHO-97-SMC-1 (separated at 30.4 arcsec), so theoretically it would be possible to obtain $\mu$ as accuracy in astrometric measurements within one hour with the UTs (130 m baseline)."
 However. for the two stars separated by 20 arcsec. there is already reduction in the interferometric fringe visibility.," However, for the two stars separated by 20 arcsec, there is already reduction in the interferometric fringe visibility."
" Thus it would be very challenging to conduct such measurement,", Thus it would be very challenging to conduct such measurement.
 It would be very difficult to routinely measure the astrometry towards SMC/LMC with because most of the single lens events in the Magellanic Clouds (14 out of 15. except MACHO-97-SMC-1) have sources fainter than 19 mag in (I in Alcocketal. 19972: 12 in Alcocketal.2000:: | in Tisserandetal.2007.. which is the same as Alcocketal.1997a.. and 2 in Wyrzykowskietal. 2000).," It would be very difficult to routinely measure the astrometry towards SMC/LMC with because most of the single lens events in the Magellanic Clouds (14 out of 15, except MACHO-97-SMC-1) have sources fainter than 19 mag in (1 in \citealp{1997ApJ...491L..11A}; ; 12 in \citealp{2000ApJ...542..281A}; 1 in \citealp{2007A&A...469..387T}, which is the same as \citealp{1997ApJ...491L..11A}, and 2 in \citealp{2009MNRAS.397.1228W}) )."
 To perform astrometric measurements for microlensing events towards M31 is beyond the limit of both and since the sources in M31 are too faint (see e.g. Riffeser et., To perform astrometric measurements for microlensing events towards M31 is beyond the limit of both and since the sources in M31 are too faint (see e.g. Riffeser et.
 al..," al.,"
 in preparation.and reference therein).," in preparation,and reference therein)."
"to conclude that the major ejection events have an imprecise connection to the X-ray ""timing state’ and possibly also to the spectral state.",to conclude that the major ejection events have an imprecise connection to the X-ray `timing state' and possibly also to the spectral state.
 In fact it is not clear how tight is the relation between the two definitions of states (see discussions in e.g. Homan Belloni 2005: Remillard MeClintock 2006: Klein-Wolt van der Klis 2007)., In fact it is not clear how tight is the relation between the two definitions of states (see discussions in e.g. Homan Belloni 2005; Remillard McClintock 2006; Klein-Wolt van der Klis 2007).
 This may imply that the jet. and maybe also the X- radiation are common “symptoms of some other change. but not themselves causally connected.," This may imply that the jet, and maybe also the X-ray radiation are common `symptoms' of some other change, but not themselves causally connected."
 The bottom line is that current radio coverage is simply not sufficient to pin down the moment of ejection to any specific part of the complex X-ray transitions we have learned about via RXTE., The bottom line is that current radio coverage is simply not sufficient to pin down the moment of ejection to any specific part of the complex X-ray transitions we have learned about via RXTE.
 In Fender. Belloni Gallo (2004) we presented a first attempt at a unified picture for the radio:X-ray coupling in black hole ray binaries.," In Fender, Belloni Gallo (2004) we presented a first attempt at a unified picture for the radio:X-ray coupling in black hole X-ray binaries."
 This pieture was based upon the study of four black 10le systems. presenting one outburst each (one oscillation event in the case of GRS 19154105).," This picture was based upon the study of four black hole systems, presenting one outburst each (one oscillation event in the case of GRS 1915+105)."
 One of the main conclusions of he paper was that relativistic ejections are associated with the high uminosity hard to soft X-ray state transition which occurs near the beginning of most outbursts., One of the main conclusions of the paper was that relativistic ejections are associated with the high luminosity hard to soft X-ray state transition which occurs near the beginning of most outbursts.
" In this paper we have investigated a ""ur larger sample of black hole X-ray binary outbursts observed by RXTE for which there is at least some radio coverage.", In this paper we have investigated a far larger sample of black hole X-ray binary outbursts observed by RXTE for which there is at least some radio coverage.
 In all cases we find that the peak of the radio emission. which is almost certainly associated with a discrete relativistic ejection event (although there will be some delay between ejection and radio peak). to be associated with the overall hard to soft state transition. but we cannot pin down some specitic phase in the intermediate states.," In all cases we find that the peak of the radio emission, which is almost certainly associated with a discrete relativistic ejection event (although there will be some delay between ejection and radio peak), to be associated with the overall hard to soft state transition, but we cannot pin down some specific phase in the intermediate states."
 This confirms the result of FBGO4: however. we also note that in several systems the radio flare / ejection event is associated with phases of X-ray flaring which are not so evident in the source. GX 339-4.," This confirms the result of FBG04; however, we also note that in several systems the radio flare / ejection event is associated with phases of X-ray flaring which are not so evident in the most-studied source, GX 339-4."
 We also find that in a large numberof cases there is signiticant radio emission in the soft state. where we have previously asserted (Fender et al.," We also find that in a large number of cases there is significant radio emission in the soft state, where we have previously asserted (Fender et al."
 1999: FBGOJ) that the jet is suppressed or ‘quenched’., 1999; FBG04) that the jet is suppressed or `quenched'.
 It seems that in all cases this radio emission is consistent with having an origin in jet-ISM interactions far from the black hole. with the core radio emission indeed switched off.," It seems that in all cases this radio emission is consistent with having an origin in jet-ISM interactions far from the black hole, with the core radio emission indeed switched off."
 The evidence for this comes in the form of optically thin radio spectra and (usually) monotonic decays in radio flux in the soft state. as well as the fact that in several sources the radio emission is indeed strongly suppressed in the soft state.," The evidence for this comes in the form of optically thin radio spectra and (usually) monotonic decays in radio flux in the soft state, as well as the fact that in several sources the radio emission is indeed strongly suppressed in the soft state."
 However. uncertainty about exactly when the jet production mechanism shuts off remains. and is unlikely to be resolved by flux monitoring observations with relatively low angular resolution instruments such as ATCA and the VLA — higher resolution VLBI and/or higher frequency observations. preferably simultaneous with X-ray observations. are going to be necessary to make progress.," However, uncertainty about exactly when the jet production mechanism shuts off remains, and is unlikely to be resolved by flux monitoring observations with relatively low angular resolution instruments such as ATCA and the VLA – higher resolution VLBI and/or higher frequency observations, preferably simultaneous with X-ray observations, are going to be necessary to make progress."
 The reactivation of the core jet in the hard intermediate state was predicted in FBGOA but there remains little direct evidence for this. and it may well be that the core jet does not reactivate until the canonical hard state is reached.," The reactivation of the core jet in the hard intermediate state was predicted in FBG04 but there remains little direct evidence for this, and it may well be that the core jet does not reactivate until the canonical hard state is reached."
 The one tentative identification of a hard intermediate state reactivation is the case of XTE 11720-318. where a weak radio source appears during the transition back to the hard state. but before the canonical hard state has been reached.," The one tentative identification of a hard intermediate state reactivation is the case of XTE J1720-318, where a weak radio source appears during the transition back to the hard state, but before the canonical hard state has been reached."
 More radio observations of the decay phases of outburst are required to investigate this further., More radio observations of the decay phases of outburst are required to investigate this further.
 We have also attempted to extend our description of the X- properties beyond just X-ray colours. but also to variability properties.," We have also attempted to extend our description of the X-ray properties beyond just X-ray colours, but also to variability properties."
 The bright intermediate states during which we have clearly established the relativistic ejections take place are also well known to be associated with the presence of strong QPOs. which generally rise in frequency as the hard to soft transition progresses (Klein-Wolt van der Klis 2007 and references therein).," The bright intermediate states during which we have clearly established the relativistic ejections take place are also well known to be associated with the presence of strong QPOs, which generally rise in frequency as the hard to soft transition progresses (Klein-Wolt van der Klis 2007 and references therein)."
 In particular. we compared zones of anomalously low X-ray r.m.s.," In particular, we compared zones of anomalously low X-ray r.m.s."
 variability. which are associated with transitions between “hard intermediate’ and ‘soft intermediate! states. with the times of radio ejection events.," variability, which are associated with transitions between `hard intermediate' and `soft intermediate' states, with the times of radio ejection events."
 These zones are simply associated with “disc dilution’ of the variability signal. but by some as yet unexplained reduction in the degree of variability of the hard X-ray component: they are also often associated with type-B QPOs.," These zones are simply associated with `disc dilution' of the variability signal, but by some as yet unexplained reduction in the degree of variability of the hard X-ray component; they are also often associated with type-B QPOs."
 In all cases where the data were good enough to measure both. the radio flares and r.m.s.," In all cases where the data were good enough to measure both, the radio flares and r.m.s."
 drops are coincident within a few days., drops are coincident within a few days.
 In the case of XTE 15502320. there are hints that a sequence of five radio flares are associated with a corresponding number of r.m.s.," In the case of XTE J1859+226, there are hints that a sequence of five radio flares are associated with a corresponding number of r.m.s."
 variability drops. superposed on a general decline in the r.m.s.," variability drops, superposed on a general decline in the r.m.s."
 towards the soft state., towards the soft state.
 An obvious speculation would be that the radio flares are associated with the ejection ofthe same coronal material which is responsible for much of the variability (as suggested previously by e.g. Rodriguez et al., An obvious speculation would be that the radio flares are associated with the ejection of the same coronal material which is responsible for much of the variability (as suggested previously by e.g. Rodriguez et al.
 2003. Vadawale et al.," 2003, Vadawale et al."
 2003: FBGO+4: see also Rodrigues Prat 2008)., 2003; FBG04; see also Rodrigues Prat 2008).
 However. in the case of GX j it appears that a strong radio flare event took place more than a day the X-ray r.m.s.," However, in the case of GX 339-4 it appears that a strong radio flare event took place more than a day the X-ray r.m.s."
" drop. contrary to expectations for such a scenario,"," drop, contrary to expectations for such a scenario."
 Therefore at present it is uncertain whether the radio flares and r.m.s., Therefore at present it is uncertain whether the radio flares and r.m.s.
 drops are simply independent symptoms of some other underlying process. or that perhaps every dip is indeed," drops are simply independent symptoms of some other underlying process, or that perhaps every dip is indeed"
quantity to be written in terms of the others.,quantity to be written in terms of the others.
 For example we deduce 4:23x€., For example we deduce $H \beta \propto C$.
 The rj coordinates of a particle can be obtained [rom the velocity according to From these equations we easily deduce that the radial coordinate r and angular coordinate @ of the particle are eiven by from which we deduce that for any. particle C7xLf as is required by the density equation (32)) and (48)).," The $x,y$ coordinates of a particle can be obtained from the velocity according to From these equations we easily deduce that the radial coordinate $r$ and angular coordinate $\theta$ of the particle are given by from which we deduce that for any particle $Cr^2 \propto H$ as is required by the density equation \ref{eq:rhoHC}) ) and \ref{eq:rhos2}) )."
We emphasize that the inferences with regard (ο the CO abundance on brown cdwarls remain the same with our updated time-constant procecure.,We emphasize that the inferences with regard to the CO abundance on brown dwarfs remain the same with our updated time-constant procedure.
 It is simply the inferences with respect to A... Chat have changed., It is simply the inferences with respect to $K_{zz}$ that have changed.
 However. because assumptions about the strength. of abmospheric mixing can affect cloud models and other theoretical predictions of the vertical transport of condensates and gas-phase species (e.g..Golimowskietal.2004:Saumon2006.2007:Leggettetal.Stephens2009:Spiegel 2009).. this change has important implications.," However, because assumptions about the strength of atmospheric mixing can affect cloud models and other theoretical predictions of the vertical transport of condensates and gas-phase species \citep[e.g.,][]{golimowski2004,saumon2006,saumon2007,leggett2007,stephens2009,spiegel2009}, this change has important implications."
 When our rate-limiting step for CO quenching is considered ancl the snuth(1998) effective length scale is adopted. the CO-based. evidence for sIuggish mixine in the ~10100-bar region of Gliese 229B (ancl potentially other brown clwarls) disappears.," When our rate-limiting step for CO quenching is considered and the \citet{smith1998} effective length scale is adopted, the CO-based evidence for sluggish mixing in the $\sim$ 10–100-bar region of Gliese 229B (and potentially other brown dwarfs) disappears."
" The quench level for CO is delined as the altitude for which 74,70)=τε.", The quench level for CO is defined as the altitude for which $\tau_{chem}(\textrm{CO})=\tau_{mix}$.
" In the time-scale approach. the quenchied CO mole fraction that is mixed to higher altitudes is equal to the equilibrium abundance achieved at the quench level (characterized by a temperature T, and pressure /7,)."," In the time-scale approach, the quenched CO mole fraction that is mixed to higher altitudes is equal to the equilibrium abundance achieved at the quench level (characterized by a temperature $T_{q}$ and pressure $P_{q}$ )."
 The results from our updated. time-scale approach for CO quenching kinetics on Gliese 229D are also illustrated in Figure 2.. where the filled circles with dotted lines indicate the quenched CO abundance for each value of A...," The results from our updated time-scale approach for CO quenching kinetics on Gliese 229B are also illustrated in Figure \ref{figure:monoxide}, where the filled circles with dotted lines indicate the quenched CO abundance for each value of $K_{zz}$."
 In each case. the abundance estimated [rom (he Gine-scale approach shows good agreement will (he results from the full thermochemical kineties and diffusion model (see Table 1)).," In each case, the abundance estimated from the time-scale approach shows good agreement with the results from the full thermochemical kinetics and diffusion model (see Table \ref{tab: CO quench}) )."
 We therefore conclude that the üime-scale approach provides a simple vel accurate method to describe the quench behavior of CO in the atmospheres of T. dwarls such as Gliese 229B provided (hat a reasonable rate limiting step and appropriate rate coefficient are used for caleulating Το. aud that the vertical mixing length scale £L advocated by Smith(1993). is used for calculating τε.," We therefore conclude that the time-scale approach provides a simple yet accurate method to describe the quench behavior of CO in the atmospheres of T dwarfs such as Gliese 229B — provided that a reasonable rate limiting step and appropriate rate coefficient are used for calculating $\tau_{chem}$, and that the vertical mixing length scale $L$ advocated by \citet{smith1998} is used for calculating $\tau_{mix}$."
" Nolte that because several plausible CO—CI, rate-limiting reactions tend (o quench in the sanie vicinity. quenching investigations using the approach of Smith(1998) (o estimate L eive results similar (ο what would be expected from our kinetics aud diffusion moclels (e.e..Cooper&Showman2006:Saumonetal.2006.2007:Geballe 2009)."," Note that because several plausible $\textrm{CO} \rightarrow \textrm{CH}_{4}$ rate-limiting reactions tend to quench in the same vicinity, quenching investigations using the approach of \citet{smith1998} to estimate $L$ give results similar to what would be expected from our kinetics and diffusion models \citep[e.g.,][]{bezard2002,cooper2006,saumon2006,saumon2007,geballe2009}."
. For some brown cdwarls. these models (e.g..Saumonetal.2006.2007:Geballe2009) indicate more slugeish mixing (ie.. lower A.. values) near the CO quench level than what our results suggest here for Gliese 229D. The updated time-scale arguments also seem to be appropriate lor describing the quenching ol methane on IID 189733b.," For some brown dwarfs, these models \citep[e.g.,][]{saumon2006,saumon2007,geballe2009} indicate more sluggish mixing (i.e., lower $K_{zz}$ values) near the CO quench level than what our results suggest here for Gliese 229B. The updated time-scale arguments also seem to be appropriate for describing the quenching of methane on HD 189733b."
 Figure 3. shows some results from the thermochemical kinetics and diffusion mocleling of Mosesetal.(2011). for an assumed. solar-metallicity gas and variable assumptions about the rate of vertical transport (characterized by A. values from, Figure \ref{figure:methane} shows some results from the thermochemical kinetics and diffusion modeling of \citet{moses2011} for an assumed solar-metallicity gas and variable assumptions about the rate of vertical transport (characterized by $K_{zz}$ values from
"catalogs of theCoDECS simulations (2) which includes the very same EXP002, EXP003 and SUGRAO003 models investigated in the present work.","catalogs of the simulations \citep[][]{CoDECS} which includes the very same EXP002, EXP003 and SUGRA003 models investigated in the present work."
" The simulations have been performed using the modified version by ? of the parallel Tree-PM N-body code (?),, that implements all the characteristic features of cDE models described above."," The simulations have been performed using the modified version by \citet{Baldi_etal_2010} of the parallel Tree-PM N-body code \citep{gadget-2}, that implements all the characteristic features of cDE models described above."
" We refer to the website for an extensive description of the numerical setup of the simulations, and we recall here only their main features."," We refer to the website for an extensive description of the numerical setup of the simulations, and we recall here only their main features."
" The ACDM-L, EXP002-L, EXP003-L, and SUGRAO003-L simulations of the database that are considered in the present work consist of a cosmological box with a size of 1 comoving Gpc/h and periodic boundary conditions, filled with 1024? CDM particles with a mass of me=5.8410? Mo/h, and with 1024? baryonic particles with a mass of m,=1.17x107° Mo/h."," The $\Lambda $ CDM-L, EXP002-L, EXP003-L, and SUGRA003-L simulations of the database that are considered in the present work consist of a cosmological box with a size of $1$ comoving $/h$ and periodic boundary conditions, filled with $1024^{3}$ CDM particles with a mass of $m_{c}=5.84\times 10^{10}$ $_{\odot}/h$, and with $1024^{3}$ baryonic particles with a mass of $m_{b}=1.17\times 10^{10}$ $_{\odot}/h$."
" Initial conditions are generated by perturbing a homogeneous distribution (?) in order to set up a random-phase realization of the initial linear matter power spectrum which is taken to be the spectrum computed by the publicly available code CAMB (?,www.camb.info) at the starting redshift of the simulations zi,=99 for the WMAP7 parameters specified in Table 1.."," Initial conditions are generated by perturbing a homogeneous distribution \citep{White_1994} in order to set up a random-phase realization of the initial linear matter power spectrum which is taken to be the spectrum computed by the publicly available code CAMB \citep[][www.camb.info]{camb}
 at the starting redshift of the simulations $z_{i}=99$ for the WMAP7 parameters specified in Table \ref{tab:parameters}."
 A common normalization of the linear perturbations amplitude atZcMB consistent with present WMAPT7 constraints is imposed to all the simulations by properly rescaling the particles displacement between zomp and z; with the specific growth factors numerically computed for each cosmology., A common normalization of the linear perturbations amplitude at$z_{\rm CMB}$ consistent with present WMAP7 constraints is imposed to all the simulations by properly rescaling the particles displacement between $z_{\rm CMB}$ and $z_{i}$ with the specific growth factors numerically computed for each cosmology.
 This procedure makes the runs more suitable to realistically quantify the impact of cDE on the halo mass function with respect to previous attempts (ase.g.by?) where a common normalization at the starting redshift of the simulations was assumed., This procedure makes the runs more suitable to realistically quantify the impact of cDE on the halo mass function with respect to previous attempts \citep[as \eg by][]{Baldi_Pettorino_2011} where a common normalization at the starting redshift of the simulations was assumed.
 A more accurate quantitative determination of the number counts deviation from ACDM can therefore be expected by using the halo catalogs., A more accurate quantitative determination of the number counts deviation from $\Lambda $ CDM can therefore be expected by using the halo catalogs.
" These are obtained by running a Friends-of-Friends (FoF) algorithm with linking length ὁ--0.2xd, where d is the mean interparticle separation."," These are obtained by running a Friends-of-Friends (FoF) algorithm with linking length $\ell = 0.2 \times \bar{d}$, where $\bar{d}$ is the mean interparticle separation."
" Since theCoDECS runs include both CDM and baryonic particles, the halo catalogs are compiled by running the FoF algorithm on the CDM particles as primary tracers and then linking the baryonic particles to the FoF group of their closest CDM neighbor."," Since the runs include both CDM and baryonic particles, the halo catalogs are compiled by running the FoF algorithm on the CDM particles as primary tracers and then linking the baryonic particles to the FoF group of their closest CDM neighbor."
 It is also important to stress here that all the simulations are started with the same initial linear transfer function and with the same random seed for the realization of the matter power spectrum in the initial conditions., It is also important to stress here that all the simulations are started with the same initial linear transfer function and with the same random seed for the realization of the matter power spectrum in the initial conditions.
" Having at hand all theCoDECS FoF halo catalogs, it is possible to compute the cumulative halo mass function for each of the models under discussion at different redshifts and to compare their relative evolution."," Having at hand all the FoF halo catalogs, it is possible to compute the cumulative halo mass function for each of the models under discussion at different redshifts and to compare their relative evolution."
 This is shown in the three panels of Fig., This is shown in the three panels of Fig.
" 6 for three choices of redshift, namely z=2.5, z=1.6 and z=0."," \ref{fig:massfunction} for three choices of redshift, namely $z=2.5$, $z=1.6$ and $z=0$."
" For convenience, the mass functions are plotted by binning halos into 15 logarithmically equispaced mass bins over the whole mass range covered by the sample at each redshift."," For convenience, the mass functions are plotted by binning halos into 15 logarithmically equispaced mass bins over the whole mass range covered by the sample at each redshift."
" As one can clearly see from the Figure, at redshifts as high as z—2.5 all the cDE models show a larger number density of halos with respect to ACDM over the whole mass range covered by the catalogs."," As one can clearly see from the Figure, at redshifts as high as $z=2.5$ all the cDE models show a larger number density of halos with respect to $\Lambda $ CDM over the whole mass range covered by the catalogs."
" This effect was already shown in the past by ? but the results of the simulations significantly extend its validity to higher masses, besides providing a more realistic quantitative determination of the overall effect thanksto"," This effect was already shown in the past by \citet {Baldi_Pettorino_2011}
 but the results of the simulations significantly extend its validity to higher masses, besides providing a more realistic quantitative determination of the overall effect thanksto"
he polvtropic iudex. | = 3) fluids generate eravitational waves with 4)) longer waveleneths han [=5/5.,"the polytropic index, but $\Gamma=2$ $\Gamma=3$ ) fluids generate gravitational waves with ) longer wavelengths than $\Gamma=5/3$."
 We cannot quantity the burst duration as casily since he late time solutions can be iuaccurate due to buildup of wmunerical errors. aud sensitivity to computational xuanieters (e.e.. Courant factor. artificial viscosity constants).," We cannot quantify the burst duration as easily since the late time solutions can be inaccurate due to buildup of numerical errors, and sensitivity to computational parameters (e.g., Courant factor, artificial viscosity constants)."
 Ilowever. a comparison of Figures 7 9 clearly shows a leugtheuiung of the pulse duration o» iuore than as the models erow stiffer.," However, a comparison of Figures \ref{fig:gw53} -- \ref{fig:gw30} clearly shows a lengthening of the pulse duration by more than as the models grow stiffer."
 Such )dliavior was observed also dy Houser&Ceutrella(1996) and Williams&Tolline(1988). iu their unnuagnotized studies: stiffer polvtropes produce more elongated bars. rotate more slowly. aud undergo more periods of spiral arm ejection aud core recontraction. resulting in longer bursts of eravitational wave signals.," Such behavior was observed also by \citet{houser96} and \citet{williams88} in their unmagnetized studies: stiffer polytropes produce more elongated bars, rotate more slowly, and undergo more periods of spiral arm ejection and core recontraction, resulting in longer bursts of gravitational wave signals."
 The addition of toroidal magnetic fields to the stellar profile does not appear to affect these behaviors appreciably as the burst duration is generally shorter than the timescale ty for naguctic braking to take effect: fp~wefey2 25-50 dviauuical (code) units at the field saturation time for all of the cases we have considered., The addition of toroidal magnetic fields to the stellar profile does not appear to affect these behaviors appreciably as the burst duration is generally shorter than the timescale $t_B$ for magnetic braking to take effect: $t_B \sim \varpi_E/v_A \gtrsim$ 25-50 dynamical (code) units at the field saturation time for all of the cases we have considered.
 Unlike the cases which start from initially toroidal magnetic field configurations. simulations performed of liiolels which begin with poloical fields evolve dierently than uninaegnetize Cases if the initial field azitucle is laveο," Unlike the cases which start from initially toroidal magnetic field configurations, simulations performed of models which begin with poloidal fields evolve differently than unmagnetized cases if the initial field amplitude is large."
", In particular. we found little qualitative difference between all the toroidal caculatious at both low (61°) aud Μο] (96°) exi resolutions. regardless of iniial field auplitude."," In particular, we found little qualitative difference between all the toroidal calculations at both low $64^3$ ) and high $96^3$ ) grid resolutions, regardless of initial field amplitude."
" For this reason. al of the results preseuted in Section Alo conmesponuded low-resolution Cases, with the added advantage of alowing for nuuiv cüffereut paraΠΟΤΟ combinations to be investigated."," For this reason, all of the results presented in Section \ref{subsec:torresults} corresponded to low-resolution cases, with the added advantage of allowing for many different parameter combinations to be investigated."
 However. for the poloidal cases. we observed an increased. sesitivity to spatial resolution as well as a exwine nupact on bur ornation with increasing feld strength. especially for the two largest anuplitude cases (POS:3B1O00 and DPG53D1ü).," However, for the poloidal cases, we observed an increased sensitivity to spatial resolution as well as a growing impact on bar formation with increasing field strength, especially for the two largest amplitude cases (PG53B100 and PG53B10)."
 All poloida results presented/ im this section are therefore shown at uch 96°) exid resolution., All poloidal results presented in this section are therefore shown at high $96^3$ ) grid resolution.
 To illustrate the effect of the maguetic field on |2111) formation. Figure 10 xlows nuages of the mass density (for the C53DIufIIBR. case) aud maenetic pressure (for the Cases POS3BLOOTIR wit LOBanin=100. and PCS3BLOTIR with Bain= 10). alli1i the equatorial plane.," To illustrate the effect of the magnetic field on bar formation, Figure \ref{fig:pimages} shows images of the mass density (for the G53BInfHR case) and magnetic pressure (for the cases PG53B100HR with $\beta_\mathrm{B,min}=100$, and PG53B10HR with $\beta_\mathrm{B,min}=10$ ), all in the equatorial plane."
 All three sets of iniages display the same contour levels of the mass deusity (0.5. 0.05. 0.005. and 0.00093. normalized to the initial maxi mass ¢CLSITY Priax.o- T," All three sets of images display the same contour levels of the mass density (0.5, 0.05, 0.005, and 0.0009), normalized to the initial maximum mass density $\rho_\mathrm{max,0}$."
hinaees 1iaklius up the left column for the case without a magnetic field are shown vat fines f —15. 17. and 21: imaees di the center colunin are shown for case PGD53DBIO00IIR at times f =17. 19.:mid 23 and images in the right οςuui are shown for case POS:SBIOTIR at times t=15. i. alvd 19. all in duanical (code) uuits.," Images making up the left column for the case without a magnetic field are shown at times $t=$ 15, 17, and 21; images in the center column are shown for case PG53B100HR at times $t=$ 17, 19, and 23; and images in the right column are shown for case PG53B10HR at times $t$ =15, 17, and 19, all in dynamical (code) units."
 The PCGC53DB1XIIR Huages are showi af later times than those for the ταinaenetized Cas| to illustrate that a bar formis wit Laslape sinülar to the no-fiehdl case. but delaved approximately two duaical times.," The PG53B100HR images are shown at later times than those for the unmagnetized case to illustrate that a bar forms with a shape similar to the no-field case, but delayed approximately two dynamical times."
 For the higher macetic Ἡeld streusth run. PCS3BLOTIR. there is no iudicatio1 tha a structure lesewibling a bar is goiug to formu at his resolutiou. a poiut woe return to beQW.," For the higher magnetic field strength run, PG53B10HR, there is no indication that a structure resembling a bar is going to form at this resolution, a point we return to below."
" The effect of an initially poloida maeuctic field oll the erowth of he bar mode Is quantified nu the ο anplitudes |,deo €1uputed as described above iu Se‘tion 3Jl."," The effect of an initially poloidal magnetic field on the growth of the bar mode is quantified in the nonaxisymmetric amplitudes $|A_m|$, computed as described above in Section \ref{subsec:torresults}."
" Tn Figures 11. and 12.. we plot the evolution of he : f the n=2 aud m={ τος». respectively, for runs EETCU!53DBIuflIR. PG53D500IIR. POS3BLOOUR. and PG53DBIOIIR."," In Figures \ref{fig:polmode53-2} and \ref{fig:polmode53-4}, we plot the evolution of the amplitudes $|A_m|$ of the $m=2$ and $m=4$ modes, respectively, for runs G53BInfHR, PG53B500HR, PG53B100HR, and PG53B10HR."
 It is apparent that for the lowest field. case (POHS3BhS00TIR}.," It is apparent that for the lowest field case (PG53B500HR),"
The brightness of the OT of GRB 091127 was measured using seeine-matchecl aperture photometry relative to a set of on-chip. nonvariable sources.,"The brightness of the OT of GRB 091127 was measured using seeing-matched aperture photometry relative to a set of on-chip, nonvariable sources."
 Relative magnitudes were converted (to apparent magnitudes by comparison. on a photometric night. with Rabin 149 Landolt standard stars (Lanclolt1992).," Relative magnitudes were converted to apparent magnitudes by comparison, on a photometric night, with Rubin 149 Landolt standard stars \citep{L92}."
. In addition to the relative measurement error. (here is a svstematic error of 0.05 mag associated wilh the uncertainties in (tliis photometric calibration.," In addition to the relative measurement error, there is a systematic error of 0.05 mag associated with the uncertainties in this photometric calibration."
 All photometry in this paper is corrected for a Galactic reddening of mag (Schlegeletal.1993)., All photometry in this paper is corrected for a Galactic reddening of $E_{B-V}=0.038$ mag \citep{Schlegel+98}.
. We obtained images of GRB 091127 using GMOS on the 8-m Genuni-South telescope., We obtained images of GRB 091127 using GMOS on the 8-m Gemini-South telescope.
 Five epochs of GMOS αμα imaging were obtained between 9 ancl 102 days post-burst (see Table 1)., Five epochs of GMOS $i'$ -band imaging were obtained between 9 and 102 days post-burst (see Table 1).
 Each set of Gemini images consisted of dithered exposures reduced and combined using the standard IRAF package., Each set of Gemini images consisted of dithered exposures reduced and combined using the standard IRAF package.
 seeing-matched. relative aperture photometry was performed on the OT of GRB 091127.," Seeing-matched, relative aperture photometry was performed on the OT of GRB 091127."
 The relative to apparent magnitude transformation utilized (wo stars common to both the SMARTS and Gemini images., The relative to apparent magnitude transformation utilized two stars common to both the SMARTS and Gemini images.
 The /-band apparent magnitudes of the stus were determined with the SDSS transformation equations of Jordietal.(2006)RITransform.htmlgtJordi2006... utilizing the stars’ Z- and H-band SATARTS magnitudes.," The $i'$ -band apparent magnitudes of the stars were determined with the SDSS transformation equations of \cite{Jordi+06}, utilizing the stars' $I$ - and $R$ -band SMARTS magnitudes."
 These Gemini /-band magnitudes were then transformed back into the Z-band to match the SALARTS photometric svstem., These Gemini $i'$ -band magnitudes were then transformed back into the $I$ -band to match the SMARTS photometric system.
 While these transformations may introduce some svstematic error into the Gemini photometry. thev do not affect the relative magnitudes.," While these transformations may introduce some systematic error into the Gemini photometry, they do not affect the relative magnitudes."
 The match between SMIARTS and Gemini values nueasured al similar epochs suggests that no significant error has been introduced., The match between SMARTS and Gemini values measured at similar epochs suggests that no significant error has been introduced.
 ISIS (Alard2000) kernel-convolved image subtraction was carried out on the Gemini images (Fig., ISIS \citep{Alard00} kernel-convolved image subtraction was carried out on the Gemini images (Fig.
 2)., 2).
 The image obtained 102 clavs post-burst was used as (he subtraction reference rame., The image obtained 102 days post-burst was used as the subtraction reference frame.
 Residual light is evident in each subtracted frame. indicating that the OT was cdimmest in (he final image.," Residual light is evident in each subtracted frame, indicating that the OT was dimmest in the final image."
 This is expected. of course. if the earlier images contain afterglow light.," This is expected, of course, if the earlier images contain afterglow light."
 llowever. both the image subtraction aud (he photometry indicate that the transient. by 0.063:0.02 mag between 9 and 15 days post-burst.," However, both the image subtraction and the photometry indicate that the transient by $0.06\pm0.02$ mag between 9 and 18 days post-burst."
 As described in 833. we interpret (his briehtening to indicate the presence of an underlying GRB-SN.," As described in 3, we interpret this brightening to indicate the presence of an underlying GRB-SN."
 UVOT observations of GRB 091127 began on 2009 Nov. 28 al 00:19:29. 53.65 min alter," UVOT observations of GRB 091127 began on 2009 Nov. 28 at 00:19:29, 53.65 min after"
maegnetogranms kurtosis. A. and properties of the elements ,"magnetogram's kurtosis, $K_0$, and properties of the elements n = (1 - )^2."
llaving found the densitv. expression (4.1)) can be used to find the root-mean-square (rms) amplitude of the flux. (03!," Having found the density, expression \ref{eq:sig_subpole}) ) can be used to find the root-mean-square (rms) amplitude of the flux, $\avg{\phi^2}^{1/2}$."
 Using the above reasoning we mav model a quiet sun magnetogram as a combination ol Gaussian white noise and a random distribution of [ιν elements., Using the above reasoning we may model a quiet sun magnetogram as a combination of Gaussian white noise and a random distribution of flux elements.
 The magnetogram in relfig:mgbb. for example. has à power spectrum which. after removal of white noise. fits an exponential S(&)ee.2/4. with dzz2.2 Mm.," The magnetogram in \\ref{fig:mg}b b, for example, has a power spectrum which, after removal of white noise, fits an exponential $S(k)\sim e^{-2kd}$, with $d\simeq 2.2$ Mm."
" The magnetogram has a standard. deviation ση=15.8 G. only o,,=8.8 G of which comes from white noise."," The magnetogram has a standard deviation $\sigma_0=15.8$ G, only $\sigma_n=8.8$ G of which comes from white noise."
 Assuming an exponential distribution of flux amplitudes (£= 6) the kurtosis. Ay=38. implies a [αν element density. i=0.0039Mam.7. from ((4.1)).," Assuming an exponential distribution of flux amplitudes $\xi=6$ ) the kurtosis, $K_0=38$, implies a flux element density, $n=0.0039\,{\rm Mm}^{-2}$, from \ref{eq:n_from_K}) )."
 Equation (4.1)) then gives the rms flux. CUN—23x10! Mx.," Equation \ref{eq:sig_subpole}) ) then gives the rms flux, $\avg{\phi^2}^{1/2}=2.3\times 10^{19}$ Mx."
 The exponential flux. distribution and zero mean value can be used to convert the rms to (όλ=1.6x10! AIx., The exponential flux distribution and zero mean value can be used to convert the rms to $\avg{|\phi|}=1.6\times10^{19}$ Mx.
 Figure HHaa shows a magnetogram svithesized [rom the distribution of sources described above., Figure \ref{fig:synth_cmp}a a shows a magnetogram synthesized from the distribution of sources described above.
 Its parameters were chosen to resemble the five-minute average low resolution magnetogram of Ibb. and the two have indisünguishable power spectra relfig:svnthanpbb).," Its parameters were chosen to resemble the five-minute average low resolution magnetogram of \ref{fig:mg}b b, and the two have indistinguishable power spectra \\ref{fig:synth_cmp}b b)."
 T hestandarddeviationandkurlosisoflhesyntheliemagnelogrem.ay =10.1 G and Ay39. are well matched to the original.," The standard deviation and kurtosis of the synthetic magnetogram, $\sigma_0=16.1$ G and $K_0=39$, are well matched to the original."
" Correcting the spectrum for an MTE with (4=1.6"" leads to à more narrowly peaked element. f(r). whose radius is r,=2.1 Mm and which has 4=13.2 (compared to Mm and \=6.4 without correction: see relfig:shape))."," Correcting the spectrum for an MTF with $\ell_0=1.6''$ leads to a more narrowly peaked element, $f(r)$, whose radius is $r_*=2.1$ Mm and which has $\chi=13.2$ (compared to $r_*=\sqrt{2}d=3.1$ Mm and $\chi=6.4$ without correction; see \\ref{fig:shape}) )."
 These more peaked elements must be distributed with greater areal density and smaller mean flux in order to mateh the observed kurtosis and standard. deviation: n=0.016Mm.7? and (joj)=5.6x105 Mx.," These more peaked elements must be distributed with greater areal density and smaller mean flux in order to match the observed kurtosis and standard deviation: $n=0.016\,{\rm Mm}^{-2}$ and $\avg{|\phi|}=5.6\times10^{18}$ Mx."
 The instruments point spread function blurs, The instrument's point spread function blurs
respectively.,respectively.
 When caleulating 47. we introduce intrinsic scatter into equation (5)) so that the reduced us of the best fit model is unity., When calculating $\chi^2$ we introduce intrinsic scatter into equation \ref{plane}) ) so that the reduced $\chi^2$ of the best fit model is unity.
 We find a smaller intrinsic scatter (o.=1.27d0.04 Alpe) in the simulated data. indicating that sight-line. variation is not responsible for all of the observed scatter (ση=1.86d 0.06).," We find a smaller intrinsic scatter $\sigma_{\rm sim}=1.27\pm0.04$ Mpc) in the simulated data, indicating that sight-line variation is not responsible for all of the observed scatter $\sigma_{\rm
 obs}=1.86\pm0.06$ )."
 While the simulations reproduce the size evolution with redshift. the luminosity dependence is not well described. with D~2 for the simulations (equation 4)) but LB~3 for the observed sample.," While the simulations reproduce the size evolution with redshift, the luminosity dependence is not well described, with $B\sim2$ for the simulations (equation \ref{nz}) ) but $ B\sim3$ for the observed sample."
 Phere are (wo explanations for this disagreement between the data and fiducial model which we now discuss in turn., There are two explanations for this disagreement between the data and fiducial model which we now discuss in turn.
 Firstly. the observed value of 2B=3 is expected if the quasars were surrounded by LIE regions. embedded. in a neutral IGM (2).," Firstly, the observed value of $B=3$ is expected if the quasars were surrounded by HII regions embedded in a neutral IGM \citep{cen2000}."
 Naivels. this could be interpreted as evidence for a significantly neutral LGAL," Naively, this could be interpreted as evidence for a significantly neutral IGM."
 To test this. we calculate the expected scatter in the near-zone relation for comparison with observation.," To test this, we calculate the expected scatter in the near-zone relation for comparison with observation."
 In. contrast to the case for à. proximity zone in an optically thin LGA. the size of an LLL region depends on the age of the quasar at the time of observation.," In contrast to the case for a proximity zone in an optically thin IGM, the size of an HII region depends on the age of the quasar at the time of observation."
" As a result. there is scatter in the observed. size even [or fixed. redshift, ancl quasar luminosity."," As a result, there is scatter in the observed size even for fixed redshift and quasar luminosity."
 We can estimate the scatter clue to the age of the quasars by noting that if there is equal probability of observing a quasar at any age during its lifetime. then the probability clistribution for the LIL region radius at fixed. luminosity £ and redshift z. given a quasar lifetime fua. Ls where A44 is the size reached after fas.," We can estimate the scatter due to the age of the quasars by noting that if there is equal probability of observing a quasar at any age during its lifetime, then the probability distribution for the HII region radius at fixed luminosity $L$ and redshift $z$, given a quasar lifetime $t_{\rm max}$, is where $R_{\rm max}$ is the size reached after $t_{\rm max}$."
 Giventhis distribution. the mean is Ην)=3/4Aus. ancl the variance is op—diRyo=INI195.," Giventhis distribution, the mean is $\langle R_{\rm p}\rangle=3/4\,R_{\rm
 max}$, and the variance is $\sigma_R^2\equiv\langle R_{\rm
 p}^2\rangle - \langle R_{\rm p}\rangle^2 = \langle R_{\rm
 p}\rangle^2/15$."
 Observationally. since we have QI)~ReyS Ape. the scatter in HIE region radius owing to random quasar age is 05;2 Alpe.," Observationally, since we have $\langle R_{\rm
 p}\rangle\sim R_{27}\sim8$ Mpc, the scatter in HII region radius owing to random quasar age is $\sigma_R\sim2$ Mpc."
" Thus the scatter in observed. quasar age accounts for all of the observed scatter (0,5;=1.863 0.06) in the near-zone sizes.", Thus the scatter in observed quasar age accounts for all of the observed scatter $\sigma_{\rm obs}=1.86\pm 0.06$ ) in the near-zone sizes.
 Llowever in the case of LILLE regions we would. also expect additional scatter in the size owing to other quantities like the quasar lifetime and the spectral index (we return to this point below). as well as scatter due to inhomogeneities in the density field and ionization structure along the dillerent quasar sight-lines.," However in the case of HII regions we would also expect additional scatter in the size owing to other quantities like the quasar lifetime and the spectral index (we return to this point below), as well as scatter due to inhomogeneities in the density field and ionization structure along the different quasar sight-lines."
 In the case of the latter. the sizes of HILL regions near the end of reionization (7) are thought to vary over the range 1-2 proper Alpe. which would. lead. to a component of scatter in addition to the ~2 Mpe expected from the quasar age.," In the case of the latter, the sizes of HII regions near the end of reionization \citep{furlanetto2004} are thought to vary over the range 1-2 proper Mpc, which would lead to a component of scatter in addition to the $\sim2\,$ Mpc expected from the quasar age."
 Phus. the total scatter in an LL region e&enerated. near-zone relation would be in excess of ap~3 Alpe.," Thus, the total scatter in an HII region generated near-zone relation would be in excess of $\sigma_R\sim3$ Mpc."
 We therefore infer that although quasar HIE regions would. lead. to a near-zone relation with the appropriate value of B3. the observed relation between near-zone size and magnitude would be too tight in this case.," We therefore infer that although quasar HII regions would lead to a near-zone relation with the appropriate value of $ B\sim3$, the observed relation between near-zone size and magnitude would be too tight in this case."
 This scatter based. constraint would be alleviated if the near-zone sizes corresponded to resonant absorption within an LUE region (the scatter would be smaller since the size is independent of lifetime in this case)., This scatter based constraint would be alleviated if the near-zone sizes corresponded to resonant absorption within an HII region (the scatter would be smaller since the size is independent of lifetime in this case).
 However. in this alternative case where resonant absorption sets the near-zone size. our modelling suggests that D—2 rather than D—3 should be observed.," However, in this alternative case where resonant absorption sets the near-zone size, our modelling suggests that $ B\sim2$ rather than $ B\sim3$ should be observed."
 As a result. LUE regions cannot provide a viable physical explanation for the observational data (seealso?)..," As a result, HII regions cannot provide a viable physical explanation for the observational data \citep[see also][]{maselli2009}."
 An alternative scenario to explain this trend. is. provided by an EUV spectral index which is luminosity dependent. so that at brighter absolute magnitudes the ionizing Lux is smaller.," An alternative scenario to explain this trend is provided by an EUV spectral index which is luminosity dependent, so that at brighter absolute magnitudes the ionizing flux is smaller."
 To quantify this point. we first note that the observed. quantities are the near-zone size and the absolute UV magnitude.," To quantify this point, we first note that the observed quantities are the near-zone size and the absolute UV magnitude."
 Given this UV magnitude. the ionization properties of the surrounding medium are dependent. on the ionizing luminosity in photons per second (CN). and the spectral index bIueward of the Lyman break.," Given this UV magnitude, the ionization properties of the surrounding medium are dependent on the ionizing luminosity in photons per second $\dot{N}$ ), and the spectral index blueward of the Lyman break."
" The relation between IN and à is where ρε, is the luminosity at the Lyman limit vy. h is Planck's constant and rugas ds the ratio between the frequeney where photons cease to contribute to ionization"," The relation between $\dot{N}$ and $\alpha$ is where $L_{\nu_{\rm Ly}}$ is the luminosity at the Lyman limit $\nu_{\rm Ly}$ , $h$ is Planck's constant and $x_{\rm max}$ is the ratio between the frequency where photons cease to contribute to ionization"
also possible.,also possible.
 Tn order to study the response of au accretion disk to an external perturbation. we make several siiuplifving assumptions.," In order to study the response of an accretion disk to an external perturbation, we make several simplifying assumptions."
 The first is to consider rot a full accretion disk but a slender torus in wdrostatic equilibrium. orbiting a central body of mass AL.," The first is to consider not a full accretion disk but a slender torus in hydrostatic equilibrium, orbiting a central body of mass $M$."
 By virtue of the pressure effects. he rotation curve is not Keplerian.- and for all he cases studied here. we consider constant distributions of specific augular momenta witlin he torus. which has low mass and is sleuder iu he sense that its mass a<M. aud its exteusiou L«R. where BR ids the distance separating it roni the mass AM.," By virtue of the pressure effects, the rotation curve is not Keplerian, and for all the cases studied here, we consider constant distributions of specific angular momentum within the torus, which has low mass and is slender in the sense that its mass $m \ll M$, and its extension $L \ll R$, where $R$ is the distance separating it from the mass $M$."
 We thus neglect the self.exavity of the torus. which is ellipsoidal iu cross section ii a qericional slice.," We thus neglect the self–gravity of the torus, which is ellipsoidal in cross section in a meridional slice."
 We additionally assume azimuthal sxainetry., We additionally assume azimuthal symmetry.
" The second asstuuption is to use a poteutial for the central πάν» Qj;=ALLexptrissfr)]£riis (Kluzuiak&Lee2002). which reproduces two features of Einstein's gravitv that are relevant in our context: (1) there is a marginallv stable orbit for test masses m circular orbits at ry). GAL. aud (2) the vertical aud radial epicvclic frequencies Gu the equatorial plane) are given by Cr)=απ]ορ] and ir)=(1/lay?(ArPyeoxpllarsDltins fr). respectively, so that their ratio is &(r)/Q(r)=(1ringr). coinciding with the exact solution in the Sclnvarzschild metric in general relativity."," The second assumption is to use a potential for the central mass $\Phi_{KL}=M[1-\exp(r_{ms}/r)]/r_{ms}$ \citep{kl02}, which reproduces two features of Einstein's gravity that are relevant in our context: (1) there is a marginally stable orbit for test masses in circular orbits at $r_{ms}=6M$ , and (2) the vertical and radial epicyclic frequencies (in the equatorial plane) are given by $\zeta^{2}(r)=(1/4\pi)^{2}(M/r^{3})\exp(r_{ms}/r)$ and $\kappa^{2}(r)=(1/4\pi)^{2}(M/r^{3})\exp(r_{ms}/r)(1-r_{ms}/r)$ , respectively, so that their ratio is $\kappa(r)/\zeta(r)=(1-r_{ms}/r)^{1/2}$, coinciding with the exact solution in the Schwarzschild metric in general relativity."
" Iu lvdrostatic equilibria. pressure and centrifugal support balance egravitv in the radial direction. and pressure alone balances eravity vertically,"," In hydrostatic equilibrium, pressure and centrifugal support balance gravity in the radial direction, and pressure alone balances gravity vertically."
 Au ideal equation of state for the fluid closes the system of equations (we have used an adiabatic index 5=1/3 throughout)., An ideal equation of state for the fluid closes the system of equations (we have used an adiabatic index $\gamma=4/3$ throughout).
 The center of the onus can be conveniently defined as the locus of naxinmni deusitv. where the rotation velocity is Iseplerian. aud its position is denoted by ry.," The center of the torus can be conveniently defined as the locus of maximum density, where the rotation velocity is Keplerian, and its position is denoted by $r_{0}$."
 Clearly a detailed answer to the eeueral problem. cine explored here requires modeling of the full accretion disk. whether it is eceometrically thin or thick.," Clearly a detailed answer to the general problem being explored here requires modeling of the full accretion disk, whether it is geometrically thin or thick."
 We will explore this in future work., We will explore this in future work.
 For he time being. analyzing the behavior of such a xleuder torus can be cousidered analogous to splitting the disk iuto thin annuli and investigating the propertics of one such ring as du analysis of vacationinduced warping (Petterson1977:Pringle1996).," For the time being, analyzing the behavior of such a slender torus can be considered analogous to splitting the disk into thin annuli and investigating the properties of one such ring — as in analysis of radiation–induced warping \citep{petterson77,pringle96}."
. The slender torus can be thought of as a density cuhancement in the accretion disk. the properties of which might be transmitted andor wuplified iuto the overall Xrav light curve observed fom je system by au uspecified 1uechauisu.," The slender torus can be thought of as a density enhancement in the accretion disk, the properties of which might be transmitted and/or amplified into the overall X–ray light curve observed from the system by an unspecified mechanism."
 The actualtori are constructed from the specified eravitationa potential and equation of state in standard fashion (see c.g. (Egumnenshicliev.Chen&Abramiowicz1996:ZurekDeuz 1986))). and them dvuamica behavior (see below) is followed using a twodimensional smooth particle lvdvodvuamies (SPII) code (Alonaghan1992: that uses evliudrical coordinates (r7.:).," The actualtori are constructed from the specified gravitational potential and equation of state in standard fashion (see e.g. \citep{ica96,zb86}) ), and their dynamical behavior (see below) is followed using a two–dimensional smooth particle hydrodynamics (SPH) code \citep{monaghan92,lrr02} that uses cylindrical coordinates $(r,z)$."
 A cross section (in density) of an equilibrium configuration thus realized is shown in Fie. 1.., A cross section (in density) of an equilibrium configuration thus realized is shown in Fig. \ref{torusIC}.
 We now detail the results obtained from using two different types of perturbations to such au initial state., We now detail the results obtained from using two different types of perturbations to such an initial state.
 As a first example. we consider an impulsive perturbation to the torus. analogous to that considered recently bv Zanotti.Rezzolla&Fout (2003).. (," As a first example, we consider an impulsive perturbation to the torus, analogous to that considered recently by \citet{zrf03}. ("
We note that these modes might also be relevant for kIIz QPOs in black hole svsteiuis: see Rezzolla.Yoshida.Maccarone&Zanotti (2003)..),We note that these modes might also be relevant for kHz QPOs in black hole systems; see \cite{rymz03}. .)
 The equilibrium torus is eiven a perturbed velocity feld at f=O and allowed to oscillate freely thereafter., The equilibrium torus is given a perturbed velocity field at $t=0$ and allowed to oscillate freely thereafter.
 The velocity field of the perturbation is purely radial (ià a cylindrical seuse)., The velocity field of the perturbation is purely radial (in a cylindrical sense).
" The kick is πα, so that the induced oscillations in the radial direction have an amplitude that is of the saleorder as the exteut of the torus itself."," The kick is small, so that the induced oscillations in the radial direction have an amplitude that is of the sameorder as the extent of the torus itself."
 The torus performs siuall oscillations im the racial direction. primarily at a frequency consistent with the local epievclie frequency Ay. as. would be expected.," The torus performs small oscillations in the radial direction, primarily at a frequency consistent with the local epicyclic frequency $\kappa_{0}$, as would be expected."
 Towever. small vertical motions are also induced owing fo pressure coupling between both modes. aud these can be clearly seen iu the vertical oscillations of the center of the torus. occurius with ereatest power at a frequency that is consistent with the local vertical epievclic frequency. cy.," However, small vertical motions are also induced owing to pressure coupling between both modes, and these can be clearly seen in the vertical oscillations of the center of the torus, occurring with greatest power at a frequency that is consistent with the local vertical epicyclic frequency, $\zeta_{0}$ ."
 Both the radial and vertical oscillations are shown in Fie. 2.. ," Both the radial and vertical oscillations are shown in Fig. \ref{RZimpulsive}, ,"
along with their Fourier trausforiis., along with their Fourier transforms.
"Pei 1995 iud the 3),=L5 models) would be ruled out at the 2c level.",Pei 1995 and the $\beta_h = 4.5$ models) would be ruled out at the $2~\sigma$ level.
" The upper right paucl shows that nearly identical constraints can be obtained by observing the four already known quasars with an aueular resolution of 0.1"". a resolution typical for observations with the (for the cases of a maxima splitting angle of 0.1"" we assumed that sufficient depth is reached that both nuages are detectable. aud did not iupose a magnitude cut. or a constraint ou the flux ratio)."," The upper right panel shows that nearly identical constraints can be obtained by observing the four already known quasars with an angular resolution of $0.1
''$, a resolution typical for observations with the (for the cases of a maximum splitting angle of $0.1 ''$ we assumed that sufficient depth is reached that both images are detectable, and did not impose a magnitude cut, or a constraint on the flux ratio)."
" Finally. the bottom rieht paucl shows that observations of 20 quasars at 0.17 resolution would enable us to put very strong constraints ou the intrinsic LF. with the current ""balbpark LFs. obtained by extrapolatio-S ch‘oun lower redshifts. ruled out at the ~σ level."," Finally, the bottom right panel shows that observations of 20 quasars at $0.1 ''$ resolution would enable us to put very strong constraints on the intrinsic LF, with the current “ball-park” LFs, obtained by extrapolations from lower redshifts, ruled out at the $\sim 3~\sigma$ level."
 Iu these examples we asstuned that no multiple images are detected., In these examples we assumed that no multiple images are detected.
 Similar calculations can of course be doue if future observations would detect oue or more multiple inages., Similar calculations can of course be done if future observations would detect one or more multiple images.
" In that case the likelihood. contours cau be closed and the parameters of the LF would be coustrained both frou, above and from below.", In that case the likelihood contours can be closed and the parameters of the LF would be constrained both from above and from below.
 To cnable interpretation of any outcome of a future search for leuses. Figure 7 shows probability contours for multiple lensing for a single +=6. D=20 quasar.," To enable interpretation of any outcome of a future search for lenses, Figure \ref{fig:contour} shows probability contours for multiple lensing for a single $z=6$, $z^*=20$ quasar."
 The curves in each of the four panels show coustaut probabilities for a lensing event detectable at four different angular resolutions (the upper right paucl assunies infinite resolution. ie. it includes all multiple lensing events).," The curves in each of the four panels show constant probabilities for a lensing event detectable at four different angular resolutions (the upper right panel assumes infinite resolution, i.e., it includes all multiple lensing events)."
 Each panel shows 8 curves. corresponding to the following probabilities (bottoni to top. iu percent): (1) Upper loft pauck: 1. 2. L 10. 20. 23. 21. 21.18: (1) Upper rieht panel: L ο. 15. 10. 80. 95. 99.3. 99.9: (1) Lower lett panel: 2. 1. 9. 20. 35. 13. ELL3. 11.55: () Lower right panel: 3. 6. 13. 33. 60. 72.5. 15.1. 75.86.," Each panel shows 8 curves, corresponding to the following probabilities (bottom to top, in percent): (i) Upper left panel: 1, 2, 4, 10, 20, 23, 24, 24.18; (i) Upper right panel: 4, 8, 15, 40, 80, 95, 99.3, 99.9; (i) Lower left panel: 2, 4, 9, 20, 35, 43, 44.3, 44.55; (i) Lower right panel: 3, 6, 13, 33, 60, 72.5, 75.4, 75.86."
" Note the ""saturation"" of the probabili&es ucar the top coutour in each panel. caused by the finite fraction of leusing eveuts that produce splittings above a given angular resolution."," Note the “saturation” of the probabilities near the top contour in each panel, caused by the finite fraction of lensing events that produce splittings above a given angular resolution."
 Varvine the intrinsic LF docs not only affect the lensing probability. but also changes the total amount of euütted quasar light. including the ionizing ciuissivity.," Varying the intrinsic LF does not only affect the lensing probability, but also changes the total amount of emitted quasar light, including the ionizing emissivity."
 Since the ioniziung backeround can i priuciple be measured. this can provide an additional constraint on the quasar LE.," Since the ionizing background can in principle be measured, this can provide an additional constraint on the quasar LF."
 Observations of the mean absorption in the a forest have been used receutlv to inter the ionizing backeround at 2~6 (Becker et al., Observations of the mean absorption in the $\alpha$ forest have been used recently to infer the ionizing background at $z\sim 6$ (Becker et al.
 2001: Con McDonald 2001: MeDonald NAiralda-Escudé 2001: Fan ot al., 2001; Cen McDonald 2001; McDonald Miralda-Escudé 2001; Fan et al.
 2002). vielding ionization rates per lydrogen atom of TowoHT/loPs+sOL.," 2002), yielding ionization rates per hydrogen atom of $\Gamma_{-12} \equiv \Gamma / 10^{-12} {\rm s}^{-1}
\approx 0.1$."
 The dashed curves in Fie., The dashed curves in Fig.
 6 show contours of fixed quasar clussivity. corresponding to Toyo=0.1 and 2 respectively.," \ref{fig:contour0} show contours of fixed quasar emissivity, corresponding to $\Gamma_{-12} = 0.1$ and 2 respectively."
 Our method for computing the ionization rate from the LF is described iu more, Our method for computing the ionization rate from the LF is described in more
The hh modulation could be caused either by an eclipse from the companion star or by the presence of à warped disk.,The h modulation could be caused either by an eclipse from the companion star or by the presence of a warped disk.
 This latter hypothesis is driven by the fact that the hh modulation in the SSS of NGC 300 was observed in only one of two observations., This latter hypothesis is driven by the fact that the h modulation in the SSS of NGC 300 was observed in only one of two observations.
 have recently reported that the X-ray binary in31.. shows regular dips at hh but not in all of their observations.," have recently reported that the X-ray binary in, shows regular dips at h but not in all of their observations."
 These authors suggested this dipping to be caused by an elongated precessing disk., These authors suggested this dipping to be caused by an elongated precessing disk.
 To summarie. the ultraluminous SSS in NGC 4631 reported in this Letter may be an X-ray binary system with a short (z hh) orbital period. where the high mass transfer rate is either due to a massive companion filling its Roche Lobe or because the system is in outburst.," To summarise, the ultraluminous SSS in NGC 4631 reported in this Letter may be an X-ray binary system with a short $\lesssim$ h) orbital period, where the high mass transfer rate is either due to a massive companion filling its Roche Lobe or because the system is in outburst."
" When matter is accreted above the Eddington rate. the excess matter Is ejected via a strong. optically-thick outflow in which case a mass of 6M, can be estimated for the black-hole companion,"," When matter is accreted above the Eddington rate, the excess matter is ejected via a strong, optically-thick outflow in which case a mass of $\text{M}_\odot$ can be estimated for the black-hole companion."
value of o to different smaller values.,value of $\alpha$ to different smaller values.
 Fig., Fig.
" 6 compares the galaxy stellar mass function resulting from alternatively considering fixed a=1.3, 1.6, and leaving a as a free parameter (cf."," \ref{fig_alph16} compares the galaxy stellar mass function resulting from alternatively considering fixed $\alpha=1.3$, 1.6, and leaving $\alpha$ as a free parameter (cf."
" Section refsec,mazml)).", Section \\ref{sec_vmaxml}) ).
" thenormalisation®* in each case has been obtained a Asbeposteriori,fore, by imposing that the integral of the stellar mass function is equal to the source number density down to the mass completeness limit."," As before, the normalisation $\Phi^\ast$ in each case has been obtained a posteriori, by imposing that the integral of the stellar mass function is equal to the source number density down to the mass completeness limit."
" Our results show that, at 3.0€z«3.5 and4.25, the best galaxy stellar mass function that we obtained with a Schechter function with fixed a=1.6 is still in a reasonable agreement with the stellar mass function computed with the 1/Vmax method."," Our results show that, at $3.0 \leq z < 3.5$ and, the best galaxy stellar mass function that we obtained with a Schechter function with fixed $\alpha=1.6$ is still in a reasonable agreement with the stellar mass function computed with the $\rm 1/V_{max}$ method."
" Instead, a fixed a=1.3 value significantly under-predicts the stellar mass function high-mass end, and at the same time over-predicts the number density of galaxies at intermediate stellar masses M—2—6x10?M5."," Instead, a fixed $\alpha=1.3$ value significantly under-predicts the stellar mass function high-mass end, and at the same time over-predicts the number density of galaxies at intermediate stellar masses $M \sim 2-6 \times 10^{10} \, \rm M_\odot$."
 These results indicate that a slope as small as a=1.3 is not adequate to describe the galaxy stellar mass function derived from our datasets., These results indicate that a slope as small as $\alpha=1.3$ is not adequate to describe the galaxy stellar mass function derived from our datasets.
" At 4.25<z«5.0, the same effect is present, although the constraints on the stellar mass function provided by our data in this redshift bin are less tight, and the case of a small o value cannot be rejected. ("," At $4.25 \leq z < 5.0$, the same effect is present, although the constraints on the stellar mass function provided by our data in this redshift bin are less tight, and the case of a small $\alpha$ value cannot be rejected. ("
See that the value a=1.3 is contained within the 20 confidence level shown in the hand panel of Fig.5)).,See that the value $\alpha=1.3$ is contained within the $\sigma$ confidence level shown in the right-hand panel of \ref{fig_mlconf}) ).
" Another test we performed to assess the robustness of a large a value consisted in restricting our ML analysis to our galaxy sample with completeness, i.e. only to sources with [4.5]<22.4 mag."," Another test we performed to assess the robustness of a large $\alpha$ value consisted in restricting our ML analysis to our galaxy sample with completeness, i.e. only to sources with $\rm [4.5] \leq 22.4$ mag."
" We only performed this test in the 3.0€z«3.5 redshift bin, where we have a sufficient number of [4.5]<22.4 galaxies as to allow both a and M* to be treated as free parameters."," We only performed this test in the $3.0 \leq z <3.5$ redshift bin, where we have a sufficient number of $\rm [4.5] \leq 22.4$ galaxies as to allow both $\alpha$ and $M^\ast$ to be treated as free parameters."
 Figure 7 shows our results., Figure \ref{fig_mf224} shows our results.
" Our maximum likelihood analysis applied only to the [4.5]<22.4 mag galaxies yields a significantly larger value of the faint-end slope, i.e. a2.4, and M*=1.8x1011Mo."," Our maximum likelihood analysis applied only to the $\rm [4.5] \leq 22.4$ mag galaxies yields a significantly larger value of the faint-end slope, i.e. $\alpha \approx 2.4$, and $M^\ast \approx 1.8 \times 10^{11} \, \rm M_\odot$."
" However, we see that the extrapolation of this stellar mass function curve would also overpredict the 1/Vmax points obtained for stellar masses lower than the strict completeness limit imposed by the [4.5]=22.4 magnitude cut."," However, we see that the extrapolation of this stellar mass function curve would also overpredict the $\rm 1/V_{max}$ points obtained for stellar masses lower than the strict completeness limit imposed by the $\rm [4.5]=22.4$ magnitude cut."
" In conclusion, our tests confirm that the galaxy stellar mass function at 3€z«5 is characterised by a high value of the slope o."," In conclusion, our tests confirm that the galaxy stellar mass function at $3 \leq z <5$ is characterised by a high value of the slope $\alpha$."
" The best slope values we obtain from our datasets are 1.8«a<2.1, but in practice somewhat more modest values such as a=1.6 could still be adequate."," The best slope values we obtain from our datasets are $1.8 < \alpha < 2.1$, but in practice somewhat more modest values such as $\alpha=1.6$ could still be adequate."
" Instead, much smaller a values as those characterising the galaxy stellar mass function at low-z can be clearly discarded."," Instead, much smaller $\alpha$ values as those characterising the galaxy stellar mass function at $z$ can be clearly discarded."
" We note that, in the Schechter function, the o value determines the slope of the stellar mass function at the faint end, but has also the role of modulating the exponential decline at M>M*."," We note that, in the Schechter function, the $\alpha$ value determines the slope of the stellar mass function at the faint end, but has also the role of modulating the exponential decline at $M \gsim M^\ast$."
" Thus, a large a value in the Schechter function is indicating the absence of a pure exponential decline at the high-mass end."," Thus, a large $\alpha$ value in the Schechter function is indicating the absence of a pure exponential decline at the high-mass end."
" This effect is particularly at play within our sample, as it mostly constrains the stellar mass function around and above M* rather than M«M*."," This effect is particularly at play within our sample, as it mostly constrains the stellar mass function around and above $M^\ast$ rather than $M \ll M^\ast$."
" In this section, we investigate in more detail the effect that the uncertainties in the zpnot and stellar mass estimates could produce on the galaxy stellar mass function."," In this section, we investigate in more detail the effect that the uncertainties in the $z_{phot}$ and stellar mass estimates could produce on the galaxy stellar mass function."
" These uncertainties are the consequence of degeneracies produced in the SED fitting, and depend on different sources of errors, including the photometric errors, the wavelength coverage, and the limited SED template grid (see e.g. Kitzbichler White 2007; Fontanot et al."," These uncertainties are the consequence of degeneracies produced in the SED fitting, and depend on different sources of errors, including the photometric errors, the wavelength coverage, and the limited SED template grid (see e.g. Kitzbichler White 2007; Fontanot et al."
 2009; Behroozi et al., 2009; Behroozi et al.
" 2010, for further discussions on this subject)."," 2010, for further discussions on this subject)."
" In particular, we focus here on the analysis of the Eddington bias (Eddington 1913), which can affect the bright end of the galaxy luminosity or stellar mass function,"," In particular, we focus here on the analysis of the Eddington bias (Eddington 1913), which can affect the bright end of the galaxy luminosity or stellar mass function,"
provides reliable. redshifts for 6.,provides reliable redshifts for 6.
 Fable 1 gives the optical positions of the galaxies. the redshifts where known. the WEPC2 / magnitudes ancl radio lluxes. and the 1105 estimates of the restframe SAd Cllz luminosities (in the form £L.) ancl corresponding SERs.," Table 1 gives the optical positions of the galaxies, the redshifts where known, the WFPC2 $I$ magnitudes and radio fluxes, and the RLK02 estimates of the restframe 8.44 GHz luminosities (in the form $\nu L_{\nu}$ ) and corresponding SFRs."
 ALL luminosities and SERs throughout are given for Ho=50 km sMpe+ and a flat Oy;=0.3. Oy=0.7 cosmology.," All luminosities and SFRs throughout are given for $H_0=50$ km $\rm s^{-1} Mpc^{-1}$ and a flat $\Omega_{M}=0.3$, $\Omega_{\Lambda}=0.7$ cosmology."
 The SERs are estimated assuming no AGN contribution to the radio flux (see Section 7.1)., The SFRs are estimated assuming no AGN contribution to the radio flux (see Section 7.1).
 The lower ancl upper values correspond respectively to the L2 5E relations of (απ (2001) and Condon (1992)., The lower and upper values correspond respectively to the $L_{rad}$ -SFR relations of Carilli (2001) and Condon (1992).
 These relations give the SER for ÀJ>SAL. strs. but here we give SItEs as totals for all masses of star. assuming an Initial Mass Function (see RLWO?P) of we=2.35 (whore urxAL *) at O.7<Al 120M.. and ae=L3 at Q.1<MO.TAL..," These relations give the SFR for $M>5M_{\odot}$ strs, but here we give SRFs as totals for all masses of star, assuming an Initial Mass Function (see RLK02) of $x=2.35$ (where ${d{\rm
N}\over d {\rm M}}\propto \rm M^{-x}$ ) at $\rm 0.7<M<120 M_{\odot}$ , and $x=1.3$ at $\rm 0.1<M<0.7 M_{\odot}$."
 The total SETts would be a factor 1.66 higher for the Salpeter LME., The total SFRs would be a factor 1.66 higher for the Salpeter IMF.
 DLINO2 give details and. plots of the spectra: important properties are brielly described. below., RLK02 give details and plots of the spectra; important properties are briefly described below.
 “Wo refers toa line equivalent width in the restframe (the observed. value divided by 1] 2)., `W' refers to a line equivalent width in the restframe (the observed value divided by $1+z$ ).
 We have no redshifts or spectra for 16V21. 16V26 or 16V30.," We have no redshifts or spectra for 16V21, 16V26 or 16V30."
 16V22 has strong emission. W(OILLI]5007)30.2A. and a high excitation (1OLD F(L3)) ratio of 2.93-E0.14. consistent with an ΤΗ galaxy.," 16V22 has strong emission, $\rm W([OIII]5007)=30.2\rm
\AA$, and a high excitation $F({\rm [OIII]})/F({\rm H\beta})$ ) ratio of $2.93\pm 0.14$, consistent with an HII galaxy."
 16V25 has moderate emission lines typical of a normal spiral. with W(OII]3727)=SSA. as do 16V31 and 16V34. with W(OLLJ5007)=6.3A and BAL respectively.," 16V25 has moderate emission lines typical of a normal spiral, with $\rm W([OII]3727)=8.8\AA$, as do 16V31 and 16V34, with $\rm
 W([OIII]5007)=6.3\AA$ and $3.4\AA$ respectively."
 For 16V31 ancl 16V34 we have excitation ratios. 0.68+0.09. and. 0.54+0.06 respectively. consistent with late-twpe or starbursting spirals but not AGN (unless obscured).," For 16V31 and 16V34 we have excitation ratios, $0.68\pm 0.09$ and $0.54\pm
 0.06$ respectively, consistent with late-type or starbursting spirals but not AGN (unless obscured)."
 16V31 also has strong H9. absorption of W= OLA. classibving it as an 'e(a) galaxy (Pogeianti and Wu 2000).," 16V31 also has strong $\rm H\delta$ absorption of $\rm W=9.1\AA$ , classifying it as an `e(a)' galaxy (Poggianti and Wu 2000)."
 S4. classed by RLKO2 as an elliptical. has moderate emission. W(OIL3727).= 7.5A. but 810. has W(OII]3727)=52.5. indicating a major starburst.," S4, classed by RLK02 as an elliptical, has moderate emission, $\rm W([OII]3727)=7.5\AA$ , but S10 has $\rm W([OII]3727)=52.5\AA$, indicating a major starburst."
 The spectral line. profiles also provided: estimates. of internal and rotationvelocities. given in RLIX02.," The spectral line profiles also provided estimates of internal and rotationvelocities, given in RLK02."
. 16V22. the only sub-L galaxy. in this sample. hac low velocities consistent with a LIL galaxy.," 16V22, the only $L^*$ galaxy in this sample, had low velocities consistent with a HII galaxy."
" Phe other five spectra all show evidence of rotation (n4,~200 km s +). consistent with OL spirals."," The other five spectra all show evidence of rotation $v_{rot}\sim 200$ km $\rm s^{-1}$ ), consistent with $\geq L^*$ spirals."
 Figure 1 shows grevscale plots of the galaxies as observed with WEPC2 and STIS., Figure 1 shows greyscale plots of the galaxies as observed with WFPC2 and STIS.
 The LIST imaging reveals many significant details not apparent in the eround-based observations (111109 Figure 1)., The HST imaging reveals many significant details not apparent in the ground-based observations (RLK02 Figure 1).
 S4 has a fainter companion. 510 and 16V21 are both highly asymmetric with multiple brighto knots (16V21 may be à mergingCIn svstem)," S4 has a fainter companion, S10 and 16V21 are both highly asymmetric with multiple bright knots (16V21 may be a merging system)."
 16V22 and 16V25 appear to be relatively unclisturbec barred. galaxies. with comparison by eve with local galaxy catalogs (e.g. Sandage and Becke 1998) suggesting approximate types SBm and SBhe respectively.," 16V22 and 16V25 appear to be relatively undisturbed barred galaxies, with comparison by eye with local galaxy catalogs (e.g. Sandage and Bedke 1998) suggesting approximate types SBm and SBbc respectively."
 16V26 is faint but obviously disturbed. and. 16V30.. 16V31 and 16V34 all have large. bright rings.," 16V26 is faint but obviously disturbed, and 16V30, 16V31 and 16V34 all have large, bright rings."
 Phese features are discussed further in Section 5., These features are discussed further in Section 5.
" We investigated the racial intensity profiles of these galaxies using ""isophotes. which. with centroids. ellipticities ancl position angles from the SExtractor catalog used as starting parameters. fits cach galaxy with a series of elliptical isophotes. providing a radial intensity profile on the semi-major axis."," We investigated the radial intensity profiles of these galaxies using `isophotes', which, with centroids, ellipticities and position angles from the SExtractor catalog used as starting parameters, fits each galaxy with a series of elliptical isophotes, providing a radial intensity profile on the semi-major axis."
" The resulting profiles were then vest-Litted with exponential. fyexp(rfr). and bulge. {0exp(7.67rfr,rr). functions."," The resulting profiles were then best-fitted with exponential, $I_0~{\rm exp}(-r/r_{exp})$, and bulge, $I_0~{\rm exp}(-7.67[r/r_{e}]^{0.25})$, functions."
" ligure 2 shows the f-bancl profiles of the 9 ealaxics. ogether with the best-fitting (lowest rms residuals) mocels and thei 572 or ray, scalelengths."," Figure 2 shows the $I$ -band profiles of the 9 galaxies, together with the best-fitting (lowest rms residuals) models and their $r_e$ or $r_{exp}$ scalelengths."
 Table 2) gives the scalelengths and central surface brightness (SB) of the best-Lr models together with the observed. central SB. averaged over the pixels at rx0.1 arcsec.," Table 2 gives the scalelengths and central surface brightness (SB) of the best-fit models together with the observed central SB, averaged over the pixels at $r\leq 0.1$ arcsec."
 S4 is closely fitted by a bulge model. with the excess a 1.5«ro2.5 aresee being due to a companion galaxy.," S4 is closely fitted by a bulge model, with the excess at $1.5<r<2.5$ arcsec being due to a companion galaxy."
 The ring around 16V30 gives the impression of a spiral. but a bulge model is adopted here as it is a much better Lit abor<OLS aresec.," The ring around 16V30 gives the impression of a spiral, but a bulge model is adopted here as it is a much better fit at $r<0.8$ arcsec."
 The other 7 galaxies are much closer to purely exponential disks. but some have large (~0.2 mag) resicuals.," The other 7 galaxies are much closer to purely exponential disks, but some have large $\sim 0.2$ mag) residuals."
 IALIXO2 estimated rest-frame blue absolute magnitudes. Ag. and S44 Cllz luminosities. Lx... for the radio IDs with known redshifts.," RLK02 estimated rest-frame blue absolute magnitudes, $M_B$, and 8.44 GHz luminosities, $L_{8.44}$ , for the radio IDs with known redshifts."
 Pirstlv. a eric of model spectral. energy distributions. representing galaxy types from cllipticals to pure starbursts over a wide range of redshifts. was generated using “Peease2” (ioe and Roeca-Volmerange 2000).," Firstly, a grid of model spectral energy distributions, representing galaxy types from ellipticals to pure starbursts over a wide range of redshifts, was generated using `Pegase2' (Fioc and Rocca-Volmerange 2000)."
" For each model SED. a recshilt-dependent correction (D,ανα) was caleulated."," For each model SED, a redshift-dependent correction $(B_{rest}-R_{obs})(z)$ was calculated."
 The observed colour of cach galaxy (DRR. B{ and/or / ÁN) was compared. with the models at the same redshift. and interpolation between the two models. closest in colour then gave an estimated (DuBouwu)z). which was used to derive Ag from the apparent {7 magnitude.," The observed colour of each galaxy $B-R$, $B-I$ and/or $I-K$ ) was compared with the models at the same redshift, and interpolation between the two models closest in colour then gave an estimated $(B_{rest}-R_{obs})(z)$, which was used to derive $M_B$ from the apparent $R$ magnitude."
" Lyi, was similarly estimated from the observed S44 Cllz luz assuming the Concon (1992) model radioSED.", $L_{8.44}$ was similarly estimated from the observed 8.44 GHz fluz assuming the Condon (1992) model radioSED.
both larger and smaller warp distortions are possible with the same satellite perturbation.,both larger and smaller warp distortions are possible with the same satellite perturbation.
 To complete the example. we describe the concurrent. in-plane distortion for m=1 and m=2 harmonics.," To complete the example, we describe the concurrent in-plane distortion for $m=1$ and $m=2$ harmonics."
" Phe overall distortion is small in the inner disk. A,SRo=s 5kpc. and dominated by the m=I term with a relative density amplitude of roughly. (4%)) for the small (Ege) LAIC mass estimate."," The overall distortion is small in the inner disk, $R_g\lesssim R_o=8.5\kpc$ , and dominated by the $m=1$ term with a relative density amplitude of roughly ) for the small (large) LMC mass estimate."
 The m=1 distortion appreciable in theouter disk. reaching," The $m=1$ distortion appreciable in theouter disk, reaching"
Figure 4. shows the normatlisec projected radii for the rotation sample as a function of Yigg.,Figure \ref{nrsini} shows the normalised projected radii for the rotation sample as a function of $T_{\rm eff}$.
 Both the DAALOT and SOO models have been used to normalise the (A?sin£s values calculatecl from equation 1 and the results are shown in the left ancl right hand. panels respectively. compared to isochrones of normalised radius from the same moclels.," Both the DAM97 and S00 models have been used to normalise the $(R\sin i)_{\rm obs}$ values calculated from equation \ref{1} and the results are shown in the left and right hand panels respectively, compared to isochrones of normalised radius from the same models."
 Lo neither case is there any evidence for a trend in (sinwfRexrer with Zip (à least squares [it gives lat line within l-sigma uncertainty in both instances). which supports the approach of using the clistribution ol (sind)on.Ian as à upindependent indicator of the true spread. in “radii (or age).," In neither case is there any evidence for a trend in $(R\sin i)_{\rm obs}/R_{\rm 3Myr}$ with $T_{\rm eff}$ (a least squares fit gives a flat line within 1-sigma uncertainty in both instances), which supports the approach of using the distribution of $(R\sin i)_{\rm obs}/R_{\rm 3Myr}$ as a $T_{\rm eff}$ -independent indicator of the true spread in radii (or age)."
 The mean values of (RsinAawn.ffovne ave 1.51d:0.08 and 1.24+( for the DAMOT ancl SOC) models respectively.," The mean values of $(R\sin i)_{\rm obs}/R_{\rm 3Myr}$ are $1.51\pm 0.08$ and $1.24\pm
0.07$ for the DAM97 and S00 models respectively."
" Hence the mean age of the ONC (as accordingjudged by the stellar radii) is significantly vounger to the DAMOT models than according to the SOO models. but in both cases is <3 MÀMyr. because (Isin), should be a lower limit to Biya."," Hence the mean age of the ONC (as judged by the stellar radii) is significantly younger according to the DAM97 models than according to the S00 models, but in both cases is $<3$ Myr because $(R\sin i)_{\rm obs}$ should be a lower limit to $R_{\rm true}$."
 The first distribution of As tested was that of a coeval population., The first distribution of $R_{\rm true}$ tested was that of a coeval population.
 The age was specified and then the cumulative distribution of (Asin?)../Rsarcr tested against the Monte-Carlo predictions.," The age was specified and then the cumulative distribution of $(R\sin i)_{\rm obs}/R_{\rm
3Myr}$ tested against the Monte-Carlo predictions."
 Ehe assumed age was adjusted to minimise the WK-S statistic and select the model Piru clistribution least different to the observational data., The assumed age was adjusted to minimise the K-S statistic and select the model $R_{\rm true}$ distribution least different to the observational data.
 This process was repeated using both the S00. and DAMO9T evolutionary models to calculate {ων," This process was repeated using both the S00 and DAM97 evolutionary models to calculate $R_{\rm
3Myr}$."
" Phe numerical results are Listed in Table 1 and illustrated. in. Fig 5 (the coeval mocdels are the rows with a dispersion in radius see section 4.3]. set to a,= 0)."," The numerical results are listed in Table \ref{results1} and illustrated in Fig \ref{gausszero} (the coeval models are the rows with a dispersion in radius [see section 4.3], set to $\sigma_{r}=0$ )."
 Initially L used. Gaussian dig uncertainties of 150k and a threshold. inclination An=3075., Initially I used Gaussian $T_{\rm eff}$ uncertainties of K and a threshold inclination $i_{\rm th}=30^{\circ}$.
 The assumed eine istribulion consists of 20 per cent of stars following a uniform. distribution. for 10«nue20kkmss 1 with the remaining SO per cent Following an exponential distribution with a decay constant of + between 10:«rine<120 ," The assumed $v_{\rm true}$ distribution consists of 20 per cent of stars following a uniform distribution for $10<v_{\rm true}<120$ $^{-1}$ with the remaining 80 per cent following an exponential distribution with a decay constant of $^{-1}$ between $10<v_{\rm
true}<120$ $^{-1}$."
Acdopting this. the observed esin distribution is well reproduced. by the model with a ντο rejection/ probability of <10 per cent (see Jellries 2007).," Adopting this, the observed $v\sin i$ distribution is well reproduced by the model with a K-S rejection probability of $<10$ per cent (see Jeffries 2007)."
 For both the DAMOT and SOO models the cata are inconsistent with the PALS population being drawn from a single coevalisochrone. at confidence levels of996 and lower-limits96.3 per cent respectively.," For both the DAM97 and S00 models the data are inconsistent with the PMS population being drawn from a single coeval isochrone, at confidence levels of 99.6 and 96.3 per cent respectively."
 These must be considered to the mocdel-rejection. confidence level because the mean age was adjusted as a free parameter to minimise the Ίντο ..., These must be considered lower-limits to the model-rejection confidence level because the mean age was adjusted as a free parameter to minimise the K-S statistic.
 The “best-fitting” ages are Log(age/Myr) of5.858 and6.25 for the DAALOF and SOO models respectively., The “best-fitting” ages are $\log_{10}$ (age/Myr) of 5.88 and 6.25 for the DAM97 and S00 models respectively.
 These ave similar to. but slightly older (han. the median ages found from the LI-R. diagrams in section 2. but note that values determined from the projected radii are independent of the assumecd distance to the ONC and unallected by the binary status of any of the stars.," These are similar to, but slightly older than, the median ages found from the H-R diagrams in section 2, but note that values determined from the projected radii are independent of the assumed distance to the ONC and unaffected by the binary status of any of the stars."
 Fig., Fig.
 5. shows that the coeval models are too narrow in &sin?’.," \ref{gausszero} shows that the coeval models are too narrow in $R
\sin i$."
 Obviously a radius (or age) spread could broaden the model cistribution. but so too could a decrease in. the assumed value of 44 or an increase in the assumed. Zr uncertainties.," Obviously a radius (or age) spread could broaden the model distribution, but so too could a decrease in the assumed value of $i_{\rm th}$ or an increase in the assumed $T_{\rm eff}$ uncertainties."
" To test this P ran the coeval SOO moclels assuming 4i,=157.", To test this I ran the coeval S00 models assuming $i_{\rm th}=15^{\circ}$.
" Fable 1. shows the ""best-Hit parameters and that the coeval model is still rejected with 290per cen confidence.", Table \ref{results1} shows the “best-fit” parameters and that the coeval model is still rejected with $\simeq 90$ per cent confidence.
" Conversely. if 44, were greater than 30° a coeva model would be an even poorer match to the data."," Conversely, if $i_{\rm th}$ were greater than $30^{\circ}$ a coeval model would be an even poorer match to the data."
 lL nex tried broadening the model A?sini clistribution bv increasing the uncertainty in Zi., I next tried broadening the model $R \sin i$ distribution by increasing the uncertainty in $T_{\rm eff}$.
 The model can still be rejected a JO per cent confidence unless the Zi uncertainties are approximately doubled to KIN. whieh is equivalent to a +2 spectral subclass (l-sigma) uncertainty in the spectra tvpes.," The model can still be rejected at $\geq 90$ per cent confidence unless the $T_{\rm eff}$ uncertainties are approximately doubled to K, which is equivalent to a $\pm 2$ spectral subclass (1-sigma) uncertainty in the spectral types."
 Note again that these. confidence levels are. lower limits because the mean age wastuned to minimise the Ix-S statistic., Note again that these confidence levels are lower limits because the mean age wastuned to minimise the K-S statistic.
 L conclude (hat unless the uncertainties in spectral Classification and ir M been significantly uncderestimated bv. Hillenbrand: (1997-- then the observed. values of /?sin? are inconsistent with at a reasonably high level of confidence.," I conclude that unless the uncertainties in spectral classification and $T_{\rm eff}$ have been significantly underestimated by Hillenbrand (1997), then the observed values of $R \sin i$ are inconsistent with coevality at a reasonably high level of confidence."
" Using model 2 (a Gaussian distribution of log),2 about a central value defined. by a single isochronal age with a standard deviation of m). E simulated a dispersion in radius about an isochronal value."," Using model 2 (a Gaussian distribution of $\log_{10} R$ about a central value defined by a single isochronal age with a standard deviation of $\sigma_r$ ), I simulated a dispersion in radius about an isochronal value."
 The central isochronal age was again adjusted to minimise the Ίντο statistic and a range of σι was tested., The central isochronal age was again adjusted to minimise the K-S statistic and a range of $\sigma_r$ was tested.
 Phe results. using the SOO models to calculate Rorxiav. ave listed in Table ancl illustrated in Fig. 6..," The results, using the S00 models to calculate $R_{\rm 3Myr}$, are listed in Table \ref{results1} and illustrated in Fig. \ref{gaussr}."
" Lf the dispersion increases to m,0.05 then this model can no longer be rejected. with ον90 per cent confidence.", If the dispersion increases to $\sigma_r>0.05$ then this model can no longer be rejected with $>90$ per cent confidence.
" The “best [it dispersion corresponds to σι=0.15. whilst the model distribution becomes too broad. and can be rejected with c90 per cent confidence if a,0.27."," The “best fit” dispersion corresponds to $\sigma_r=0.15$, whilst the model distribution becomes too broad and can be rejected with $>90$ per cent confidence if $\sigma_r>0.27$."
 The results using the DAALOT mocels are similar niodels with 0.08<a«0.24 cannot be rejected. with better than 90 per cent confidence — but the required. central isochronal age is still smaller udage/Myr) is 5.88 compared with 6.25 when using the SOO models κους Table 1)), The results using the DAM97 models are similar – models with $0.08<\sigma_r<0.24$ cannot be rejected with better than 90 per cent confidence – but the required central isochronal age is still smaller $\log_{10}$ (age/Myr) is 5.88 compared with 6.25 when using the S00 models – see Table \ref{results1}) ).
 The results above cannot be used to estimate confidence intervals on the best fitting value of σι. because the central isochronal age has been optimised in each case.," The results above cannot be used to estimate confidence intervals on the best fitting value of $\sigma_r$, because the central isochronal age has been optimised in each case."
 The right hand panel of Fie., The right hand panel of Fig.
 6. shows a normalisecl probability distribution as a function of σι (caleulatecl using the S00 models). where the probability has been integrated over a wide range of possible mean ages.," \ref{gaussr} shows a normalised probability distribution as a function of $\sigma_r$ (calculated using the S00 models), where the probability has been integrated over a wide range of possible mean ages."
" This PM that the st fitting m, is indeed about 0.15. NMwith90 per cent of the xobabilitv. distribution. contained 0:05 and.0.24."," This illustrates that the best fitting $\sigma_r$ is indeed about 0.15, with 90 per cent of the probability distribution contained between 0.08 and 0.24."
" The results using the D.AMOT models are very similar and eive a slightly narrower 90 per cent confidence interval of VIOThe«m,< 0.22."," The results using the DAM97 models are very similar and give a slightly narrower 90 per cent confidence interval of $0.10 <
\sigma_r < 0.22$ ."
 Alonte Carlo models suggest. that. the observed Rsiné distribution can be well represented if the observed »pulation has a spread. amounting to a fullwicth at," The Monte Carlo models suggest that the observed $R\sin i$ distribution can be well represented if the observed population has a spread, amounting to a full-width at"
SIxL acknowledges funding from a Mathematics Iesearch Fellowship from Southampton University.,SKL acknowledges funding from a Mathematics Research Fellowship from Southampton University.
 Fhis work was supported by SPEC through grant number PP/IE001025/1 and by Compstar. a Research Networking Programme of the European Science Foundation.," This work was supported by STFC through grant number PP/E001025/1 and by CompStar, a Research Networking Programme of the European Science Foundation."
 We thank Kostas Ixokkotas. Ixostas Clampecakis and the anonvmous referee for their helpful comments on this work.," We thank Kostas Kokkotas, Kostas Glampedakis and the anonymous referee for their helpful comments on this work."
"n, have well-known clegeneracies wilh 7. in CAB parameter extraction (Spergel 2007: Dunklev 2008).",$n_s$ have well-known degeneracies with $\tau_e$ in CMB parameter extraction (Spergel 2007; Dunkley 2008).
" The derived parameters may change in future CMD data analyses. as the constraints on 7, continue to evolve."," The derived parameters may change in future CMB data analyses, as the constraints on $\tau_e$ continue to evolve."
" In addition. inaccuracies in the incomplete recombination epoch and residual ionization history. c,(2). add uncertainties to the CMD radiative transler. the damping of (-modes. and the polarization signal used to derive an overall 7."," In addition, inaccuracies in the incomplete recombination epoch and residual ionization history, $x_e(z)$, add uncertainties to the CMB radiative transfer, the damping of $\ell$ -modes, and the polarization signal used to derive an overall $\tau_e$."
 We now discuss the contribution of residual electrons in the IGM following the recombination epoch al z21000., We now discuss the contribution of residual electrons in the IGM following the recombination epoch at $z \approx 1000$.
" Scattering [rom (hese electrons is significant and is normally accounted Lor in CMD transport codes such as CMDFAST (Seljak Zaldarriaga 1996) through the recombination IGM ionization history. Όρο),"," Scattering from these electrons is significant and is normally accounted for in CMB transport codes such as CMBFAST (Seljak Zaldarriaga 1996) through the post-recombination IGM ionization history, $x_e(z)$."
 Hllowever. a number of past papers are vague on how the ionization historv is (reated and on precisely which electrons contribute to total optical depth z..," However, a number of past papers are vague on how the ionization history is treated and on precisely which electrons contribute to total optical depth $\tau_e$."
 This has led to confusion in how much residual optical depth anc damping of CMD power has been subtiracted [rom the CMD signal., This has led to confusion in how much residual optical depth and damping of CMB power has been subtracted from the CMB signal.
 It is important to be clear on the definition of the integrated 7. when using it to constrain the amount of high-z ionization from first-Heht sources., It is important to be clear on the definition of the integrated $\tau_e$ when using it to constrain the amount of $z$ ionization from first-light sources.
 Modern. calculations of how the IGM became neutral have been done by Seager (2000). although their code (RECFAST) continues to be modified to deal with subtle effects of the recombination epoch and the atomic physics of hydrogen (n5—15 and nd— 1s) two-photon transitions (Chluba Sunvaev 2007).," Modern calculations of how the IGM became neutral have been done by Seager (2000), although their code (RECFAST) continues to be modified to deal with subtle effects of the recombination epoch and the atomic physics of hydrogen $ns \rightarrow 1s$ and $nd \rightarrow 1s$ ) two-photon transitions (Chluba Sunyaev 2007)."
" To illustrate the potential effects of hieh-z residual electrons. we have used numbers [rom Figure 2 of Seager (2000). (he top-panel model. which assumed a cosmology wilh Qi=1. Qj= 0.05. h=0.5. Y=0.24. and Teay,=2.728 Ix. At low redshifts. z25z,. just. before reionization. they find a residual electron [raction c,2:10.ο,"," To illustrate the potential effects of $z$ residual electrons, we have used numbers from Figure 2 of Seager (2000), the top-panel model, which assumed a cosmology with $\Omega_{\rm tot} = 1$, $\Omega_b = 0.05$ , $h = 0.5$, $Y = 0.24$, and $T_{\rm CMB} = 2.728$ K. At low redshifts, $z \approx z_r$, just before reionization, they find a residual electron fraction $x_{e,0} \approx 10^{-3.3}$."
" We fitted their curve Lor log zr, out to z500 to the formula: where a52.303x10"".", We fitted their curve for log $x_e$ out to $z \approx 500$ to the formula: where $\alpha \approx 2.303 \times 10^{-3}$.
" More recent recombination calculations (W. Y. Wong D. Scott. private communication) using WALAPparameters (Qj=0.04. h=0.73. €),=024. Q4— 0.76) and Y=0.244 find somewhat lower values. r422LO withazz2.12x10.7."," More recent recombination calculations (W. Y. Wong D. Scott, private communication) using WMAPparameters $\Omega_b = 0.04$, $h = 0.73$, $\Omega_m = 0.24$, $\Omega_{\Lambda} = 0.76$ ) and $Y = 0.244$ find somewhat lower values, $x_{e,0} \approx 10^{-3.67}$ with $\alpha \approx 2.12 \times 10^{-3}$."
 The lower Όρη to the faster recombination rates arises trom their higher assumed barvon density. Q?=0.0213. compared to O;/?=0.0125 in Seager (2000).," The lower $x_{e,0}$ to the faster recombination rates arises from their higher assumed baryon density, $\Omega_b h^2 = 0.0213$, compared to $\Omega_b h^2 = 0.0125$ in Seager (2000)."
" To compute the electron-scattering of the CMD from these ""Irozen-out electrons. we use (he same integrated opticaldepth formula (equation 1). in the high-z limit. where (df(/dz)= 77."," To compute the electron-scattering of the CMB from these “frozen-out"" electrons, we use the same integrated opticaldepth formula (equation 1), in the $z$ limit, where $(d \ell /dz) = (1+z)^{-1} [c/H(z)] \approx (c/H_0) \Omega_m^{-1/2} (1+z)^{-5/2}$ ."
 We integrate over (he residiual-electron. history.," We integrate over the residual-electron history,"
We interpret the turbulent line width parameter € to be a measure of the velocity fluctuations in the cloud turbulence.,We interpret the turbulent line width parameter $\xi$ to be a measure of the velocity fluctuations in the cloud turbulence.
" If solar wind turbulence is a good model for the cloud turbulence, this turbulence is Alfvénnic, and the velocity fluctuations should be perpendicular to the large scale interstellar magnetic field Bo."," If solar wind turbulence is a good model for the cloud turbulence, this turbulence is Alfvénnic, and the velocity fluctuations should be perpendicular to the large scale interstellar magnetic field $\vec{B}_0$."
" If this is the case, the measured value of & should vary with position on the sky."," If this is the case, the measured value of $\xi$ should vary with position on the sky."
 The reasoning behind this statement is illustrated in Figure 1., The reasoning behind this statement is illustrated in Figure 1.
" In certain directions on the sky, we are looking across Bs, and the turbulent fluctuations should be along the line of sight (more properly, one of the two fluctuating magnetic field components in a plane perpendicular to Bo will be aligned with the line of sight)."," In certain directions on the sky, we are looking across $\vec{B}_0$, and the turbulent fluctuations should be along the line of sight (more properly, one of the two fluctuating magnetic field components in a plane perpendicular to $\vec{B}_0$ will be aligned with the line of sight)."
" For other directions, we are looking along Bo, and the turbulent velocity fluctuations are mainly"," For other directions, we are looking along $\vec{B}_0$, and the turbulent velocity fluctuations are mainly"
Variable absorption in (he inner jel region mieht have an ellect on the observed. siructure.,Variable absorption in the inner jet region might have an effect on the observed X-ray structure.
 The optical extinction. Ay. in (he inner jel region varies between 0.5 and 3.0 magnitudes (Schreiere/al.1996).," The optical extinction, $A_V$, in the inner jet region varies between 0.5 and 3.0 magnitudes \citep{sch96}."
. Adopting a standard Galactic gas-to-clist ratio. this corresponds to an X-ray column of 0.9-5.6x L0? ei.7 (SmithandDwek1993).," Adopting a standard Galactic gas-to-dust ratio, this corresponds to an X-ray column of $\times$ $^{21}$ $^{-2}$ \citep{smi98}."
". For a spectrum with photon index = 2.2. (his variation in Ny, would correspond to a variation ol a factor of ~2 in count rate in ACIS-I in the 0.4-2.5 keV bandpass of the ACIS-L. although in the region from (he core to AN (before the dark dust lanes are encountered) the positional varlalions in X-rav count rate contributed bv the absorption are expected to be less than105."," For a power-law spectrum with photon index = 2.2, this variation in $N_H$ would correspond to a variation of a factor of $\sim$ 2 in count rate in ACIS-I in the 0.4-2.5 keV bandpass of the ACIS-I, although in the region from the core to AX4 (before the dark dust lanes are encountered) the positional variations in X-ray count rate contributed by the absorption are expected to be less than."
.. The actual relationship between the X-ray emission [rom the jet and anv intervening absorbing material is probably more complex for (wo reasons., The actual relationship between the X-ray emission from the jet and any intervening absorbing material is probably more complex for two reasons.
 First. the angle of the jet to the line of sieht is poorly constrained. so the geometric relationship of the jet relative (o the gas associated with the optically obscuring dust is bv no means clear.," First, the angle of the jet to the line of sight is poorly constrained, so the geometric relationship of the jet relative to the gas associated with the optically obscuring dust is by no means clear."
 Second. (le X-ray spectral fitting (described below) suggests that the absorbing column of the brightest knots of the inner jet CAXI-AXA is considerably larger (Nyyοκ 107! em.Da7) than one would expect based on the extinction map of Schreierοἱa£. (1996)...," Second, the X-ray spectral fitting (described below) suggests that the absorbing column of the brightest knots of the inner jet (AX1-AX4) is considerably larger $N_H\sim$ $\times$ $^{21}$ $^{-2}$ ) than one would expect based on the extinction map of \citet{sch96}. ."
 In fact. (his X-ray. column. density is at the high end of the range inferred [rom 2h) over most or all of the inner jet.," In fact, this X-ray column density is at the high end of the range inferred from $A_V$ over most or all of the inner jet."
 We note that the morphological features of the inner jet seen in (he broad-band X-ray. image are still present when X-ravs in the 1-3 keV. band only are selected. so the appearance of the inner jel is probably not signilicantlv distorted because of variable absorption.," We note that the morphological features of the inner jet seen in the broad-band X-ray image are still present when X-rays in the 1-3 keV band only are selected, so the appearance of the inner jet is probably not significantly distorted because of variable absorption."
 To determine which of these knots are extended and which are pointlike aud may therefore be XRDs unrelated to the jet. we have simulated point sources al five positions separated by 1 along the jet starting at the nucleus using MARX.," To determine which of these knots are extended and which are pointlike and may therefore be XRBs unrelated to the jet, we have simulated point sources at five positions separated by $1'$ along the jet starting at the nucleus using MARX."
 We only used data from the first (CODSID 00316) observation as the jet is closer to the best focus. and coaclding the second data set at a different roll angle would add considerable svstematie uncertainty.," We only used data from the first (OBSID 00316) observation as the jet is closer to the best focus, and coadding the second data set at a different roll angle would add considerable systematic uncertainty."
" The ralio of the number of counts within a 1"" radius circle to the number of counts within a 1” to 2"" annular ring was determined for each of these simulated point sources.", The ratio of the number of counts within a $1''$ radius circle to the number of counts within a $1''$ to $2''$ annular ring was determined for each of these simulated point sources.
 A third-order polynomial was fit to this ratio as a function of distance from the nucleus in order to estimate (his ratio at an arbitrary position along the jet., A third-order polynomial was fit to this ratio as a function of distance from the nucleus in order to estimate this ratio at an arbitrary position along the jet.
 The measured ratio for each of the detected enhancements was then compared to the simulated ratio., The measured ratio for each of the detected enhancements was then compared to the simulated ratio.
 If (he measured ratio is less (han 30 below the simulated ratio. (he enhancement is considered a point source.," If the measured ratio is less than $\sigma$ below the simulated ratio, the enhancement is considered a point source."
 On the basis of this test. we find that three of the enhancements are consistent with point sources (see Table 2)).," On the basis of this test, we find that three of the enhancements are consistent with point sources (see Table \ref{knottab}) )."
 The normalized surface brightness profiles of the two brightest knots. AXI and DX2. and the MARX simulations of the PSFs at the locations of those knots is plotted in Figure 8..," The normalized surface brightness profiles of the two brightest knots, AX1 and BX2, and the MARX simulations of the PSFs at the locations of those knots is plotted in Figure \ref{sbp}."
 We have evaluated (his procedure by testing other sources located near the jet. but clearly outside the diffuse emission. and find that four of the five sources are consistent with being point sources.," We have evaluated this procedure by testing other sources located near the jet, but clearly outside the diffuse emission, and find that four of the five sources are consistent with being point sources."
 The fifth source is obviously distorted. aud by visual inspection aloneil is clear (hat it should not be considered a point source., The fifth source is obviously distorted and by visual inspection aloneit is clear that it should not be considered a point source.
 The position.," The position,"
 from the GC region are shown., from the GC region are shown.
 High luminosity LMXDs with à neutron star (Zsources. 1ο. left) are very bright in the standard X.ray band. but are weak above —30 keV. On the contrary BIICs (Fig.2 right) have »ealkk verv at the energy of —100 keV. while in standard X.rav band hey are Luminosityrelatively weak.," High luminosity LMXBs with a neutron star (Z–sources, Fig.2 left) are very bright in the standard X–ray band, but are very weak above $\sim$ 30 keV. On the contrary BHCs (Fig.2 right) have peak luminosity at the energy of $\sim$ 100 keV, while in standard X–ray band they are relatively weak."
 An intermediate eroup is constituted by lower uminosity LAINB with a neutron star (twpically Xray bursters. Fig.2 micelle). which are often switched between softer ancl harder states.," An intermediate group is constituted by lower luminosity LMXB with a neutron star (typically X–ray bursters, Fig.2 middle), which are often switched between softer and harder states."
 The alter sources appear part of the time as objects in the standard Xrav band and part of the time as bright brightobjects in the hard. band., The latter sources appear part of the time as bright objects in the standard X–ray band and part of the time as bright objects in the hard band.
 Even in the hard state spectra of Xray bursters are still softer (in ternis of the at which maximum luminosity is emitted) than those of BlICs energyGoldwurm et al., Even in the hard state spectra of X–ray bursters are still softer (in terms of the energy at which maximum luminosity is emitted) than those of BHCs (e.g. Goldwurm et al.
 1994. Cilfanoy et al.," 1994, Gilfanov et al."
 1995. Churazoy et al.," 1995, Churazov et al.,"
 997)., 1997).
 (c.g.Indeed. using the thin plasma emission model to erucdely characterize hardness of source optically in the 35-150 keV. band. one can conclude that best fit to spectrathe spectra of cach NS LMXD seen in the SIGALA image (Fig.1) are temperaturesclustered around 50 keV or below. while vest fit for DIICS (c.g. 151740.7-2942. €GBS1758-258) are all around. temperatures," Indeed, using the optically thin plasma emission model to crudely characterize hardness of source spectra in the 35-150 keV band, one can conclude that best fit temperatures to the spectra of each NS LMXB seen in the SIGMA image (Fig.1) are clustered around 50 keV or below, while best fit temperatures for BHCs (e.g. 1E1740.7-2942, GRS1758-258) are all around 100 keV or above."
" Phe LOO1E1740.7-2942keVor above.and GRSIT5S-258 are the hardest. sources in the ield. of the (η, in units AclTomταthel +) at he havingof peaks~100 keV. Their spectraspectral resemble those of the energv BLICs."," The 1E1740.7-2942 and GRS1758-258 are the hardest sources in the field, having peaks of the spectra $\nu F_\nu$ in units $keV^2~cm^{-2}~s^{-1}~keV^{-1}$ ) at the energy of $\sim$ 100 keV. Their spectral properties resemble those of the dynamically proven BHCs."
 However while most of propertiesthe BILCs in the Galaxy are dynamicallytransients. proven111740.7-2042 and GISSI758-258 are persistent variable sources.," However while most of the BHCs in the Galaxy are transients, 1E1740.7-2942 and GRS1758-258 are certainly persistent though variable sources."
 Shown in are the 40.150 keV certainlylight curves of hough1121740.7-2942 and the transient Fie.’GRSITI6-249 (Nova 93 also ocated in the GC region) for most of SLGALA observations in Oph1990./—1998., Shown in Fig.3 are the 40–150 keV light curves of 1E1740.7-2942 and the transient GRS1716-249 (Nova Oph 93 – also located in the GC region) for most of SIGMA observations in 1990–1998.
enrichment phases from [Fe/H] <3.0. 3.0)< [Fe/H] 2.0 and [Fe/H] 7—2.0 are given in the panels from top to bottom.,"enrichment phases from [Fe/H] $< -3.0$ , $-3.0 <$ [Fe/H] $< -2.0$ and [Fe/H] $> -2.0$ are given in the panels from top to bottom."
 The solid line shows the relative frequency of observed halo stars per [Si/Fe] bin for each enrichment phase and the dashed line the relative frequency of computed model stars per bin., The solid line shows the relative frequency of observed halo stars per [Si/Fe] bin for each enrichment phase and the dashed line the relative frequency of computed model stars per bin.
 To account for the effect of observational errors on our data. we added a random. normally distributed error with standard deviation 0.1 dex in the [EI/Fe] and [Fe/H] ratios to the model stars.," To account for the effect of observational errors on our data, we added a random, normally distributed error with standard deviation 0.1 dex in the [El/Fe] and [Fe/H] ratios to the model stars."
 The bin size in the [Si/Fe] ratio is 0.1 dex for observed and computed stars. while the position of the histogram for the model stars is shifted by 0.01 dex to the left for better visibility.," The bin size in the [Si/Fe] ratio is 0.1 dex for observed and computed stars, while the position of the histogram for the model stars is shifted by 0.01 dex to the left for better visibility."
 The total number of stars included in the plot is given in the upper left corner of each panel. where ιν. and Nia are the number of observed stars and of model stars. respectively.," The total number of stars included in the plot is given in the upper left corner of each panel, where $N_{\mathrm{obs}}$ and $N_{\mathrm{mod}}$ are the number of observed stars and of model stars, respectively."
 In the upper panel. the distributions of both the 22 observed and the 4226 model stars show a spread in the [Si/Fe] ratio of more than one dex.," In the upper panel, the distributions of both the 22 observed and the 4226 model stars show a spread in the [Si/Fe] ratio of more than one dex."
 The distribution of the model stars shows two wide. protruding wings and a faint peak at |Si/Fe] z0.2.," The distribution of the model stars shows two wide, protruding wings and a faint peak at [Si/Fe] $\approx 0.2$."
" The ""right wing shows a shallow rise from [Si/Fe] —1.1 to the peak.", The “right” wing shows a shallow rise from [Si/Fe] $\approx 1.1$ to the peak.
 The “left” wing ts not as extended and shows a rather steep cutoff at [Si/Fe] z—0.3., The “left” wing is not as extended and shows a rather steep cutoff at [Si/Fe] $\approx -0.3$.
 This asymmetry is due to the nucleosynthesis models of core-collapse SNe. which show a more or less constant value of [Si/Fe] ~0.3 for progenitor masses in the range of LO)198. as can be seen in Fig. 2..," This asymmetry is due to the nucleosynthesis models of core-collapse SNe, which show a more or less constant value of [Si/Fe] $\approx
-0.3$ for progenitor masses in the range of $10-13 \, \mathrm{M}_{\sun}$, as can be seen in Fig. \ref{scatter}."
 The distribution of the halo stars peaks at the same location as the model stars but extends only down to [Si/Fe] z0.1.," The distribution of the halo stars peaks at the same location as the model stars but extends only down to [Si/Fe] $\approx
-0.1$."
 We attribute this to the poor statistic of the data set. since this gap is filled in the middle panel.," We attribute this to the poor statistic of the data set, since this gap is filled in the middle panel."
 The middle panel of Fig., The middle panel of Fig.
 [4. shows the same distribution for the intermediate mixing stage of the ISM., \ref{sihist} shows the same distribution for the intermediate mixing stage of the ISM.
 The distribution of the model stars now has smaller wings. and peaks at [Si/Fe] zz0.3.," The distribution of the model stars now has smaller wings, and peaks at [Si/Fe] $\approx 0.3$."
 It is still broader than | dex. but the majority of the stars fall near the IMF averaged [Si/Fe] ratio.," It is still broader than 1 dex, but the majority of the stars fall near the IMF averaged [Si/Fe] ratio."
 The prominent peak is caused by the already well-mixed regions. whereas the broad distribution shows that the halo ISM ts still chemically inhomogeneous.," The prominent peak is caused by the already well-mixed regions, whereas the broad distribution shows that the halo ISM is still chemically inhomogeneous."
 The peak of the observational sample has shifted by about 0.2 dex to the right and lies now at [Si/Fe] zz0.1., The peak of the observational sample has shifted by about 0.2 dex to the right and lies now at [Si/Fe] $\approx 0.4$.
 Compared to the prediction of the model. the relative frequency of the halo stars is too high in the wings of the distribution and too low to the left of the peak.," Compared to the prediction of the model, the relative frequency of the halo stars is too high in the wings of the distribution and too low to the left of the peak."
 The lower panel shows the late stage. where the halo ISM is well mixed.," The lower panel shows the late stage, where the halo ISM is well mixed."
 The broac wings have completely disappeared and only the very prominent peak at the IMF averaged value remains., The broad wings have completely disappeared and only the very prominent peak at the IMF averaged value remains.
 The distributions of the 11 observed stars and the 0000 model stars are in good agreement., The distributions of the 11 observed stars and the 000 model stars are in good agreement.
 At this metallicity no SN of Type Ia should have polluted the by now well mixed ISM and the metal abundance is high enough to restrict the impact of single SN II events on the ISM., At this metallicity no SN of Type Ia should have polluted the by now well mixed ISM and the metal abundance is high enough to restrict the impact of single SN II events on the ISM.
 The most prominent feature which characterizes the different enrichment phases. is the intrinsic scatter in. the abundances of metal-poor stars.," The most prominent feature which characterizes the different enrichment phases, is the intrinsic scatter in the abundances of metal-poor stars."
 This can be seen in Fig. 5..," This can be seen in Fig. \ref{sidis},"
 which shows the standard deviation of [Si/Fe] as a function of metallicity [Fe/H] for the model and the halo stars., which shows the standard deviation of [Si/Fe] as a function of metallicity [Fe/H] for the model and the halo stars.
 The bin size used to compute the standard deviation was 0.1 dex in netallicity., The bin size used to compute the standard deviation was 0.1 dex in metallicity.
 The solid line shows the scatter of the unmodified nodel stars., The solid line shows the scatter of the unmodified model stars.
 The influence of observational errors on our data was simulated by adding a random. normally distributed error with standard deviation 0.1 and 0.2 dex in both [Si/Fe] and Fe/H].," The influence of observational errors on our data was simulated by adding a random, normally distributed error with standard deviation 0.1 and 0.2 dex in both [Si/Fe] and [Fe/H]."
 The resulting scatter in dependence of metallicity is given by the dashed and dotted lines., The resulting scatter in dependence of metallicity is given by the dashed and dotted lines.
 In the range of {8< Fe/H] <3.0 the scatter has a more or less constant value of approximately 0.4 dex., In the range of $-4.0 <$ [Fe/H] $< -3.0$ the scatter has a more or less constant value of approximately 0.4 dex.
 It declines rather steeply in the range 3.0< [Fe/H] <—2.0 and levels off again at metallicities higher than 2.0. depending on the assumed observational errors of 0.0. 0.1 or 0.2 dex.," It declines rather steeply in the range $-3.0 <$ [Fe/H] $< -2.0$ and levels off again at metallicities higher than $-2.0$, depending on the assumed observational errors of 0.0, 0.1 or 0.2 dex."
 These curves show that for errors in this range the scatter at low metallicities is dominated by the intrinsic differences in the element abundances of single stars., These curves show that for errors in this range the scatter at low metallicities is dominated by the intrinsic differences in the element abundances of single stars.
 For comparison. the scatter in the [Si/Fe] ratio of observed halo stars is represented by filled squares.," For comparison, the scatter in the [Si/Fe] ratio of observed halo stars is represented by filled squares."
 The observations were binned with a bin size of 0.5 dex to compute the standard deviations., The observations were binned with a bin size of 0.5 dex to compute the standard deviations.
 To estimate the reliability of their scatter in [Si/Fe]. we built several new data sets by adding a normally distributed random error with standard deviation 0.1 dex to the [Si/Fe] ratio and the metallicity of the stars.," To estimate the reliability of their scatter in [Si/Fe], we built several new data sets by adding a normally distributed random error with standard deviation 0.1 dex to the [Si/Fe] ratio and the metallicity of the stars."
 For each new data set. the standard deviation in the different bins was computed.," For each new data set, the standard deviation in the different bins was computed."
 The standard deviation for the results from these artificial data sets is given in the plot as 1-6 error-bars., The standard deviation for the results from these artificial data sets is given in the plot as $\sigma$ error-bars.
 The scatter of the observed abundance ratios shows nicely the features already seen in the curves for the model stars., The scatter of the observed abundance ratios shows nicely the features already seen in the curves for the model stars.
 At the first stage of the enrichment. it is approximately constant. followed by a steady decline in the intermediate mixing phase.," At the first stage of the enrichment, it is approximately constant, followed by a steady decline in the intermediate mixing phase."
 At higher metallicities. the scatter levels off again.," At higher metallicities, the scatter levels off again."
 Since the scatter in [Si/Fe] at [Fe/H] =1.0 is about 0.1 dex the observational errors have little influence on the analysis at these low metallicities. unless unknown systematic or confusion errors were large enough to inflate the scatter at [Fe/H] =—1.0 to also about 0.1 dex.," Since the scatter in [Si/Fe] at [Fe/H] $=-4.0$ is about $0.4$ dex the observational errors have little influence on the analysis at these low metallicities, unless unknown systematic or confusion errors were large enough to inflate the scatter at [Fe/H] $=-4.0$ to also about $0.4$ dex."
 On the other hand. observational errors do dominate the scatter at. metallicities [Fe/H] >—2.0. when the halo ISM is well mixed and the intrinsic scatter of the stars is negligible compared to the observational errors.," On the other hand, observational errors do dominate the scatter at metallicities [Fe/H] $> -2.0$, when the halo ISM is well mixed and the intrinsic scatter of the stars is negligible compared to the observational errors."
 As expected. the IMF averaged |EI/Fe] ratios for O and Mg reproduce the mean abundance of the observed metal-poor stars nicely.," As expected, the IMF averaged [El/Fe] ratios for O and Mg reproduce the mean abundance of the observed metal-poor stars nicely."
 The [O/Fe] ratio seems to be slightly too low. whereas [Mg/Fe] is slightly too high. but both deviations are smaller than 0.1 dex.," The [O/Fe] ratio seems to be slightly too low, whereas [Mg/Fe] is slightly too high, but both deviations are smaller than 0.1 dex."
 No trend in the observational data of Mg can be seen and a trend in O only becomes visible if the observations of Israelian et al. (1998)), No trend in the observational data of Mg can be seen and a trend in O only becomes visible if the observations of Israelian et al. \cite{is98}) )
 are considered., are considered.
 An important fact is that the scatter in the data. although increasing at lower metallicities. does not match the large scatter of more than two dex predicted by the stellar vields.," An important fact is that the scatter in the data, although increasing at lower metallicities, does not match the large scatter of more than two dex predicted by the stellar yields."
 Since no other mixing effects than the overlapping of SN remnants are included in our model. the expected scatter is determined by thenucleosynthesis yields.," Since no other mixing effects than the overlapping of SN remnants are included in our model, the expected scatter is determined by thenucleosynthesis yields."
 If gas flows and the random motion of stars in the halo accelerated the chemical mixing. a smaller scatter in the model data would be expected.," If gas flows and the random motion of stars in the halo accelerated the chemical mixing, a smaller scatter in the model data would be expected."
οπου» slightlv from the original paper.,differs slightly from the original paper.
 The cillusion cocllicients 7 and 2 used. by Heger.Langer&Woosley are equivalent ο Dine and Days|Dor respectively., The diffusion coefficients $\nu$ and $D$ used by \citet{Heger00} are equivalent to $D_{\rm shear}$ and $D_{\rm shear}+D_{\rm eff}$ respectively.
 Heger.Langer&Woosley(2000) take fo= which is what we use here., \citet{Heger00} take $f_{\rm c}=1/30$ which is what we use here.
 The parameter fj usce in lHleger.Langer&Woosley(2000). is taken to be zero., The parameter $f_{\mu}$ used in \citet{Heger00} is taken to be zero.
" Alean molecular weight gradients play an important part in chemical mixing near the core however we have performec a number of test runs with f,=0.05.", Mean molecular weight gradients play an important part in chemical mixing near the core however we have performed a number of test runs with $f_{\mu}=0.05$.
 Although there were some cdillerences. they were not significant and coul be largely masked by modifving the other free. parameters associated with this case.," Although there were some differences, they were not significant and could be largely masked by modifying the other free parameters associated with this case."
 The model cilfers [rom the origina formulation ofHeger.Langer&Woosley(2000). in that we are unable to useο to consistently compute non-loca quantities such as the spatial extent of instability regions used in some of the expressions for the various clillusion cocllicicnts., The model differs from the original formulation of \citet{Heger00} in that we are unable to use to consistently compute non-local quantities such as the spatial extent of instability regions used in some of the expressions for the various diffusion coefficients.
 We do not expect this to have a significan ellect on the results since Mes dominates the total diffusion coefficient. and its limiting length scale is the pressure scale height rather than the extent of the unstable region., We do not expect this to have a significant effect on the results since $D_{\rm ES}$ dominates the total diffusion coefficient and its limiting length scale is the pressure scale height rather than the extent of the unstable region.
 This model is calibrated. by mocdifving the dominant diffusion coellicient. for transport. owing to meridional circulation. Des. by a constant of order unity to give the same Ελλ nitrogen enrichment as case 1 for a 20 sstar with initial surface angular velocity of 300knis1.," This model is calibrated by modifying the dominant diffusion coefficient for transport owing to meridional circulation, $D_{\rm ES}$, by a constant of order unity to give the same TAMS nitrogen enrichment as case 1 for a $20$ star with initial surface angular velocity of $300\,{\rm km\,s^{-1}}$."
 This model has p=2 and Dou=Dy., This model has $n=2$ and $D_{\rm conv}=D_{\rm mlt}$.
 This is a reproduction of the original model of Zahn(1992) and is included: as a baseline to highlight the cilferences in predictions of stellar rotation from the original model., This is a reproduction of the original model of \cite{Zahn92} and is included as a baseline to highlight the differences in predictions of stellar rotation from the original model.
 In this model where Ax ds the thermal cillusivity and o is the same as in case 1., In this model where $K$ is the thermal diffusivity and $\alpha$ is the same as in case 1.
 1n this moclel and Cy and C» are constants used. for. calibration., In this model and $C_1$ and $C_2$ are constants used for calibration.
 We constrain C'; and CS by matching as closely as possible the TANIS nitrogen enrichment and luminosity of a 20 eese lstariilhinitialsurfacerolationof 300kms.," We constrain $C_1$ and $C_2$ by matching as closely as possible the TAMS nitrogen enrichment and luminosity of a $20$ $\,$ star with initial surface rotation of $300\,{\rm km\,s^{-1}}$."
 We find that C;=0.019 which is surprisingly small., We find that $C_1=0.019$ which is surprisingly small.
 This is because this model does not take into account mean molecular weight gradients and this leads to far more mixing between the convective core ancl the radiative envelope. than in case 1., This is because this model does not take into account mean molecular weight gradients and this leads to far more mixing between the convective core and the radiative envelope than in case 1.
 Phe PAAIS luminosity is always greater than case 1 and so we minimize it with respect to Cb so Cb5X., The TAMS luminosity is always greater than case 1 and so we minimize it with respect to $C_2$ so $C_2\to\infty$.
 This is realised by setting Dap=O and is the case when the horizontal diffusion completely dominates. over he meridional circulation and so is consistent with our assumption of shellular rotation., This is realised by setting $D_{\rm eff}=0$ and is the case when the horizontal diffusion completely dominates over the meridional circulation and so is consistent with our assumption of shellular rotation.
 Apart from ignoring mean molecular weight. gradients. he main objection to this model is that in the formulation of Dy we assume that. if the horizontal variation in the angular velocity along isobars takes the form Q=Q2(r)L2(eos8). hen ο)ΟΙ is constant and. this is not. physically justified.," Apart from ignoring mean molecular weight gradients, the main objection to this model is that in the formulation of $D_{\rm h}$ we assume that, if the horizontal variation in the angular velocity along isobars takes the form $\tilde{\Omega}=\Omega_2(r)P_2(\cos\theta)$, then $\Omega_2(r)/\Omega(r)$ is constant and this is not physically justified."
 Again we set η=2 and Doa=Dun., Again we set $n=2$ and $D_{\rm conv}=D_{\rm mlt}$.
" Lor these cases we use the same ao, and Jy, as in case 1 but we set n=0 to produce uniform specific angular momentum through the convective zones and test the elfect of varying the convective dillusion coellicient. Dos.", For these cases we use the same $D_{\rm shear}$ and $D_{\rm h}$ as in case 1 but we set $n=0$ to produce uniform specific angular momentum through the convective zones and test the effect of varying the convective diffusion coefficient $D_{\rm conv}$.
 We have also calculated the evolution in cases 1. 2 and 3 for the same masses ancl velocities but with Z=0.001.," We have also calculated the evolution in cases 1, 2 and 3 for the same masses and velocities but with $Z=0.001$."
 We shall represent. these cases with a superscriptZ (e.g. Case 1 is the low metallicity analogue of Case 1)., We shall represent these cases with a superscript (e.g. Case ${\rm 1}^Z$ is the low metallicity analogue of Case 1).
 Whilst there are many potential observables which may he used to distinguish between dillerent mocels. it is important to choose the ones that are most. easily. compared: with observational data.," Whilst there are many potential observables which may be used to distinguish between different models, it is important to choose the ones that are most easily compared with observational data."
 From our stellar evolution calculations we find a number of important dillerences between the test Cases., From our stellar evolution calculations we find a number of important differences between the test cases.
 First it is helpful to briefly. examine the internal evolution that occurs., First it is helpful to briefly examine the internal evolution that occurs.
 We consider here the main-sequence evolution, We consider here the main-sequence evolution
crushes for rapid C burning.,crushes for rapid C burning.
" Once a star evolves to produce a H-exhausted core we calculate the binding energy of its envelope and accordingly Aj, and Ay. both with and without the internal enerev of the stellar matter."," Once a star evolves to produce a H-exhausted core we calculate the binding energy of its envelope and accordingly $\lambda_{\rm b}$ and $\lambda_{\rm g}$, both with and without the internal energy of the stellar matter."
 ln Figs., In Figs.
" 1 ancl 2. we show some examples of the evolution of Aj, and A, with respect to the stellar radius 2."," \ref{fig1} and \ref{fig2} we show some examples of the evolution of $\lambda_{\rm
b}$ and $\lambda_{\rm g}$ with respect to the stellar radius $R$."
 since a star experiences bot expansion and shrinkage throughout its life. we divide its evolution into three stages alter the star leaves (he main-sequence according to the change of the stellar radius. to make the fitting of A more practicable.," Since a star experiences both expansion and shrinkage throughout its life, we divide its evolution into three stages after the star leaves the main-sequence according to the change of the stellar radius, to make the fitting of $\lambda$ more practicable."
 Stage 1 begins at the center 1 exhaustion and ends when the star starts to shrink (i.e.. near center He ignition).," Stage 1 begins at the center H exhaustion and ends when the star starts to shrink (i.e., near center He ignition)."
 Stage 2 follows and ends when the star starts (o expandagain?., Stage 2 follows and ends when the star starts to expand.
. Stage 3 begins after that and continues till the end of the evolution., Stage 3 begins after that and continues till the end of the evolution.
" Figures | and 2 show that both Aj, and A, vary during the evolution of stars.", Figures \ref{fig1} and \ref{fig2} show that both $\lambda_{\rm b}$ and $\lambda_{\rm g}$ vary during the evolution of stars.
" For LAL, star. both Aj, and A, decrease with 7. but their magnitudes are around unity. before the lle flash."," For $1
M_{\odot}$ star, both $\lambda_{\rm b}$ and $\lambda_{\rm g}$ decrease with $R$ , but their magnitudes are around unity before the He flash."
" After that the values of A have a big decrease along with the stellar radius. but Aj~2A, throughout theevolution."," After that the values of $\lambda$ have a big decrease along with the stellar radius, but $\lambda_{\rm b} \sim 2
\lambda_{\rm g}$ throughout theevolution."
 More massive stars often experience rapid increase in A in stage 3., More massive stars often experience rapid increase in $\lambda$ in stage 3.
" For stars with mass [from e3 to 5A/. (the mass range is related (ο metallicitw). Aj, and A, take the values ~1 belore the star reaches stage 3. during which the internal enerev dominates. and the total binding energy finally becomes positive."," For stars with mass from $\sim 3$ to $5M_{\odot}$ (the mass range is related to metallicity), $\lambda_{\rm b}$ and $\lambda_{\rm g}$ take the values $\sim 1$ before the star reaches stage 3, during which the internal energy dominates, and the total binding energy finally becomes positive."
" The resulting Aj, increases rapidly and eventually turns out to be infinity. while A, remains to be around 0.5."," The resulting $\lambda_{\rm b}$ increases rapidly and eventually turns out to be infinity, while $\lambda_{\rm g}$ remains to be around 0.5."
 For starsmassive than 6M... the binding energy decreases in stage 3 but never becomes," For starsmassive than $6 M_\odot$ , the binding energy decreases in stage 3 but never becomes"
We have modelled the exteuded: emission in terius of combinations of hot thermal plasiua d power-law models.,We have modelled the extended emission in terms of combinations of hot thermal plasma and power-law models.
 A single componeit does uot describe the spectrum of the NW extenisio, A single component does not describe the spectrum of the NW extension.
 jerefore. the data were itted to a two-couponent model cousisting of thermal bremsstraliltlg al yowel-law continuuini {noclel B+P).," Therefore, the data were fitted to a two-component model consisting of thermal bremsstrahlung and a power-law continuum (model B+P)."
 This inodel gave an acceptable fit to the data with 4?=sí yw 229 d.o.L..," This model gave an acceptable fit to the data with $\chi^{2} = 28.9$ for 22 d.o.f.,"
 the best-fitting pa‘ameters beine given in Table 3.., the best-fitting parameters being given in Table \ref{tbl-3}.
 Several line features are evident iu e spectrum (Figure 5) . Uuel uost promiuent being those at 1.775nn;ioe (consistent with Si IN a) and 6.37040iio ΚΟΝΕν (consisent with Fe Ίνα).," Several line features are evident in the spectrum (Figure \ref{fig8}) ), the most prominent being those at $1.775^{+0.025}_{-0.025}$ (consistent with Si $\alpha$ ) and $6.37^{+0.10}_{-0.06}$ keV (consistent with Fe $\alpha$ )."
 The line at 1.78 keV is cke li energy ile Si Ίνα fluorescence line in he backeround of the $3 chip (see Table 3 of Charas et al., The line at 1.78 keV is close in energy to the Si $\alpha$ fluorescence line in the background of the S3 chip (see Table 3 of Chartas et al.
 2000)., 2000).
 Tius. we consider whet!er this line inight be au artefac left over rom the backerouil subtraction or moclelling.," Thus, we consider whether this line might be an artefact left over from the background subtraction or modelling."
" The (backgrounc subtracted) flux of the 1.75 keV lije in the data is (ss12)107 photons >2s Hl, whereas the flux of the Si Isa liue iu the bacseround spectrur1 (scaled to the area of the NW extensii) ls 6.:)xlO? photons 2.4 "," The (background subtracted) flux of the 1.78 keV line in the data is $(8.8^{+4.9}_{-4.5}) \times 10^{-7}$ photons $^{-2}$ $^{-1}$, whereas the flux of the Si $\alpha$ line in the background spectrum (scaled to the area of the NW extension) is $6.3 \times
10^{-9}$ photons $^{-2}$ $^{-1}$."
The'efore. it is unlikely that the line is à residual [rom the background subtraction or modeliug.," Therefore, it is unlikely that the line is a residual from the background subtraction or modelling."
 Replaciug the tiermal bremsstrahluug continuum with a 1uodel (Neweetal.1995). gives a sliehly better fit to the cata for solar abuudances (model MI+P: Table 3))., Replacing the thermal bremsstrahlung continuum with a model \citep{mew95} gives a slightly better fit to the data for solar abundances (model M1+P; Table \ref{tbl-3}) ).
 However. the couma density ds below the Galactic value so the model is unphysical.," However, the column density is below the Galactic value so the model is unphysical."
 A significant (at >96% conidence) inmprovemeu in the fit is obtaiued for a metal abuudauce of 0.0520.0170.0247 and a column density coinsistent wili the Galactic value finocdel Ml2+P: Table κ)+) )).," A significant (at $> 96$ confidence) improvement in the fit is obtained for a metal abundance of $0.052^{+0.047}_{-0.023}$, and a column density consistent with the Galactic value (model M2+P; Table \ref{tbl-3}) )."
 A two MERALs (boh with solar abutdances) mocel (model MI-MI: Table 3 )) gives a simular quality fit to the daa as the MI+P nyodel. but the column density. is agal1 well below the Galactic value.," A two s (both with solar abundances) model (model M1+M1; Table \ref{tbl-3}) ) gives a similar quality fit to the data as the M1+P model, but the column density is again well below the Galactic value."
 A signifint (ad ος co1idence) improvement in the fit is obtained wleu we allow the metal abuudaice to vary trou le solar value (1nodel. M2--M2. otl MEWKALS have tle sune metallicity. Table 3)).," A significant (at $> 97$ confidence) improvement in the fit is obtained when we allow the metal abundance to vary from the solar value (model M2+M2, both s have the same metallicity, Table \ref{tbl-3}) )."
" However. the temperature of t]e hotter COLL;»onent is very bieh (AT,50 keV. whicl is the hottest teiiperature at which the model is alilated) ane ullcoistrained. making it inpossible to cisinetish the M24-M2 rom the M2+P LOCel."," However, the temperature of the hotter component is very high $kT_{\rm h} = 80$ keV, which is the hottest temperature at which the model is tabulated) and unconstrained, making it impossible to distinguish the M2+M2 from the M2+P model."
 The temperature of the cooler (AT~0.6 keV) agrees well wit1 the collisionalt ionization equilibjul1 model of Sakoetal.(2000)., The temperature of the cooler $kT \sim 0.6$ keV) agrees well with the collisional ionization equilibrium model of \citet{sak00}.
. T1e acditiou of a secoudAL. componeut o either τμ. or M2--P models does not signiCallM7 (al oτοῖς σοι[icleice) improve t it.," The addition of a second component to either the M1+P or M2+P models does not significantly (at $\simgreat
70$ confidence) improve the fit."
 The best fittiig uodels in Table 3 have column «leusiles consistent wih the Galactic val (Ny(Cal)=3x1yet> 7)., The best fitting models in Table \ref{tbl-3} have column densities consistent with the Galactic value $N_{\rm H} (\rm Gal) = 3 \times 10^{21}$ $^{-2}$ ).
" This result is expectec ""nce he NW 'egion lies ou tlie near side o he Circiuus galaxy clisς, along the rotation axis."," This result is expected since the NW region lies on the near side of the Circinus galaxy disk, along the rotation axis."
 Nore of he moclels adequately. reproduces t strength of the Fe ha Iine. whose observe equivaleul wiclt is 2.7>πι keV.T In the M2+P mocel. the best-fit: power-law pjo0ton 1dex is E0.00.|o. which is close to he value observed in tle nuclear spectrur - Circinus.," None of the models adequately reproduces the strength of the Fe $\alpha$ line, whose observed equivalent width is $2.7^{+2.4}_{-1.9}$ keV. In the M2+P model, the best-fit power-law photon index is $\Gamma =
0.0^{+0.5}_{-1.9}$, which is close to the value observed in the nuclear spectrum of Circinus."
" Of COUIse. he spectral index of the hard yower-law is very unce‘tain (Table 3)): it ‘Ousistent wit the observed value (22 0.2) for the iucleus. which we interyretecl as a result of relection from a1 optically thick torus. aud marginally consistent."" («ντ>ca 6) \vith the putative unolosceured index (P= 1.7)."," Of course, the spectral index of the hard power-law is very uncertain (Table \ref{tbl-3}) ); it is consistent with the observed value $\Gamma \simeq 0.2$ ) for the nucleus, which we interpreted as a result of reflection from an optically thick torus, and marginally consistent $\Delta\chi^{2} \simeq 6$ ) with the putative unobscured index $\Gamma = 1.7$ )."
 In evaluating the plivsical mature of this hard component. we first consier whether it wight result [rom scattering of nuclear shotous by the telescope mirrors.," In evaluating the physical nature of this hard component, we first consider whether it might result from scattering of nuclear photons by the telescope mirrors."
 Frou estitvates of the telescope PSF at 6.1 keV. some 0.25% ," From estimates of the telescope PSF at 6.4 keV, some $0.25$ "
ünteusitv bx Ménndez (1978) is à lower LimitἘν ISL. (for D=s0 ype} and is very sensitive to the extinction.,intensity by Ménndez (1978) is a lower limit$>$ 43 (for $D$ =800 pc) and is very sensitive to the extinction.
 The 1111uber of ioizing photons we derive from the observed radio flux at G cimi (86 νι Milne aud. Aller 1975) aud from tie tota Πα flux (Walsh 1983) is at least τς10° photons iqassumnidue no escape of ionizing photons aud an average optica depth iu Πα~ 0.7). consistent with L.~250L.... mt not with lower values of (seo Fig.," The number of ionizing photons we derive from the observed radio flux at 6 cm (86 mJy; Milne and Aller 1975) and from the total $\alpha$ flux (Walsh 1983) is at least $2-4 \times 10^{45}$ photons $^{-1}$ (assuming no escape of ionizing photons and an average optical depth in $\alpha \sim 0.7$ ), consistent with $\sim$ 250, but not with lower values of (see Fig."
 3 of NII98)., 3 of NH98).
 Tf 22250L... the niondetection of he white dwarf star in the visual is nof surprising: assundns. for simplicity. that the A star and the white dwuf spectrum can be represented by black-bodies at 500H Ix and 1.5< 101. having hunuinosities of 15 aud 250L.... respectively. we find that the white dwarf is a factor 51 weaker than the A-type star at 5500A. a factor of 10 at aand that the two stars become comparable onlv at ~2000A.," If 250, the non-detection of the white dwarf star in the visual is not surprising; assuming, for simplicity, that the A star and the white dwarf spectrum can be represented by black-bodies at 8500 K and $1.5\times 10^5$ K, having luminosities of 15 and 250, respectively, we find that the white dwarf is a factor 54 weaker than the A-type star at 5500, a factor of 10 at and that the two stars become comparable only at $\sim$."
. This last is consistent with the UV excess (vith respec to the flux expected for the A star) measured by he ultraviolet satelite ANS and reported by Méndez (1978)., This last is consistent with the UV excess (with respect to the flux expected for the A star) measured by the ultraviolet satellite ANS and reported by Ménndez (1978).
 All together. we suspect that the white dwarf ΠΕκ is roughly oftιο order of 250L.," All together, we suspect that the white dwarf luminosity is roughly of the order of 250."
"... Tn anv case. we have also computed a model where we have artificially reduced the stellar Iuuünositv by a factor 5 at all times: he deusitv of this mode (Mocdol 5). shown as a cashed curve in Fie. 1,"," In any case, we have also computed a model where we have artificially reduced the stellar luminosity by a factor 5 at all times; the density of this model (Model 5), shown as a dashed curve in Fig. \ref{fig:PDR},"
 isp=τν10%7., is $n_0=7\times 10^3$.
 The predicted ine huninositv scales approximately with the hIuminositv of the ceutral core., The predicted line luminosity scales approximately with the luminosity of the central core.
 A value 2550 (although uot predicted by auv evolutionary track) is still roughly consistent with the observed line intensity. especially if we consider the uncertaüutv on the PN age estimate.," A value 50 (although not predicted by any evolutionary track) is still roughly consistent with the observed line intensity, especially if we consider the uncertainty on the PN age estimate."
 Dowever. this model predicts an intensity lower than observed (by a factor 310) for all the Hines we neasured.," However, this model predicts an intensity lower than observed (by a factor 3–10) for all the lines we measured."
 The best fit to the LL-OS(1) observations is provided by models with low density (ay13s10! 7). in good aereemeut with the low electron deusitv (<10° ?)) derived. for the ionized part of the nebula (Liu et al.," The best fit to the 1-0S(1) observations is provided by models with low density $n_0\sim 1-3\times 10^4$ ), in good agreement with the low electron density $\simless 10^3$ ) derived for the ionized part of the nebula (Liu et al."
 1995: Melkeuua Keenan 1996)., 1995; McKenna Keenan 1996).
 Azsuniug pressure equilibriun between the ionized aud the neutral eas. aud à PDR temperature ~HOO Ik. we expect a ueutral deusitv about LO times the clectrou density.," Assuming pressure equilibrium between the ionized and the neutral gas, and a PDR temperature $\sim$ 500 K, we expect a neutral density about 40 times the electron density."
 The low deusitv we require is in rough agreement with the Bachiller et al. (, The low density we require is in rough agreement with the Bachiller et al. (
1989) estimate that the neutral density is fea«10?,1989) estimate that the neutral density is $few \times 10^3$.
" Tn these low-deusity models, at f~2500 vr. the 1-OS(1) euission is mostly due to collisionally excitedIT... kept wari by the heating of the soft N-ravs cuutted by the ceutral core."," In these low-density models, at $t\sim 2500$ yr, the 1-0S(1) emission is mostly due to collisionally excited, kept warm by the heating of the soft X-rays emitted by the central core."
 As discussed in NII98. N-ravs determine the chemical and physical evolution of the neutral gas around ligh-uass PN cores. after a short initial phase (about 1000 vr for a 0.7 ccore) where UW photons dominate.," As discussed in NH98, X-rays determine the chemical and physical evolution of the neutral gas around high-mass PN cores, after a short initial phase (about 1000 yr for a 0.7 core) where UV photons dominate."
 Tf the ταν effects are neelected. PDR models precict a πιο lower iuteusitv of the nunolectlar ues.," If the X-rays effects are neglected, PDR models predict a much lower intensity of the molecular lines."
 Time-dependent effects in the cchemistry are important., Time-dependent effects in the chemistry are important.
 For 00.7 aand psxfPοι FLOPo43 vx. the mass ofa jonized+ σας increases+ with time.," For 0.7 and $n\propto t^{-2}$, $t\simgreat 10^3$ yr, the mass of ionized gas increases with time."
 Iu these conditions. at each tine step a new aver of molecular gas is exposed ο the N-rvayv heating radiation. as unmolecules are advected frou deep iu he PDR slab OWale the radiated surface.," In these conditions, at each time step a new layer of molecular gas is exposed to the X-ray heating radiation, as molecules are advected from deep in the PDR slab toward the irradiated surface."
 Therefore. compared to the xedietious of equilibrium calculations. a larger amount of rot molecular gas is formed. which cuits strouecr yvibrationally excited lines.," Therefore, compared to the predictions of equilibrium calculations, a larger amount of hot molecular gas is formed, which emits stronger vibrationally excited lines."
 This effect. discussed im detail in NII98. is larger in models with lower deusitv. so that he 1-0S(1) intensity is eher iu uodels with lower ».," This effect, discussed in detail in NH98, is larger in models with lower density, so that the 1-0S(1) intensity is higher in models with lower $n$."
 The Opposlite is true in models where the cchenistrv is treated under the assumption of stationary equiWrit., The opposite is true in models where the chemistry is treated under the assumption of stationary equilibrium.
 These mocels predict at £—2500 vr a 1-08(1) line about 7-10 times weaker (for jy<2.1«104 7). mostly due to fluorescence in ppuuiped by UV photons. aud lower iu models with lower n.," These models predict at $t\sim 2500$ yr a 1-0S(1) line about 7-10 times weaker (for $n_0\leq 2.1\times 10^4$ $^{-3}$ ), mostly due to fluorescence in pumped by UV photons, and lower in models with lower $n$ ."
 The τοςicted intensities of all the oobserved lines have been conrmited using a code which caleulates f1ο level population for the W=299 hound states with rotational quanti ΠΠ 7 <29 of the nuuolecule., The predicted intensities of all the observed lines have been computed using a code which calculates the level population for the $N$ =299 bound states with rotational quantum number $J\leq$ 29 of the molecule.
 The code inchde fje effects of UV. pumping by an external radiation field as well as collisions with ILIT. We. electrons ane protons (Draine Bertoldi 1996).," The code include the effects of UV pumping by an external radiation field as well as collisions with H, He, electrons and protons (Draine Bertoldi 1996)."
 We have used as input the physical conditions (uzünely. the radiation field at the inner οσο of the PDR and the run with the depth in the PDR of tempcrature aud fractional abundances of IT. IT»... Πο electrous aud protons) computed with the NII98 code for £=2500 ντ.," We have used as input the physical conditions (namely, the radiation field at the inner edge of the PDR and the run with the depth in the PDR of temperature and fractional abundances of H, , He, electrons and protons) computed with the NH98 code for $t=2500$ yr."
 The models agree rather well with the observations for all thelines., The models agree rather well with the observations for all thelines.
 Fig., Fig.
 5 shows a Boltzmann plot for the, \ref{fig:h2col} shows a Boltzmann plot for the
minima alternatelv become higher and lower.,minima alternately become higher and lower.
 The upper right panel of Figure & shows the effect of increasing ay: the minima of ave shifted upwards. while the maxima are not substantially affected.," The upper right panel of Figure \ref{fig_param} shows the effect of increasing $\eta_{H}$: the minima of are shifted upwards, while the maxima are not substantially affected."
 The explanation for the upward shift is that jj determines the amount of flux which crosses the equator and (hus directly influences (he axial dipole moment., The explanation for the upward shift is that $\eta_{H}$ determines the amount of flux which crosses the equator and thus directly influences the axial dipole moment.
 There is also a weak but noticeable 22-vear component. with the minima of alternating cvcles being weaker.," There is also a weak but noticeable 22-year component, with the minima of alternating cycles being weaker."
 This 22-vear component is present because we have not recalibrated D., This 22-year component is present because we have not recalibrated $B_0$.
 The middle left panel of Figure & shows the effect of increasing 7., The middle left panel of Figure \ref{fig_param} shows the effect of increasing $\eta_r$.
 The enhanced decay of the field not only reduces around the minima but also dung the rise phase a cvcle., The enhanced decay of the field not only reduces around the minima but also during the rise phase a cycle.
 This leads to too low minima ancl a delay of (he rising phase., This leads to too low minima and a delay of the rising phase.
 There is again a 22-vear component because £j has not been recalibrated., There is again a 22-year component because $B_0$ has not been recalibrated.
 The middle right panel shows the effect of varying the Ull angle reduction [actor. 4. from 0.7 to 1. which modifies the magnitude of the polar fields and axial dipole moment.," The middle right panel shows the effect of varying the tilt angle reduction factor, $g$, from $0.7$ to 1, which modifies the magnitude of the polar fields and axial dipole moment."
 The signature is therefore an increase in (he magnitude of the changes in the dipole moment (ancl (hus Fopen)) is minima. so that the effect almost cancels after two cycles.," The signature is therefore an increase in the magnitude of the changes in the dipole moment (and thus ) its minima, so that the effect almost cancels after two cycles."
 This also produces a slrong 22 vear periodicitv in the minima., This also produces a strong 22 year periodicity in the minima.
 We comment (hat g=0.7 is required to obtain the correct ratio between the maxima and minima of the open flux. as it essentially scales the low-order axial multipoles whilst barely affecting the equatorial multipoles.," We comment that $g=0.7$ is required to obtain the correct ratio between the maxima and minima of the open flux, as it essentially scales the low-order axial multipoles whilst barely affecting the equatorial multipoles."
 Introducing yg does not affectwhetheror not the polar fieldsreverse (hie 22 vear periodicitv. when g is varied in isolation. can be removed by an appropriate choice of D.," Introducing $g$ 	does not affect	whether	or not the polar fields	reverse – the 22 year periodicity, when $g$ is varied in isolation, can be removed by an appropriate choice of $B_0$."
" The lower left panel shows that increasing J...) in isolation weakensF5,5,.", The lower left panel shows that increasing $R_{\mathrm{cusp}}$ in isolation weakens.
. The effect is strongest during the maxima as i( preferentially reduces (he contribution from higher order multipoles., The effect is strongest during the maxima as it preferentially reduces the contribution from higher order multipoles.
 The influence is (hus qualitatively different from that of the other parameters in that it changes the relative contributions of the different multipoles., The influence is thus qualitatively different from that of the other parameters in that it changes the relative contributions of the different multipoles.
 In the panels discussed so [ar we have kept μας. the scaling factor for the total flux οἱ newly emerging BAIRs. constant.," In the panels discussed so far we have kept $B_{\mathrm{max}}$, the scaling factor for the total flux of newly emerging BMRs, constant."
" Varving i, as was done in the middle left panel changes the total amount of unsigned fIux. and so affects the calibration of μις."," Varying $\eta_r$ as was done in the middle left panel changes the total amount of unsigned flux, and so affects the calibration of $B_{\mathrm{max}}$."
 La the bottom right panel we therefore show the effect of a change in 5. together with the corresponding change in D., In the bottom right panel we therefore show the effect of a change in $\eta_r$ together with the corresponding change in $B_{\mathrm{max}}$.
" Since the entire svstem is linear in D. changing By», merely rescales the result hence (he result in the lower right panel is just a scaled version of the result shown middle left panel."," Since the entire system is linear in $B_{\mathrm{max}}$, changing $B_{\mathrm{max}}$ merely rescales the result – hence the result in the lower right panel is just a scaled version of the result shown middle left panel."
" We note Chat varying 75, also affects the calibration.", We note that varying $\eta_{H}$ also affects the calibration.
 This brief study of the effect of varying the parameters illustrates the kind of changes which occur., This brief study of the effect of varying the parameters illustrates the kind of changes which occur.
 However. it does not rule out other choices for the parameters which also could provide a &ood fit to the observations.," However, it does not rule out other choices for the parameters which also could provide a good fit to the observations."
" In particular we do not claim that non-zero values of jg, are excluded. although we can sav that. al least for eveles 1521. a good fit to the"," In particular we do not claim that non-zero values of $\eta_r$ are excluded, although we can say that, at least for cycles 15–21, a good fit to the"
emission.,emission.
 The well defined X-ray slope deduced from the observations strongly constrains the second index Πο in the electron energy distribution (see Eq. (I]), The well defined X-ray slope deduced from the observations strongly constrains the second index $n_2$ in the electron energy distribution (see Eq. )
) and significantly reduces the parameter space., and significantly reduces the parameter space.
 The solid blue line in Fig., The solid blue line in Fig.
" B| presents the resulting SED emitted when one consider a single blob moving along the line of sight in the jet formation zone with 6,=8.", \ref{fig:M87_SED_bij_broad} presents the resulting SED emitted when one consider a single blob moving along the line of sight in the jet formation zone with $\delta_b = 8$.
" The corresponding parameters can be found in column 2 of Table[I], where 0 is defined as the angle between the line of sight and the velocity vector of the single blob."," The corresponding parameters can be found in column 2 of Table \ref{tab:param}, where $\theta$ is defined as the angle between the line of sight and the velocity vector of the single blob."
 Obviously this model describes the observations much better., Obviously this model describes the observations much better.
" However, as pointed out in Sect. i"," However, as pointed out in Sect. \ref{sec:bij},"
tis based on an assumption., it is based on an assumption.
" Moreover, it is difficult to Bl.""keep"" the generated IC bump below the EGRET upper limit although we assume a low state for the activity of the AGN."," Moreover, it is difficult to “keep” the generated IC bump below the EGRET upper limit although we assume a low state for the activity of the AGN."
" Throughout this paper, our results are not fits to the data, but rather solutions of models which are meant to describe best the data."," Throughout this paper, our results are not fits to the data, but rather solutions of models which are meant to describe best the data."
 Our purpose is to figure out whether our model can describe correctly the current available data for different objects., Our purpose is to figure out whether our model can describe correctly the current available data for different objects.
 We do not intend to fine-tune the parameters of our model but to sort orders of magnitude out for these parameters., We do not intend to fine-tune the parameters of our model but to sort orders of magnitude out for these parameters.
" One SED of 887 generated within the multi-blob model is presented in Fig. A],"," One SED of 87 generated within the multi-blob model is presented in Fig. \ref{fig:M87_SED1},"
 with parameters very similar to the single blob model of Fig., with parameters very similar to the single blob model of Fig.
 B] (see column 3 in Table [ip)., \ref{fig:M87_SED_bij_broad} (see column 3 in Table \ref{tab:param}) ).
" Since the former is a generalization of the latter, the resulting spectrum is rather similar, as one would expect."," Since the former is a generalization of the latter, the resulting spectrum is rather similar, as one would expect."
" In this case, the value of the individual blob radius r; is so small that all the blobs are moving close to the line of sight."," In this case, the value of the individual blob radius $r_b$ is so small that all the blobs are moving close to the line of sight."
" The *on-blob"" and the ""inter-blob"" cases give the same contribution to the SED and are overlaid in Fig. B].", The “on-blob” and the “inter-blob” cases give the same contribution to the SED and are overlaid in Fig. \ref{fig:M87_SED1}.
" The blob radius is rather small in this case, resulting in a VHE emitüng zone smaller than the Schwarzschild radius."," The blob radius is rather small in this case, resulting in a VHE emitting zone smaller than the Schwarzschild radius."
" It should be noted that features small compared to the Schwarzschild radius, possibly responsible for the VHE emission, can develop beyond the Alfvénn surface due to turbulence or reconfined shocks, but this issue is beyond the scope of this work."," It should be noted that features small compared to the Schwarzschild radius, possibly responsible for the VHE emission, can develop beyond the Alfvénn surface due to turbulence or reconfined shocks, but this issue is beyond the scope of this work."
 However it is commonly believed that the size of the VHE emitting zone cannot be much smaller than the Schwarzschild radius which is a natural scale for the processes in the vicinity of the SMBH., However it is commonly believed that the size of the VHE emitting zone cannot be much smaller than the Schwarzschild radius which is a natural scale for the processes in the vicinity of the SMBH.
 Moreover the emitting zone must be large enough to allow the acceleration of particles to develop., Moreover the emitting zone must be large enough to allow the acceleration of particles to develop.
" Very small blobs may disappear rapidly, in 10 mminutes due to adiabatic expansion which is especially important in the broadened zone of the jet."," Very small blobs may disappear rapidly, in $\sim 10$ minutes due to adiabatic expansion which is especially important in the broadened zone of the jet."
" However a long, stable emission is possible, even from small blobs."," However a long, stable emission is possible, even from small blobs."
" The emitting zone can be located at a stable stationary shock front, above the Alfvénn surface."," The emitting zone can be located at a stable stationary shock front, above the Alfvénn surface."
" It initiates the acceleration and thus the radiation of particles of a large number of small blobs continuously crossing the shock, thus providing a quiescent background of VHE emission."," It initiates the acceleration and thus the radiation of particles of a large number of small blobs continuously crossing the shock, thus providing a quiescent background of VHE emission."
 Density fluctuations in the injection of material could then generate flares as seen at VHE., Density fluctuations in the injection of material could then generate flares as seen at VHE.
" In fact, the only problem with small blobs is that in this case the paving of the jet is not complete because of the discretization applied in our code."," In fact, the only problem with small blobs is that in this case the paving of the jet is not complete because of the discretization applied in our code."
" In order to be more conservative and to fulfill the constraint rpZrg, we analyze another possibility with a low magnetic field."," In order to be more conservative and to fulfill the constraint $r_b \ga r_g$, we analyze another possibility with a low magnetic field."
 It is presented in Fig., It is presented in Fig.
 B] in blue lines with associated parameters in column 4 of Table [I]., \ref{fig:M87_SED2} in blue lines with associated parameters in column 4 of Table \ref{tab:param}.
" In that case, the result predicted by MHD models with a strong magnetic field in the vicinity of the central engine is not strictly fulfilled."," In that case, the result predicted by MHD models with a strong magnetic field in the vicinity of the central engine is not strictly fulfilled."
 However a local decrease of the magnetic field can be achieved by, However a local decrease of the magnetic field can be achieved by
Groups of galaxies are ubiquitous: at least half of all local galaxies are located within groups (Lully 1987).,Groups of galaxies are ubiquitous; at least half of all local galaxies are located within groups (Tully 1987).
 A significant raction of the total mass of the Universe may also be located in groups., A significant fraction of the total mass of the Universe may also be located in groups.
 In hierarchical models ofthe growth of structure in the Universe. groups forni before clusters and. are the xilding-blocks from which clusters assemble.," In hierarchical models of the growth of structure in the Universe, groups form before clusters and are the building-blocks from which clusters assemble."
 The evolution with redshift of galaxy groups has. rowever. received little observational attention.," The evolution with redshift of galaxy groups has, however, received little observational attention."
 This is arecly because of the lack of reliable samples of high redshift galaxy groups., This is largely because of the lack of reliable samples of high redshift galaxy groups.
 Groups at high redshift are difficult to find in two-dimensional optical surveys because of their very ow contrast against the foreground and background galaxy distribution., Groups at high redshift are difficult to find in two-dimensional optical surveys because of their very low contrast against the foreground and background galaxy distribution.
 Although surveys around. radio galaxies have aac some success (eg., Although surveys around radio galaxies have had some success (eg.
 Allineton-Smith 1998). X-rav surveys have the potential to unambiguously identify clusters anc groups at high. redshifts via the thermal X-rav emission [rom the hot gas trapped in the cluster eravitational potential.," Allington-Smith 1993), X-ray surveys have the potential to unambiguously identify clusters and groups at high redshifts via the thermal X-ray emission from the hot gas trapped in the cluster gravitational potential."
 X-ray observations have shown that eroups contain a hot intragroup medium (IGM) which is à scaled down version of that found. in clusters of galaxies (Alulcehaey 1996. Ponman L996).," X-ray observations have shown that groups contain a hot intragroup medium (IGM) which is a scaled down version of that found in clusters of galaxies (Mulchaey 1996, Ponman 1996)."
 Εμ N-ray emitting eas in groups may well constitute the largest observed: component of the barvon mass of the Universe (Fukugita 1998)., This X-ray emitting gas in groups may well constitute the largest observed component of the baryon mass of the Universe (Fukugita 1998).
 The smaller. potential wells of groups. compared. to clusters. imply that the global X-ray properties of the inter-group medium (OAL) are not only determined by the dark matter potential but are also sensitive to other heating (or cooling. Bryan 2000) processes (eg.," The smaller potential wells of groups, compared to clusters, imply that the global X-ray properties of the inter-group medium (IGM) are not only determined by the dark matter potential but are also sensitive to other heating (or cooling, Bryan 2000) processes (eg."
 Cavaliere 1997)., Cavaliere 1997).
 Ividence has recently accumulated for non-gravitational energv input into the IGM., Evidence has recently accumulated for non-gravitational energy input into the IGM.
 This energy. is responsible for breaking the self-similar scaling of cluster properties. most strongly in low mass svstenis (Ixaiser 1991. Evrard Henry 1991).," This energy is responsible for breaking the self-similar scaling of cluster properties, most strongly in low mass systems (Kaiser 1991, Evrard Henry 1991)."
 Such additional heating can explain the shape of scaling relations such as the steepening slope of the X-ray Iuminositv-tempoerature relation from clusters to groups (Cavaliere 1999. Wu. Fabian Nulsen 1905. 2000. Balogh. Babul Patton 1999. Bower 2000. Tozzi Norman 2001. Lowenstein 2000).," Such additional heating can explain the shape of scaling relations such as the steepening slope of the X-ray luminosity-temperature relation from clusters to groups (Cavaliere 1999, Wu, Fabian Nulsen 1998, 2000, Balogh, Babul Patton 1999, Bower 2000, Tozzi Norman 2001, Lowenstein 2000)."
 The cdiscoverv of a, The discovery of a
"After lixing the basic stellar parameters M. 2. and (Q (more generally. M ancl an Eos). (he model has (wo free parameters. f, and Ya.","After fixing the basic stellar parameters $M$ , $R_s$ and $Q$ (more generally, $M$ and an EoS), the model has two free parameters, $f_m$ and $Y_{\rm gl}$."
 Ho must predicts three observables: the interval between glitches. ancl the jumps in angular velocity. anc acceleration during a glitch.," It must predicts three observables: the interval between glitches, and the jumps in angular velocity and acceleration during a glitch."
 In the case of Vela. the average observed values are Aly23 νους and AQ.=L2x10! Lz (Lyneetal.2000): we already mentioned that early observations gave Δονοςzm102.," In the case of Vela, the average observed values are $\Delta t_{\rm gl}\approx3$ years and $\Delta\Omega_{\rm gl}=1.2\times10^{-4}$ Hz \citep{lyn00}; we already mentioned that early observations gave $\Delta\dot{\Omega}_{\rm gl}/\dot{\Omega}_{\infty}\approx10^{-2}$."
" More recent. data. however. indicate much lareer values: in particular. (he vear 2000 elitch (Dodsonetal.2002) added to the already known short-. middle-. and long-time relaxation components (7;£101,105.105 s. with οος20.44.0.044.0.009 for i=1.2.3). a fourth andvery short one. wilh 7;=1.240.2 minutes and AQ,/0.=1846 (one sigma errors)."," More recent data, however, indicate much larger values; in particular, the year 2000 glitch \citep{dod02} added to the already known short-, middle-, and long-time relaxation components $\tau_i\approx10^4,10^5,10^6$ s, with $\Delta\dot{\Omega}_i/\dot{\Omega}_{\infty}\approx0.44,0.044,0.009$ for $i=1,2,3$ ), a fourth and short one, with $\tau_4=1.2\pm0.2$ minutes and $\Delta\dot{\Omega}_4/\dot{\Omega}_{\infty}=18\pm6$ (one sigma errors)."
 In the 2004 etch. however. such a component was observed only barely above noise and no firm conclusion could be drawn from the weak data (Dodsonetal.2001).," In the 2004 glitch, however, such a component was observed only barely above noise and no firm conclusion could be drawn from the weak data \citep{dod07}."
 Waiting for Duture observations. there is nonetheless evidence thataffer a glitch AQ.UO is larger (han unity.," Waiting for future observations, there is nonetheless evidence that a glitch $\Delta\dot{\Omega}_{\rm gl}/\dot{\Omega}_{\infty}$ is larger than unity."
 In order to test the model against observations. we consider a standard neutron star with AJ—1M...R.-—10 A and Q=0.95.," In order to test the model against observations, we consider a standard neutron star with $M=1.4 M_{\odot}, R_s=10$ km, and $Q=0.95$."
" If we take RE—]1xl10P dyn !hom ecqualions find 3-Bwehaloes,=I0.01 Iz. and thence ""—3.1 vears and AL.)=9.5xLO” erg s (also. AFP=6.7x10"" erg)."," If we take $f_m=1.1\times10^{15}$ dyn $^{-1}$, from equations \ref{eq2}$ $-$ \ref{eq7} we find that $\omega_{\rm max}=0.01$ Hz, and thence $\Delta t_{\rm gl}=3.1$ years and $\Delta L_{\rm gl}=9.5\times10^{39}$ erg s (also, $\Delta E_{\rm gl}=6.7\times10^{41}$ erg)."
" we then take Y44=0.05. ""nnfrom equation 9 we obtain AQ.=1.3x10.! Hz and .NO4/O0,=9.3. in good general wilh observations."," If we then take $Y_{\rm gl}=0.05$, from equation 9 we obtain $\Delta\Omega_{\rm gl}=1.3\times10^{-4}$ Hz and $\Delta\dot{\Omega}_{\rm gl}/\dot{\Omega}_{\infty}=9.3$, in good general agreement with observations."
 In Paper I we analyze the parameter dependence of these results: we find that the model is equite robust under physically meaningful variations of all the basic parameters (M.Re.Qepi.py. p).," In Paper I we analyze the parameter dependence of these results; we find that the model is quite robust under physically meaningful variations of all the basic parameters $M,R_s,Q,\rho_c,\rho_m,\rho_d$ )."
" 1n conclusion. assuming continuous vortices throughout the star. we find that maximum pinning forces of order fj,zz10P dvn |1 can accunnilate ©1055 vortices in the inner crust of a standard neutron star. and release (hem every zz3 vears. transferring an angular monentum ALz10!U ero s, This is one order of magnitude smaller than what inferred from the (microscopically inconsistent) assumption of disconnected vortices."," In conclusion, assuming continuous vortices throughout the star, we find that maximum pinning forces of order $f_m\approx10^{15}$ dyn $^{-1}$ can accumulate $\approx10^{13}$ vortices in the inner crust of a standard neutron star, and release them every $\approx3$ years, transferring an angular momentum $\Delta L_{\rm gl}\approx10^{40}$ erg s. This is one order of magnitude smaller than what inferred from the (microscopically inconsistent) assumption of disconnected vortices."
 Yet. it v_ the observed glitch parameters. provided one assumes a small coupled fraction iesως105.," Yet, it yields the observed glitch parameters, provided one assumes a small coupled fraction $Y_{\rm gl}<10\%$."
 The model is compatible with post-eliteh recovery and with thepresently known the nunmerical results follow from implementing both spherical geometry ancl a realistic density profile. ancl (hey are robust.," The model is compatible with post-glitch recovery and with thepresently known microphysics; the numerical results follow from implementing both spherical geometry and a realistic density profile, and they are robust."
 This work was supported by Compstar. a Research Networking Programme of the European Science Foundation /www.compstar-esLorg/)).," This work was supported by CompStar, a Research Networking Programme of the European Science Foundation )."
tidal excess rotation of the star must lead. to a shortening of the orbital period (we neglect the contributions from. planctary rotation and orbital cireularisation).,tidal excess rotation of the star must lead to a shortening of the orbital period (we neglect the contributions from planetary rotation and orbital circularisation).
 Therefore. under the assumption that. for the objects identified above. the stellar excess rotation is cue to tidal interaction. one can recover the initial orbital distance. by putting the angular momentum. of the excess rotation. back in the planetary orbit.," Therefore, under the assumption that, for the objects identified above, the stellar excess rotation is due to tidal interaction, one can recover the initial orbital distance, by putting the angular momentum of the excess rotation back in the planetary orbit."
 This will be anunderestimale. since. part of the angular momentum imparted to the star will be cissipated by the extra magnetic breaking caused by the faster spin.," This will be an, since part of the angular momentum imparted to the star will be dissipated by the extra magnetic breaking caused by the faster spin."
 Figure 5. shows the resulting minimal initial orbital distance obtained in this way for the two objects with precisely measured rotation velocity. HD. 189733 and Exo-2. assuming the moment of inertia of the Sun (1/4447= 0.06) for host stars.," Figure \ref{mp} shows the resulting minimal initial orbital distance obtained in this way for the two objects with precisely measured rotation velocity, HD 189733 and Corot-Exo-2, assuming the moment of inertia of the Sun $I/MR^2=0.06$ ) for host stars."
" Although only two ""Που Jupiters"" can be analysed in this way. the result is extremely suggestive: computing the initial distance places these two objects back at the typical distance of less massive hot Jupiters. therefore exactly compensating the observed. mass-perioc relation shown ?.."," Although only two “hot Jupiters” can be analysed in this way, the result is extremely suggestive: computing the initial distance places these two objects back at the typical distance of less massive hot Jupiters, therefore exactly compensating the observed mass-period relation shown \citet{maz05}."
 This suggests that the mass-perioc relation may be entirely due to secular tidal spin-up and orbital decay for the heaviest hot Jupiters. after an initial masscincilLerent pile-up near P?=3 days.," This suggests that the mass-period relation may be entirely due to secular tidal spin-up and orbital decay for the heaviest hot Jupiters, after an initial mass-indifferent pile-up near $P=3$ days."
" This scenario has another important consequence: companions ending up near P=3 cavs with masses near 2 Aly, and higher would have a strong. enough coupling with the star to spiral inwares all the way to the Roche limit within the lifetime of the star. a scenario probably resulting in their destruction."," This scenario has another important consequence: companions ending up near $P=3$ days with masses near 2 $M_{Jup}$ and higher would have a strong enough coupling with the star to spiral inwards all the way to the Roche limit within the lifetime of the star, a scenario probably resulting in their destruction."
 At higher masses GMmugMua aV. the heaviest planets will have enough angular momentum to bring the star to synchronisation before spiralling all the way into the star. and reach a tically locked. state. provided: their. starting position lies beyond a certain critical distance.," At higher masses $M_{pl}>\frac{I_*}{M_* R_*^2} M_*R_* V_{\rm synch}/a V_{\rm orb}^{\rm init}$ ), the heaviest planets will have enough angular momentum to bring the star to synchronisation before spiralling all the way into the star, and reach a tidally locked state, provided their starting position lies beyond a certain critical distance."
 Although initially unexpected. the wide range of planetary eccentricities is now well established (c.g.7.forarecentclis-cussion) from the large sample ofplanets detected by racial velocity.," Although initially unexpected, the wide range of planetary eccentricities is now well established \citep[e.g.][for a recent discussion]{hal05} from the large sample of planets detected by radial velocity."
 The elfect of tidal circularisation is also clearly seen: orbits shorter than 6 cavs are usually circular., The effect of tidal circularisation is also clearly seen: orbits shorter than 6 days are usually circular.
 The exceptions. — very short. poriod. eccentric orbits are often attributed to possible cecentricity-pumping by an unseen planetary companio.," The exceptions – very short period, eccentric orbits -- are often attributed to possible eccentricity-pumping by an unseen planetary companio."
 However. it is remarkable that on the lower panel of Figure 2. that the transiting planets with markedly cecentric orbits are all situated at the outer edge of the sample in terms of scales relevant to tides.," However, it is remarkable that on the lower panel of Figure \ref{tides} that the transiting planets with markedly eccentric orbits are all situated at the outer edge of the sample in terms of scales relevant to tides."
 ligure 3. shows the same plot for non-transiting planets., Figure \ref{Doppler} shows the same plot for non-transiting planets.
 The location of planets with eccentric orbits in this plane is also compatible with a single limit., The location of planets with eccentric orbits in this plane is also compatible with a single limit.
 In the most populated part of the parameter space. this limit it comparable to that defining excess stellar rotation suggesting a separation between svstems stronely allected by tidal evolution and others.," In the most populated part of the parameter space, this limit it comparable to that defining excess stellar rotation – suggesting a separation between systems strongly affected by tidal evolution and others."
 C'onsequenthy. an extraneous cause for eccentric orbits is not required for any. planet. and in all cases the eecentricity could be a relie of the initial orbit after formation. possibly decreased by incomplete cireularisation. without the need to invoke the influence of another planet or star.," Consequently, an extraneous cause for eccentric orbits is not required for any planet, and in all cases the eccentricity could be a relic of the initial orbit after formation, possibly decreased by incomplete circularisation, without the need to invoke the influence of another planet or star."
 Remarkably. this is also the case for GJ486b. whose short orbital period is compensated by the small scale of the system.," Remarkably, this is also the case for GJ436b, whose short orbital period is compensated by the small scale of the system."
 The very low mass of GJ 436b suggests that the tidal quality factor Q may be in a significantly dillerent regime than gas giant planets., The very low mass of GJ 436b suggests that the tidal quality factor $Q$ may be in a significantly different regime than gas giant planets.
 Therefore. while the existence of an eccentric orbit at such a small orbital distance (2.6 days) is surprising at [ace value and has been thought to require an additional planetary companion. when the system is scaled in size. it. turns out that the tidal effects. are comparable to other cases that have kept their eccentric orbit.," Therefore, while the existence of an eccentric orbit at such a small orbital distance (2.6 days) is surprising at face value and has been thought to require an additional planetary companion, when the system is scaled in size, it turns out that the tidal effects are comparable to other cases that have kept their eccentric orbit."
 “Pherefore the eccentricity of GJ436 could be a relie of formation., Therefore the eccentricity of GJ436 could be a relic of formation.
 One of the most remarkable feature of the present. sample of transiting planets is the Large spread. in radius of hot Jupiters. and the presence of several planets. with sizes much larger than predicted. by structure. models.," One of the most remarkable feature of the present sample of transiting planets is the large spread in radius of hot Jupiters, and the presence of several planets with sizes much larger than predicted by structure models."
 Several types of explanations have been proposed to account. for these “bloated” μοι Jupiters. such as increased. opacities (?).. transformation of part of the incident stellar Dux into mechanical energv (7).. and tidal heating. with (7) or without (2?) requiring the presence of an additional planet.," Several types of explanations have been proposed to account for these ""bloated"" hot Jupiters, such as increased opacities \citep{bur07}, transformation of part of the incident stellar flux into mechanical energy \citep{gui06}, and tidal heating, with \citep{win06} or without \citep{jac08} requiring the presence of an additional planet."